258 Prof. J. G. MacGregor on the 



route of some lost luggage which has turned up at a distant 

 station in however battered and transformed a condition " *. 



I need not discnss here the question whether even matter 

 can be said to have the kind of identity here specified, whether 

 in fact we can label a bit of it and follow it in its wanderings. 

 We certainly cannot, in general, do so practically. Whether 

 or not we can do so ideally may, I think, be found to depend 

 upon our hypothesis as to the constitution of material bodies. 



That energy, however, has this kind of identity seems to 

 me to be a much more definite proposition than the one 

 considered above, and not by any means to be implied in it. 

 Indeed, that the contact-action conception of energy does not 

 confer npon it the capability of being thus followed in its 

 motion may, 1 think, be proved. We cannot be said to be 

 able to follow a "bit " of energy iu its wanderings unless we 

 are able at all stages to localize it. If in the course of its 

 peregrinations it enter a system of bodies and get so hidden 

 away that we can only say of it that it is in some body or 

 other of the system or is distributed in unknown proportions 

 among them, then we have lost it even more completely than 

 we should have lost our luggage in a railway collision if we 

 knew only that it was distributed somewhere among the 

 debris. Now we have seen that the assumption of contact- 

 action alone does not enable ns to localize potential energy. 

 While, therefore, the introduction of the axiom of contact- 

 action confers upon energy a certain kind of continuity, 

 telling us that it must pass from one body to another or to 

 others, it does not enable us to follow a bit of energy and to 

 trace its route, because it does not in all cases enable us to 

 localize it. If we wush to be able to trace its route com- 

 pletely, we must introduce a further axiom which, with 

 contact -action and the third law, will make our conception of 

 the transference of energy sufficiently complete. Then we 

 shall be able to localize energy under all circumstances, and 

 the first condition of following its motion will be satisfied. 



But more than mere localization is necessary in order to 

 label and follow a " bit " of energy. We must also be able 

 to distinguish it from other bits when several of them at the 

 same time get into the same body ; and here the chief diffi- 

 culty seems to arise. It is easy enough to frame an hypothesis 

 of acting mechanism which will localize energy in all cases, 

 provided we do not mind much whether or not it coordinates 

 for us dynamical phenomena generally ; but how we are to 

 distinguish between the portions of energy which are trans- 

 ferred simultaneously, say, to a particle by the various elements 

 of the medium in contact with it, is not so apparent. To my 

 * Phil. Mag. [5] vol. xix. p. 482. 



