462 DEFINITION OF WORK DONE — MACGREGOR. 



assumption that the distance action is due to contact action 

 through an elastic medium, we would require to re-define work 

 done for the purpose. It would surely be more convenient to 

 define work done in such a way that the same conception of it 

 might be employed in both classes of problems. 



Prof. 0. J. Lodge has proposed* to define work done in the 

 following way : — 



" Whenever a body exerting a force moves in the sense of the 

 force it exerts, it is said to do work ; and whenever a body 

 exerting a force moves in the sense opposite to that of the force 

 it exerts, it is said to have work done upon it or to do anti- 

 work, the ([uantity of work being measured in each case by the 

 product of the force into the distance moved through in its own 

 direction." 



The definition is not quite precise ; for it is not clear whether 

 the " distance moved through " is by the body or by the point 

 of application of the force it exerts. In cases of contact action 

 with a view to which Dr. Lodge proposed this definition, the 

 distance moved through by both w^ould be the same. For his 

 purpose, therefore, it was not necessary to be more precise. If, 

 however, we are to form a judgment as to the relation of this 

 definition to the one ordinarily used, greater precision is neces- 

 sary. That it was the distance moved through by the place of 

 application of the force that was meant seems clear from the 

 definition of working power which follows that quoted above, 

 viz. : " The working power of a body is measured by the aver- 

 age force it can exert, multiplied by the range or distance 

 through which it can exert it." The distance contemplated in 

 the definition is thus the distance through which the force is 

 exerted, i.e., through which its point of application moves. And, 

 indeed, had the distance contemplated been that moved through 

 by the body exerting the force the proposed definition w^ould 

 have been practically equivalent to the one it was intended to 

 displace. 



To compare this definition with the usual one, let A and B be 



* Philosophical Magazine, Ser. 5, Vol. VIII (1879), p. 278. 



