Page:Proceedings of the Royal Society of London Vol 4.djvu/344

Rh 2. " Researches in the Theory of Machines." By the Rev. H. Moseley, M.A., F.R.S., Professor of Natural Philosophy and Astro- nomy in King's CoUege, London.

Of the various names, such as " useful effect/' " dynamical effect," " efficiency," " work done," " labouring force," " work," which have been given to that operation of force in machinery which consists in the union of a continued pressure with a continued motion, the au- thor gives the preference to the term work, as being that which con- veys, under its most intelligible form, this idea of the operation of force, and as being the literal translation of the word " travail," which among French writers on mechanics has taken the place of every other.

The single unit, in terms of which this operation of force is with us measured, viz. the work of overcoming a pressure of one pound through one foot, he considers to be distinguished sufficiently, and expressed concisely enough, by the term unit of ivork, rejecting as unnecessary, and as less likely to pass into general use, the terms " dynamical unit," and " dynam," which it has been proposed to apply to it.

Having thus defined the terms work and unit of work, and paid a tribute of respect to the valuable labours of M. Poncelet in the theory of machines, and expressed admiration of the skill with which he ha& applied to it the well-known principle of vis viva under a new and more general form, the author proceeds to remark, that the inter- pretation which M. Poncelet has given to that function of the velo- city of a moving body which is taken as the measure of its vis viva, associates with it the definitive idea of a force opposed to all change in the state of the bodies' rest or motion, and known as its " vis in- erti(B," " vis insita," &c. The author conceives that the introduction of the definitive idea of such a force into questions of elementary and practical mechanics is liable to many and grave objections ; and he proposes a new interpretation of it, '^dz. "that one half of this func- tion represents the number of units of work accumulated in the moving body, and which it is capable of reproducing upon any resistance opposed to its progress." This interpretation he establishes by me- chanical considerations of an elementary kind. Taking, then, this new interpretation of the function representing one half the vis viva, and dividing the parts of a machine into those which receive the operation of the moving power (the moving points) and those which apply it (the working points), he presents the principle of vis viva in its application to machines under the following form : — "The number of units of work done by the moving power upon the moving points of the machine is equal to the number yielded at the working points, plus the number expended upon the prejudicial resistances, plus the number accumulated in the various parts of the machine which are in motion." So that the whole number of units of work done by the moving power, or upon the moving points, is expended, partly in that work done at the working points, whence results immediately the useful product of the machine, and partly upon the prejudicial resistances of friction, &c. opposed to the motion of the machine in