56 Mr. P. G. Tait on the History of Energy. 



torum usu " which, for brevity, I omitted in the quotation from 

 the Principia, appear to him to alter the meaning and applica- 

 tion of the passage. Now I consider them to involve precisely 

 that restriction [" in ordinary mechanics "] under which I made 

 the assertion about Newton. In fact the three English words 

 form a perfectly complete, though not literal, translation of the 

 four Latin ones. Any rigid body, subject to such forces as pres- 

 sures, gravitation, &c, is really a machine— whether it be em- 

 ployed for mechanical purposes or not. I took care to indicate 

 the omission of this qualifying clause, though it had, in fact, been 

 supplied in my general statement. 



I regret that the Treatise on Natural Philosophy, on which 

 Prof. W. Thomson and I have been for a long time engaged, is 

 not yet published. The portion bearing on my present subject 

 was printed off considerably more than a year ago. I shall not, 

 however, quote from it, but from a ' Sketch of Elementary Dy- 

 namics '* published in October 1863 for the use of students in 

 Glasgow and Edinburgh. In that pamphlet — after quoting 

 Newton's memorable words — we proceed (p. 30), 



"In a previous discussion Newton has shown what is to be 

 understood by the velocity of a force or resistance ; i. e., that it is 

 the velocity of the point of application of the force resolved in the 

 direction of the force, in fact proportional to the virtual velocity. 

 Bearing this in mind, we may read the above statement as 

 follows : — 



"■ If the action of an agent be measured by its amount and its 

 velocity conjointly ; and if, similarly, the Reaction of the resistance 

 be measured by the velocities of its several parts and their several 

 amounts conjointly, whether these arise from friction, cohesion, 

 weight, or acceleration ; — Action and Reaction, in all combinations 

 of machines, will be equal and opposite." 



We then show, in passing, that D'Alembert's principle is dis- 

 tinctly pointed out, and proceed thus (p. 31) : 



" The foundation of the abstract theory of energy is laid by 

 Newton in an admirably distinct and compact manner in the 

 sentence of his scholium already quoted, in which he points out 

 its application to mechanics. The actio agentis, as he defines it, 

 which is evidently equivalent to the product of the effective com- 

 ponent of the force, into the velocity of the point on which it 

 acts, is simply, in modern English phraseology, the rate at 

 which the agent works. The subject for measurement here is 

 precisely the same as that for which Watt, a hundred years 

 later, introduced the practical unit of a 'Horse-power/ or the rate 

 at which an agent works when overcoming 33,000 times the 



* Edinburgh : Maclachlan and Stewart. Pp. 44. 



