DEFIXITIONT OF WORK DONE — MACGREGOR. 463 



two bodies between which a stress acts, let F^b and Fba be the 

 forces exerted by A on B and by B on A respectively, andlet S^ 

 and Sb be the distances moved through in the line of the stress 

 by A and B respectively ; then the work done by A and by B 

 i-espectively would be, according to Lodge's definition, F.^b Snand 

 and Fba S.^and according to the ordinary definition, — Fba SAand 



— Fab Sb • Since in all dynamical problems the Third Law of 

 iSIotion holds, we may put Fab = — Fba- Hence the work done by 

 A and B respectively is, according to Lodge's definition, Fab Sr 

 and — F^B Sa and according to the ordinary definition Fae Sa and 



— Fab Sb . The term work done will therefore, in general, have 

 different denotations according to the two definitions, and con- 

 sequently theorems involving work done and working-power or 

 energy which have been established in terms of the old defini- 

 tion would not hold in terms of the new one. The law of the 

 conservation of energy would no longer be generally true. 



In the particular case of contact action, Sa = Sb- Hence in 

 this case the work done by A and B respectively would be the 

 same according to both definitions, and both definitions would 

 thus have the same denotation. For cases of contact action 

 therefore, established theorems involving work done and energy 

 would still hold notwithstanding the change of definition. 



The advantage of Lodge's definition is that in cases of contact 

 action it indicates directly that a body in doing positive or 

 negative work respectively, loses or gains working power, or as 

 he puts it, that it is the thing which does the work which possesses 

 energy. This result, however, follows from the ordinary defin- 

 ition by a single step. For as already seen, by putting Sa 

 equal to Sb the work done by A and B respectively is seen to 

 be the same according to both definitions. Any advantage 

 which Lodge's definition offers in dealing with cases of contact 

 action is therefore afforded by the ordinary definition as well. 



If we always employed the assumption of contact action in 

 dynamical reasoning it might be worth while to change the 

 definition of work done in the way suggested. But whatever 

 may be the future of this mode of treatment, we cannot at 

 present apply it in all cases, and even in cases in which it 



