Hypotheses of Dynamics. 251. 



nition, whatever energy the one loses the other gains. In 

 other words : in all cases of activity, energy is simply trans- 

 ferred from one body to another, without alteration in 

 quantity." Now it is obvious that we cannot pass by definition 

 from work done or activity to energy, for energy has been 

 defined as the result of work done or activity, the line-integral 

 of a force considered as a quantity which can be stored. We 

 must first pass from the equality and opposition of the works 

 done (or line-integrals of the forces) to the equality and 

 opposition of the results of the works done (or of the line- 

 integrals of the forces considered as quantities ivhich can be 

 stored). How is this passage made ? We are not told. But 

 it is obviously by the assumption that work done on a body 

 is equal to the result of work done, or that the line-integral 

 of a force may be considered as a quantity which can be 

 stored. And as obviously, this assumption is the law of the 

 conservation of energy. Thus the conclusion of the argu- 

 ment, which, as in former deductions, is clearly conservation 

 during transference only, is obtained by assuming the law of 

 conservation generally. 



It would indeed be a remarkable thing if it were possible, 

 in the case of systems whose parts act upon one another only 

 when in contact or at constant distance, to deduce the con- 

 servation of energy during transference from the third law 

 of motion alone. When we make no assumption as to the 

 distance at which action may occur, we require, in order to 

 obtain the law of transference, to obtain first the general law 

 of conservation, for which purpose we have to assume the 

 second law of motion, and some such axiom as the impossi- 

 bility of the perpetual motion. Having obtained from these 

 axioms the general law of conservation, the third law then 

 gives us the law of transference. Why, then, when we 

 restrict our attention to systems exhibiting constant distance 

 action * only, should it be possible to deduce the law of 

 transference independently of the law of conservation? 

 This is a logical question to which it should be possible to 

 give a clear answer, if it is possible to make the deduction 

 referred to. 



(5) Prof. Lodge's Deduction of Contact-action. 

 In former papers t Prof. Lodge claimed to prove the 



* Prof. Lodge's argument assumes constant distance action, not spe- 

 cifically contact-action ; for " if they move they must move over the 

 same distance" is true of actions at all constant distances, not merely 

 of actions at distance zero. 



t PM1. Mag. [5] viii. p. 279, xi. p. 36. 



S 2 



