﻿128 The Rev. J. M. Heath on Athermogenic Condensation. 



ciple, that when (P — Q)o# = Q, P can generate no motion, but 

 with the remarkable reservation that this is to be understood 

 only of motion in the point or body to which P and Q are actu- 

 ally applied : but it seems to be held that, under certain cir- 

 cumstances at least, P may augment the motions of other bodies 

 to which it is not applied. 



In order to maintain the equality of the forces acting upon 

 the piston during its descent, and therefore the uniformity 

 of its motion, it is necessary, since Q increases during the con- 

 traction of V, to augment P also by a quantity constantly 



du 

 equal to the augmentation of Q. Mr. Rankine finds M-7-, 



where M is the mass of the piston, and u its velocity, for the 

 value of this increment of P. And he finds the expression 

 2m. u .(u + v) for the increment of the internal energy of the gas 

 caused by the descent of the piston through the space udt. He 

 states as his final result that Vudt -f Mudu = 2mu . (u -\-v)dt, 

 which he interprets in words to mean that the internal energy 

 of the gas will be increased by a quantity represented by the 

 work done byV + the energy lost by the piston through retardation. 



I cannot admit the correctness of the equation in which Mr. 

 Rankine has expressed the final result of this his corrected in- 

 vestigation. If I have myself rightly apprehended the argument 

 he has followed, the result should have been symbolically ex- 

 pressed as follows. 



Before the motion the equality of action and reaction gives 



P . udt=Qudt ) 



during and after the motion we have 



P . udt + Mudu = Qudt + 2mu (u + v)dt; 

 therefore 



Mudu = 2mu(u + v) dt. 



And this result, being independent of both P and Q, is conclu- 

 sive against the proposition it was advanced to support, viz. that 

 the energy generated was to be proportional to the whole action 

 of P through udt or to Vudt. 



But, on the other hand, I must admit that although it sup- 

 ports the principle I have been contending for, that when new 

 energy is generated it is due to the difference between P and Q 

 and not to the entire action of either of them, yet so far as it 

 seems to show that some new energy is generated in contraction, 

 even while P and Q are always in equilibrium, I aui bound tore- 

 move this difficulty, or else to admit that a contrary opinion to my 

 own has been, at least to a certain extent, established. 



The energy of repulsion by which the piston repels the par- 



