HYPOTHESES OP DYNAMICS. IS 



a host of other investigators, that the principle of energy presented itself in the 

 form which now renders it the one principle of the greatest utility in the dis- 

 cussion of natural phenomena." According to these and other writers ' who 

 take the same view, Newton's statement is an enunciation of the law of the conservation 

 of energy so far as mechanical energy is concerned, in fact of what Thomson and Tait call 

 " the law of energy in abstract dynamics," viz., " The whole work done in any time on any 

 limited material system by applied forces is equal to the whole effect in the forms of 

 potential and kinetic energy produced in the system, together with the work lost in 

 friction." As between this view and that of G-arnett, the latter would seem to be the more 

 tenable. For whatever Newton's statement may mean, he undoubtedly made the same 

 statement about the work done against friction, molecular forces, gravity and the " resist- 

 ance to acceleration." If, therefore, the statement was an enunciation of the law of the 

 conservation of energy in the case of the last three, it must have been an enunciation 

 of the same law in the case of the first. On the other hand, if Newton did not 

 assert the law of the conservation of energy in the case of the work done against 

 friction (and Graruett himself states' that such work done was supposed by Newton to be 

 lost), his statement cannot be an enunciation of the law of the conservation of energy at 

 all. Thus internal evidence would seem to show that both these interpretations of 

 Newton's statement are untenable. 



Lest, however, the above internal evidence should not be considered sufficient to dis- 

 prove an assertion made so widely and by such authoritative writers, it may be well to note 

 that Thomson and Tait, having obtained from the second law the analytical expression of 

 Newton's statement given above,^ proceed to deduce from it " the law of energy in abstract 

 dynamics," which they do of course in two steps, first showing that the second member 

 is equal to the rate of increment of kinetic energy, and next, that in the particular case of 

 a conservative system the first member is equal to the rate of decrement of potential 

 energy. Whether or not Newton ever took these steps, which would doubtless have been 

 but small strides for such a giant as he was, we need not inquire. It is sufiicient for our 

 present purpose to have shown that after the statement under consideration has been 

 accepted, these steps remain to be taken before the law of the conservation of energy, even 

 in the restricted form in which Newton is supposed to have enunciated it, can be 

 reached.* 



■ W. W. R. Ball in his Short Account of the History of Mathematics, p. 313, takes a different view of Newton's 

 statement from both Garnett's and Tail's. He says : " If this second interpretation had been extended to include 

 work done by or against molecular forces, which of course Newton did not intend, it would have been equivalent 

 to the statement that the work done by an agent on a system is equivalent to the increase of kinetic energy plus 

 the increase of potential energy, which is the principle of the conservation of energy." And yet there would 

 seem to be little doubt that Th.omson and Tait are quite justified in translating co/iimo, by the term molecular 

 force. 



' Elementary Treatise on Heat (1878), p. 172. 



■■' Thomson and Tait call this expression, the equation of energy. The name seems unfortunate, because none 

 of the terms of the equation are expressions of energy. The first member expresses merely the rate at which the 

 forces acting on the various parts of the systeui are doing work, and the second, the rate at which work is being 

 done against the " resistance to acceleration." 



* 1 had not seen when I wrote this address, Prof. W. W. Johnson's paper on " The Mechanical Axioms or Laws 

 of Motion" (Bull. N.Y. Math. Soc. Vol. I. (1892) p. 129), in which Prof .Tohnson takes the same position as I have, 

 though on different grounds, with respect to the interpretation of Newton's statement referred to above. 



