16 J. G. MacGEEGOE on THE 



Passing now to the third law of motion, we find Lodge ' apparently claiming to 

 have deduced the law of the conservation of energy from it. The passage in which he 

 seems to do so is the following : — " All this indeed, [that it is as impossible to create 

 energy as it is to create matter, and that whenever energy appears as the result of work, 

 it is always at the expense of some other form of energy which was previously existing] 

 in a much more complete and accurate form — more complete, because it involves the non- 

 destruction of energy as well as its non-creation — follows from Newton's third law of 

 motion, provided we make the assumptions (justified by experiment as above [on the sub- 

 ject of the ' perpetual motion ' and others]), 1st, that just as something called energy is 

 generated whenever positive work is done, so whenever nega'ive work is done something 

 so like the first as properly to be called energy too, is destroyed ; and 2nd, that quantity of 

 energy is measured by the work done or undone in producing or destroying it. For the 

 third law tells us that whenever force is exerted and therefore (a fortiori) whenever 

 work is done, the two things concerned — the body which acts, and the body which is acted 

 upon or reacts — exert equal and opposite forces ; hence whatever quantity of work one 

 body does, the other has done upon it ; or the positive and negative works are equal. The 

 agent or body which does the positive work, loses a certain quantity of energy. The body 

 which has the work done upon it gains the same amount. Hence, on the whole — that is, 

 taking both bodies into account — no energy is lost, and, algebraically speaking, no work 

 is done. The energy is merely transferred, and the act of transfer involves two opposite 

 works." With regard to this argument it is to be noted that while the only fundamental 

 hypothesis formally recognized is the third law, the " assumptions justified by experi- 

 ment," to which appeal is made, and the assumption of the impossibility of action at a 

 distance (involved in the conclusion " hence whatever work one body does, the other has 

 done upon it ") constitute additional hypotheses, and that therefore the deduction is not 

 made from the third law alone. That Lodge only apparently claims to have made it 

 without other hypotheses is obvious from the fact that he himself directs attention to the 

 assumptions based on experiment. It may be well to note also that the law of the conser- 

 vation of energy which he thus deduces is, as pointed out by himself, - " probably not iden- 

 tical with that currently accepted." 



If we regard it as established that the deduction of the conservation of energy requires 

 more fundamental hypotheses than the three laws of motion supply, we must ask next 

 what additional hypothesis should be adopted as a fourth law of motion that such 

 deduction may be possible. 



It is obvious from what has just been said that the necessary addition will depend on 

 whether we aim at deducing the law of the conservation of energy in its ordinary form, 

 or in the form given it by Lodge. It would be interesting to inquire into the hypotheses 

 employed by Lodge in deducing his law of the conservation of energy both in the above 

 passage and in subsequent publications.^ But it would be foreign to our present purpose. 

 For while Lodge's law may be the law of the future, and is, perhaps, in some form, likely to 

 be, (for the tendency of dynamics seems to be towards the denial of action at a distance), it 



' Elementary Mechanics Q88.5), p. S2. 



2 Phil. Mag., Ser. 5, Vol. xi. (1881), p. 533. 



' Phil. Mag., Ser. 5, Vol. viii. (1879), p. 278, Vol. xi. (1881), p. 533, and Vol. xix. (1885), p. 483. 



