292 Mr. R. Moon on the Measure of Work 



and the distance throughout which that force is overcome " 

 (Theory of Heat, 1871, p. 87). 



"¥s is the work done by the force F acting on the body [M] 

 while it moves in the direction of F through a space 5 " (ibid, 

 p. 89). 



Interpreting the latter of these sentences by the former, it is 

 clear that in the case considered the resistance offered to the 

 action of the force F is treated as exactly equivalent to, and as 

 capable of being represented by, F. The question arises, there- 

 fore, What is F ? 



The phrases " the absolute force," "the force acting at a 

 point/' are so constantly in use among us that we are apt to 

 lose sight of their purely conventional character. 



Force can only be measured by its effects ; and in order that 

 force may produce any effect, it must operate throughout an 

 interval of time. As a matter of fact F is the amount of mo- 

 mentum generated by a force acting uniformly during a unit of 

 time ; and what F truly represents is the force acting on a body 

 during a unit of time*. If, therefore, F can be accepted in any 

 degree as the representative of the resistance offered in the above 

 case, it must represent the resistance offered in a unit of time. 

 Thus, if we adopt the above definition of work, it follows from 

 the simple rules of arithmetic, not less than I trust that I have 

 already shown it to result from sound mechanical principles, 

 that the work done by the force F acting during the time T is 



FT 2 



FT, and not —=— as, if the measure of work above proposed 



were admissible, it would be, supposing the body to move from 

 rest under the influence of the uniform force F throughout the 

 time T. 



2. Suppose a body whose mass is M to be moving in a certain 

 direction with a velocity V L , and that the force F is applied to 

 the body in the direction of its motion. Then, as before, if F 

 be uniform we shall have 



Fs=4(MV 2 -MV2), 



where s represents the space described by the body while the 

 velocity changes from V, to V ; and putting Y = Y l +v,we shall 

 have 



work = Fs = 4M(t; 2 + 2*;V i ) («) 



We thus arrive at the entirely inadmissible conclusion, that 

 while the body moves through the space s, the work done 

 upon it by the force F, and therefore, according to the above 



* The test of uniformity, and necessarily the only test, being that the 

 force generates equal amounts of momentum in equal times. 



