FLUXION, fluk'shon, (1) in medicine, an unnatural flow or determination of blood or other humor toward any organ; a catarrh. (2) In mathematics, a method of calculation resulting from the operation of fluents, or flow ing numbers. Thus a mathematical line may be considered as produced by the fluxion or flowing of a point; a surface by the fluxion of a line, and a solid by the fluxion of a surface. A mathematical point in motion will really make a line; a revolving radius which is a line will make a circle which is a surface, and its revolu tion about its diameter will generate a sphere which is a solid. The same principle may be applied to purely numerical calculations, like the formulae of algebra. This branch of the higher mathematics was invented by Newton in 1665. In 1676 he communicated his method to Oldenburg in a sentence with all the letters dis arranged so that his correspondent could not possibly have put them in order. If he had succeeded in doing this the sentence would have been Data equatione quotcunque fluentes tates involvente fluxiones invenire et vice versa.
[°Given it makes no matter how many equations involving fluent quantities, fluxions are to be discovered, and the reverse is true" (that is, where fluxions occur the fluents are to be found).] Leibnitz received this letter in 1677,
and in 1684 explained a discovery which he had made. It was that of the differential calculus, which was essentially the same as that of flux ions. What Newton called fluxions, Leibnitz called differences. An angry controversy sub sequently arose between Newton and Leibnitz as to the priority of discovery, the Royal Soci ety of London taking the .part of the former, who was then its president, and the scientific men of Germany that of the latter, who was their countrythan. Both appear to have made the discovery independently. In the slight dif ferences of method which exist, the advantage lay with Leibnitz, and while the term fluxions is now scarcely ever used, that of differential calculus is in common use. The first element ary treatise on fluxions in England was by John Harris in 1702. A description of the process by Newton himself followed in in his 'Quadrature of Curves.' See