432 The Rev. J. M. Heath on the Principles of Thermodynamics' 



vis viva to the particles without losing any of its own — contrary 

 to the principle which he himself appeals to, that of the conser- 

 vation of force. He finds + (u + v) for the velocity of the particle 

 relatively to the piston after impact ; and to get the absolute 

 velocity of the particle, he adds this to u, the velocity of the 

 piston before the impact, forgetting that that velocity has been 

 altered by the impact. The consequence of this oversight is that 

 the velocity of the centre of gravity of the two bodies, and also 

 the sum of their vis viva, are both greater after impact than before 

 it — results impossible according to the true laws of impact. I 

 claim, therefore, at least for the present, to say that Mr. Ran- 

 kine has failed to prove that his proposition is true, and that I 

 have tendered a proof, as yet uncontroverted, that it is false. 



I will now pursue the remainder of the main argument, and 

 examine the contrast between my own opinions and those repre- 

 sented by Mr. Rankine, as to cases where the force meets with 

 no resistance, and does, therefore, no work. When Q=0, the 



mv 

 general equation of vis viva takes the form PSv= — j and it is 



obvious that in this case all the force is employed in producing 

 acceleration, and none of it in " storing up energy/'' All the 

 force, to use the ordinary language of mechanics, is employed 

 dynamically, or is doing dynamical work, and none is producing 

 statical work, which is pressure. If a gun-barrel is placed ho- 

 rizontally and no friction or atmospheric resistance acts to resist 

 the motion of the ball through its length, the vis viva it has at 

 the muzzle measures the expenditure of the internal energy of the 

 exploded charge, which has become externalized, and is now no 

 longer internal energy in the gas, but actual energy of motion 

 in the bullet. All this, therefore, is energy lost to the gas. But, 

 say the thermodynamists, this gas has met with no resistance, 

 done therefore no work, and can have lost no heat. Have I mis- 

 represented them ? Or how do they explain such a monstrous 

 conclusion ? 



Lastly, I will take the equation in its general form, where 

 forces are employed in both the ways that we have now consi- 

 dered separately, viz. both statically and dynamically, in pro- 

 ducing both pressure and motion. The use of this equation, 

 properly treated, will be to enable us to distinguish these forces 

 into two groups, which, as Mr. Rankine tells us, is the business 

 of thermodynamics, but which I contend has not as yet been 

 properly done. 



mv 

 The equation (P — Q)8»= -^r-may be written 



(P-Q'+Q'-Q)Sf=~- 



