Dr. W. J. M. Ranking on Thermodynamics. 293 



The aggregate energy of the mass m of particles before the 

 collision is — , and after the collision — ^—^ — —\ therefore the 

 increase of the energy of the moving particles in one second is 



- {{v + 2u)*-v*\=2m(uv + u 2 ), ... (2) 



being exactly equal to the work done in pushing the piston 

 inwards. 



For the sake of simplicity, the preceding demonstration has 

 been applied to elastic particles striking a piston and rebounding; 

 but the same principle can be proved for any mode of internal 

 motion of matter in a confined space ; and when the particles 

 exert attractions and repulsions, it can be proved for the work 

 done by that term in the value of the external pressure which is 

 equal and opposite to the outward pressure due to the motions 

 of the particles — a term which, according to the second law of 



thermodynamics, is found by performing the operation r-r- upon 



CLT 



the external pressure, r being the absolute temperature. For 

 example, when a mass of saturated vapour occupying the space 

 S, at the pressure p, and absolute temperature t, is compressed 

 into the liquid state, occupyingthen the volume s, the temperature 

 and pressure during the compression being maintained constant 

 by abstracting the heat produced, the principle just mentioned 

 gives for the amount of that heat in dynamical units 



a result which is known to be exactly confirmed by experiments 

 on various fluids. 



For detailed information, however, on this and other points I 

 must again refer to Professor Tait's treatise on Thermodynamics, 

 and to the original papers referred to in that treatise. 

 I am, Gentlemen, 



Your most obedient Servant, 



W. J. Macquorn Rankine. 

 Glasgow, September 10, 1870. 



