464 DEFINITION OF WORK DONE — MACGREGOR. 



can be applied, it is frequently more convenient to make use- 

 of the assumption of action at a distance. Should Lodge's defi- 

 nition be adopted as a general definition, then in all cases in 

 which we either must employ the action-at a-distance method 

 or find it more convenient to do so, the simple law of the conser- 

 vation of enery must be replaced by a more complex law of 

 energy, and the labor involved in the solution of problems must 

 be largely increased. Should it be adopted as a special definition 

 applicable in cases of contact action, it would be necessary to 

 employ a difl^erent definition in dealing with cases of distance 

 action and of mixed contact and distance action, a necessity 

 which w^ould give rise to new difficulty in the elementary teach- 

 ing of the subject and even to confusion in more advanced 

 work. 



It seems clear, therefore, with regard to both of the proposed 

 modifications referred to above, that the better course is to retain 

 the old definition of work done, with the dynamical reference 

 system specified, as a general definition applicable in all cases 

 whether of contact action, of action at a distance, or of mixed 

 contact and distance action ; and in dealing with cases of wholly 

 distance action or wholly contact action respectively, to prove at 

 the outset, if it be considered desirable, that the statements which 

 Prof. Newcomb and Prof. Lodge wish to use as definitions are 

 particular cases of the general definition, applicable, the one in 

 cases of action at a distance, the other in cases of contact action. 



