Hypotheses of Dynamics. 253 



is merely a particular case of the ordinary law (p. 137 of 

 my paper.) 



In reference to his statement that his law is as axiomatic 

 as the ordinary law, I showed that the latter is the more 

 general in its applicability to dynamical problems. Prof. 

 Lodge declares himself to be in entire agreement with this ; 

 but he adds that it is no discredit to " the true law not to 

 lend itself to fictions/' and that, while it is often permissible 

 to work in a fictitious or incomplete manner, ignoring 

 communicating mechanism, such " omissions and slurrings " 

 should not be made in laying foundations, and that the habit 

 of thus ignoring unknown essentials may lead to the treat- 

 ment of fictions as if th^y were realities. There seems to me 

 to be confusion here between the fictitious and the general*. 

 There is nothing fictitious in the ordinary law of the con- 

 servation of energy. Work being said to be done by a body 

 when the body moves (relatively, of course, to a dynamical 

 reference system) against an opposing force, and energy being 

 defined as power of doing work f, the ordinary law asserts 

 that energy is conserved. It is sometimes expressed in terms 

 of the fiction of action at a distance and sometimes also in terms 



* It is this confusion, I think, which has led Prof. Lodge, in his com- 

 parison of our respective types of mind, to make the entirely erroneous 

 statement that I am willing " to base Physics on action at a distance " 

 (p. 2, footnote). To it is due also the statement of p. 16 in which the 

 ordinary conception of potential energy is ascribed to " the believer in 

 action at a distance." 



t Prof. Lodge's extraordinary objections to this definition are easily 

 met. — (1) It is " vague." Doubtless it is to one who can make the state- 

 ments quoted below. Compare its precision with that of the definitions 

 by which it is to be replaced : — " effect of work done ; " " result of work 

 done ; " " line -integral of a force considered as a quantity which can be 

 stored." The formal definition of his ' Mechanics ' : — " Energy is that part 

 of the effect produced when work is done upon matter, which is not an 

 accidental concomitant, but really owes its origin to the work, and could 

 not, so far as we know, have been produced without it ; and which, 

 moreover, confers upon the body possessing it an increased power of 

 doing work," — would seem to imply that he rightly considers his own 

 definition so vague as to require to be supplemented by the ordinary 

 definition. (2) " Plenty of energy has no power of doing work, at least, 

 no power that we can get hold of." Nor can it have according to the 

 definition. Probably what is meant is that plenty of bodies possess 

 energy which we cannot utilize ; but oar ability to get hold of power is 

 no criterion of its existence. (3) "A given amount of energy may have 

 an infinite working-power, since it can do work at every transfer without 

 itself diminishing." As just stated, according to the definition, energy 

 cannot be said to have any working-power at all. It is the body or 

 system of bodies possessing the energy vvhich has the power. (4) " It is 

 bold to maintain the conservation of working-power in face of the 

 doctrine of the dissipation of energy." The conservation o^ power of any 

 kind is quite consistent with diminishing opportunity of exercising it. 



