CHARACTERISTIC. A term variously ion ',toyed in mathematics, requiring speeitic defini tion in each ease. The integral part of a logarithm is called its eharacteristie; thus, in loots,) = 2.0909. 1e0.013 = 2.1139. log5 = It 0990, the characteristics of the three are, il-speetively. 2, —2, and 0. The character ist ie of the common logarithm of a number con taining an integral part is one less than number of integral places; that of a decimal is negative. and is one more. in actual than the number of eiphers preceding the first sig nificant figure. On aeeount of this simple rela tion, the is not ordinarily given in the tables of common logarithms.
In the method of characteristics due to Chasle: (q.v.), which appeared in the Contptcs rtm/as (18(4), may be found the first trace of the 'nu merative geometry,' the object being to determine Low many geometric figures of given definition satisfy a certain number of conditions. A num ber expresses how many simple singulari ties may replace a higher singularity of an alge braic eurve or surfaee is called a eharaetcristie number. The elementary right-angled triangle,
whose hypotentist• is sell-dilly equal to the ele ment of the are of a curve. was called by Pascal the characteristic triangle. In the application of determinants (q.v.) to the solution of equation: the minors of a certain order in the resultant may not all vanish, while all minors of higher order become zero. in which case the equations have a known number of solutions. The number expressing the highest order in which some minor does not vanish is vaned the characteristic of the determinant. In the theory of functions (q.v.), certain rational integral functions are called characteristic functions. In the theory of dif ferential equations. there are certain algebraic every root of which determine; an in tegral of the given differential equations. (See CALcutus.) These are called characteristic equa tions.