Hypotheses of Dynamics. 255 



plete than it is now. We may have acquired more definite 

 conceptions as to the character of certain forms of energy, as 

 to the mode of transference of energy, and as to the place of 

 residence of potential energy ; but as the law of conservation 

 makes no statement on such points which will thereby be 

 completed, our present ignorance with regard to them does 

 not render it incomplete. 



While in the event of some hypothesis as to acting 

 mechanism becoming axiomatic there would be some re- 

 adjustment in the ordinary conception of potential energy, 

 there would not be nearly so much as Prof. Lodge supposes; 

 for though his account of this conception (p. 16) is obviously 

 a burlesque, he clearly does believe that it involves an 

 " erroneous localization of energy/' that, e. g., in the case of 

 a raised stone, the potential energy must be supposed, nearly 

 all at any rate, to be resident in the stone *. This impression, 

 however, may readily be shown to be erroneous. The poten- 

 tial energy (see the definitions of work done and energy, 

 given above) may be said to belong to the system of earth 

 and stone, because work may be done by the earth or by the 

 stone or by both during the approach of these bodies. That 

 it cannot be said to belong to either, is obvious from the con- 

 sideration that, if either be held fixed relatively to a dynamical 

 reference system, the work done during approach is then 

 done by the other. How much of the work done during 

 approach is done by the one and how much by the other, 

 when both are in motion, depends upon the forces against 

 which they move and their respective displacements relative 

 to such system. It is thus obvious that according to the 

 ordinary conception we can assert no more than that the 

 potential energy belongs to the system, that this conception 

 therefore involves no localization of the energy in the system, 

 and consequently no erroneous localization. 



This of course arises from the fact that the ordinary con- 

 ception of potential energy involves no assumption as to 

 acting mechanism. Should some sufficiently definite hypo- 

 thesis of this kind become axiomatic, it would then become 

 possible to localize potential energy. If, e.g., we should 

 come to hold that bodies consist of rigid particles connected 

 by, and acting on one another through, an elastic medium, it 



* He objects to the ordinary conception of potential energy as 

 being " a mere receptacle for stowing away any portion of energy which 

 it is not convenient for the moment to attend to," yet admits (p. 24) 

 that his own potential energy belongs to the same " temporary order of 

 ideas." He also deties " any one to realize it as a thing." If he will 

 define u thing " we may perhaps try. 



