FLUXIONS. The name 'method of fluxions' was given by Sir Isaac Newton to his calculus, and was generally employed in England and America until well along in the nineteenth cen tury. The name, the symbolism. and the fun damental idea upon which the method rests, were then supplanted by those of the Leibnitz calculus. Newton defined a as a quantity eonsiderod as and indefinitely increas ing (flowing, fluxing). and added: "The velocities at which these fluents move I call fluxions"— "Quus l'clocitates appello Fluxiones,aut simplici ter l'elocitates cc! Celeritates." ( Colson edi tion. London, 173G, vol. i., p. 54.) Briefly, his plan was this: Consider a curve described by a moving point P = (x, in, and let the rate at which x increases (flows, fluxes) he designated Icy X, and be called the fluxion of x. In the same way let j be called the fluxion of y. Then 7 is the tangent of the angle made by the tangent to the curve at P, with the x-axis. It is therefore
:ft y seen that -- is merely the d — of the Leibnitz calculus. The fundamental objection to the prin ciple is that it is based upon the idea of veloc ity, which involves that of time. To this ob jeetion must be added that of the unfortunate notation employed by Newton. While this has some advantages in certain problems in physics, it becomes unwieldy when one desires to express successive differentiations. The method of flux ions was used by Newton as early as 1666, and is found in the AIS. of his De dnalysi per /Equa tiones :Varner() Terminoram Inlinitas, which was circulated anion:: his students. in 1669, and in the Meth od as Flaxi(mum et Serierant Infinitaram, which he wrote about 1075. The term 'fluxion' seems to have been suggested to him by Cava lieri's work. See CALCULUS; NEWTON.