in the Theory of Energy. 293 



measure of work, the resistance offered by the body to the action 

 of the force, will be greater when the body has an initial velocity 

 Vj urging it in the direction in which it is solicited by the force 

 (in which case V, and v have the same sign), than it has when 

 the body moves from rest, — nay, more, that when the space s 

 through which the body moves (and therefore v) is indefinitely 

 small, the resistance offered in the former case (which will be 

 MvVJ will be infinitely greater than in the latter, when it will 

 be pit; 2 . 



3. The vice, or rather one vice of the measure of work above 

 proposed, is manifest from the formula (a) of the preceding 

 article. In the production of what is there offered as the work 

 done by the force, it is clear that the initial velocity (that which 

 the body had before the force began its work) has been an 

 agent. 



This view of the suhject may be further illustrated as follows. 

 Suppose that Y l is the velocity of the body at the beginning of 

 the time T, and that throughout T the motion of the body is 

 counteracted by the uniform force F, which is of such amount 

 as to reduce the body to rest at the end of T. Under these cir- 

 cumstances two things will have been done during the time T : — 



(1) Space will have been described. 



(2) Velocity will have been destroyed. 



The space manifestly has not been described by the agency of 

 the force, the only product of which is the destruction of velo- 

 city ; in other words, V, (in this case =FT) measures the work 

 done by the force. 



4. It may be an object of curiosity to some of my readers to 

 know how the above measure of work came to be adopted. On 

 this point I am sorry to be unable to afford them very precise 

 information. If my memory serves me rightly, Helmholtz, in 

 his paper in Taylor's ' Scientific Memoirs' for 1852, treats it as 

 a thing "well known;" and in Thomson and Tait's 'Natural 

 Philosophy ' it appears to be regarded in the same light. Pro- 

 fessor Maxwell informs us that " If a body whose mass is one 

 pound is lifted one foot high in opposition to the force of gra- 

 vity, a certain amount of work is done, and this quantity is 

 known among engineers as a foot-pound." 



If this passage may be taken to afford the true clue, we can 

 hardly fail to be struck with the originality of the suggestion 

 that a great philosophical principle may be established by 

 " engineering evidence." 



5. I have already said that "force can only be measured by 

 its effects," which in popular language is tantamount to the 

 assertion that force is measured by the work it does. The 

 establishment of the foregoing measure of work, therefore, is in 



