FLUXIONS (ante). Imagine a point to move uniformly in the direction of a fixed line, and, at the same time, to have a variable transverse motion depending upon a law which determines the character of the curve or line thus generated. The indefinite part of the curve up to any point, as D E in the diagram, is the fluent and the exceedingly small element of the curve that is generated in the next infini- E/ F tesimal, but constant, period of time, as E G, is the fluxion, These are both vit•iable except in the case of straight lines.
Let E denote the location of the generating point at any time, t; C A the straight line in the direction of which motion D is uniform, and C D a line perpendicular to C A. Let E F be the distance through which E moves parallel to C 4, and F G the distance parallel to C D in the next infinitesimal though constant space of time d t. Then, at the end of the time t d t the point will be at G, and E G will be the part of the curve generated in the time d t. C B A Passing from the consideration of the motion of a Point in a plane to that of a point in space, it is evident that the generating point will describe a straight line, or a curve of single or double curvature. Equations can be constructed formulating laws of motion which will cause the general point to trace any Curve what ever, and from these equations the natures of the curves can be discovered. The
science of fluents and fluxions is based upon the above principles.
Any plane figure can be generated by the motion of a straight line, and any volume by the motion of a plane figure. In all cases, the portion of a plane figure or volume generated in the time t is the fluent, while that generated in the time d t is the fluxion. In practice, the method of integrals and differentials has superseded the system of fluents and fluxions, chiefly because the rotation of the latter is too cumbersome. The •fluxion of a fluent is represented by a dot over a letter, or, in complicated expressions, by a dot occupying the position of an exponent outside of a parenthesis; thus x denotes (? x, —y —y the fluxion of z, and denotes the fluxion of For fluxions of a higher order a dot is written over the fluent or without the parenthesis for each unit in the order.
FLY, a popular name often given to insects of the order diptera (q.v.) generally, sometimes extended to insects of other orders, and sometimes limited to the museides (q.v.). It is often used with a prefix, as house-fly, blow-fly, etc., to designate particular kinds of insects.