250 Prof. J. G. MacGregor on the 



the reiteration of his old claim with this admission we are 

 not told. 



With regard to my criticism of his earliest mode of making 

 this deduction, he replies that the appeal to experience which 

 I pointed out as having been made in his argument was a mere 

 piece of politeness, which might have been omitted without 

 affecting the argument. I think if he will look into the 

 matter he will find that if he had been less polite his 

 reasoning would have been faulty. It is unnecessary to 

 occupy space in proving this, however, because the new de- 

 duction, given in the present paper and referred to below, 

 embodies exactly the same fallacy as the old one. 



In reply to my criticism of the law of conservation de- 

 duced by the argument of his third paper (quite a different 

 law as I pointed out from that obtained in the earlier paper, 

 though Prof. Lodge does not seem to realize this), viz , that 

 it was of the same nature as the law of the conservation of 

 momentum, his energy as defined in that paper being con- 

 stant in quantity, because equal quantities of positive and 

 negative energy must always be produced together, he states 

 that his law is deduced from a less obvious assumption than 

 the conservation of momentum. This is possibly true ; but 

 it does not affect the nature of the law deduced. The law of 

 the conservation of electrical quantity is obtained in a dif- 

 ferent way from either, but is nevertheless a law of the same 

 kind. 



The new version of the deduction of the conservation of 

 energy from the third law and the assumption of contact- 

 action, is based upon a new definition of energy as "the 

 result of work done," or "the result of activity lasting a 

 finite time." As this is rather vague, work done on a body 

 having a variety of results, Prof. Lodge proceeds to expound 

 his definition and tells us that energy " is a name for the 

 line-integral of a force, considered as a quantity that can be 

 stored " *. Here, again, is the appeal to experience, — that 

 the line-integral of force may be considered as a quantity 

 which can be stored. If it is introduced merely out of 

 politeness, it must not be used in the argument. If used in 

 the argument, it forms an unacknowledged assumption. 



The argument is as follows : — (i Bodies can only act on one 

 another while in contact, hence if they move they must move 

 over the same distance ; but their action consists of a pair 

 of equal opposite forces ; therefore the works they do, or 

 their activities, are equal and opposite ; therefore, by defi- 



* His comments show that lie should have added here the words u in 

 a body." But this doesfnot affect the present argument. 



