The Rev. J. M. Heath on the Principles of Thermodynamics. 433 



And this, again, if we suppose Q' = Q, may be resolved into two 

 separate equations, a statical one, 



(Q'-Q)8t>=0, (1) 



and a dynamical one, 



(P_Q!)fe=S* (2) 



Whenever, therefore, P is not equal to (here supposed greater 

 than) Q, we may resolve it into two parts, Q' = Q, which is 

 therefore the reaction of the lower surface of the piston equal 

 and opposite to the pressure of the gas below, and P — Q', the 

 remaining part of P, which acts upon the particles of the gas as 

 if they were perfectly free. The effect of P— - Q' upon the gas is 

 therefore wholly dynamical ; it does not alter the pressure, and 

 its entire effect is the generation of motion. Thermodynamists 

 teach (as far as I may venture to speak of teachings which I can 

 give no mental assent to, and may therefore unintentionally mis- 

 represent in consequence of misunderstanding them) that the 

 whole gain of heat is determined by the first, or statical one, of 

 our two equations. The force Q' (part of P) presses down the 

 piston through 8v against the resistance Q, and the work done 

 is QSv, and it is done by Q', a part only of P ; and the remainder, 

 P — Q', being an unresisted force, has no effect either on the 

 work done or on the gain of heat. I think this is a true repre- 

 sentation of what they would say, because it appears to me to be 

 what they must say if the case is reversed, and we consider, in- 

 stead of a condensation by piston, the case of expansion, as the 

 discharge of a bullet from a gun-barrel. If P is considered to 

 represent the explosive force of the charge of a gun, and Q the 

 resistance arising from friction, the weight of the bullet, and the 

 pressure downwards of the external air, then Q is a fixed quan- 

 tity, and the whole energy V8v expended can do no more work 

 than QSv ; that is to say, that the largest charge that can be 

 put into the gun can do, technically, no more work, and can 

 therefore expend no more heat, than that small charge Q' which 

 is just able to counterbalance Q, so that the ball may move uni- 

 formly along the barrel and fall to the ground when it reaches 

 the muzzle. In this case I apprehend thermodynamists must 

 relegate the excess of gas-force, P— Q', over the resistance, into 

 that group which we have already discussed, of forces which do 

 no work and exhaust no heat. 



The truth is, I have never seen anywhere any recognition 

 among writers on this subject of the case of unequal forces acting 

 in this way in condensing or in expanding the gas ; and although 

 the opinion is wholly untenable, I believe that the general con- 

 ception is, at all events when the load on the piston descends 



