The Rev. J. M. Heath on the Principles of Thermodynamics. 219 



Mr. Rankine's second proposition is, that if the body's elasti- 

 city is the result of the mere motion of particles having inertia 

 but not acting upon each other by forces of attraction and repul- 

 sion, then in the compression of such a body by external force 

 all the force employed imparts motion to the particles of the gas, 

 and that the addition so made to the previous vis viva of those 

 particles is the same as the vis viva which the same force acting 

 through the same space would have generated supposing the par- 

 ticles had been previously at rest, — or, in other words, that the 

 compressing force will descend through the same space whether 

 there be any resistance to its motion or none. 



These two propositions (if indeed I have rightly understood 

 them) appear to me to involve a conclusion completely subversive 

 of the whole doctrine of thermodynamics, viz. that the production 

 of heat in different bodies by compression depends upon their 

 molecular constitution — and, furthermore, that upon no hypo- 

 thesis as to the constitution of a body will the production of heat 

 be in accordance with the true mechanical laws of the production 

 of vis viva. If the body consists of particles which mutually repel 

 each other, Mr. Rankine thinks no heat can ever be generated 

 by impact or compression in such a body, although it is certain 

 that vis viva can be generated among its particles. If the body 

 consists of only moving and impinging particles without repulsive 

 forces, Mr. Rankine thinks that the new heat generated by con- 

 densation in such a body will be equal to what a merely mecha- 

 nical solution of the question teaches us would be the total vis 

 viva — i. e. the sum of what there was at first, added to the addi- 

 tion made by the work done by the force. 



I believe my own analysis of what is objectionably called the 

 " overcoming of resistance by a force " to be true in mechanics, 

 and to be free from each of the objections above stated. 



If the area of the piston by which a volume of gas is com- 

 pressed is unity, and P is the external load put upon it, andjt? 

 is the internal pressure of the gas opposing its descent, then P 

 may, at every point of the descent, be considered as consisting of 

 two parts, one =jo which we will call p', and the remainder, 

 which therefore will be P— p 1 . 



p and p ! constantly increase as the piston descends and the 

 volume of the gas diminishes; and P— p' consequently is dimi- 

 nishing during the whole descent. Let P— p'=0, or P=j»', 

 when v has become v'. The whole amount of deduction, there- 

 fore, which has to be made from the action of P through the space 



dv. The question is, What has been the employ- 



v—v is I p Y 



Jvt 



ment of this force ? My answer is, that it is the sum of all the 

 pressures which, at every point of the descent, have held the elastic 



Q2 



