The Rev. J. M. Heath on the Principles of Thermodynamics. 431 



mv 2 



equal to Q, as in the case we are considering, — is nothing ; 



A 



that is, no vis viva is generated in a body by the action of 

 two equal and opposite forces. I do not know how Mr. Ran- 

 kine, and those whose opinions he shares, explain this fact 

 consistently with their belief that it is under these conditions, 

 and these only, that P accelerates molecular motions and there- 

 fore generates heat, and does not store up energy in Q. 

 But, " speaking under all reserve," I suppose that they con- 

 trive to continue to attribute the character of a dynamical 

 equation to the equation (P — Q)8z;=0 which it had when 



mv 

 it retained its full form (P — Q)o>= — , and imagine that P 



does drive the body m along the length Bv against all the efforts 

 of Q, and that it is in doing this that it generates heat. But 

 if this is the view of any one, I think that person will not 

 see the truth in this matter very clearly until he has discarded it. 

 If P could by any possibility do any one thing which Q could 

 not prevent, then the motion P would communicate to m would 

 be accelerated, not uniform, as it is assumed to be. Those, if 

 there are any, who deliberately maintain such an opinion as this, 

 have not observed that(P — Q)8v is no longer the equation of vis 

 viva at all, but has become the statical equation of virtual velo- 

 cities, and that in that equation the motion of m through Sv is 

 not the work of either of the two forces P or Q, but any arbi- 

 trary possible motion derived from an external cause. In the 

 dynamical equation the motion is due to the forces in action. In 

 the statical equation it is independent of and unaffected by those 

 forces ; and the supposed case of work done is a case of statics 

 only and not of dynamics. I rely upon this, therefore, for the 

 proof of one half of my assertion, viz. that no acceleration, and 

 therefore no heat, is generated by the action of forces which are 

 in equilibrium, and subject to the equation of virtual velocities, 

 or, in other words, of forces in that condition in which they are 

 said to do work. 



Mr. Rankine has adduced a mathematical demonstration, de- 

 rived from the theory of the collision of elastic bodies, which he 

 relies on as a positive argument on the other side. What I have 

 just now given is a direct and positive proof that the force above 

 the piston cannot accelerate, so long as it is equilibrated by the 

 resistance below. Mr. Rankine's argument is, in form, equally 

 direct and positive to prove that it does. I shall simply point out 

 a very important mistake which vitiates the whole of his proof; 

 and unless he can maintain that his reasoning is souud, the pro- 

 position he attempts to support must be taken as disproved. His 

 mistake is this. He represents the piston, in fact, as imparting 



