On the Proof of the Second Law of Thermodynamics. 369 



enabled us to predict the position and inclination of these lines. 

 Neither are the water-worths of the salts as ciyohydrates nor 

 their solubilities in water at 0° C. in any obvious accord with 

 their known properties. 



[To be continued.] 



XL IV. On the Proof of the Second Law of Thermodynamics. 

 By E. C. Nichols *. 



IN the last January Number of the Philosophical Magazine 

 appeared two papers intended to demonstrate what is 

 called the second law of thermodynamics, or the principle of 

 Carnot and Clausius, by showing that the differential of the 

 quantity of heat communicated to a gas, and thereby causing 

 work to be done, divided by the temperature, is an exact dif- 

 ferential. The paper of Mr. Burbury proceeds upon the basis 

 of the theory of Boltzmann, and demonstrates that this conclu- 

 sion can be deduced from Boltzmann's results by a simpler pro- 

 cess than that made use of by M. Boltzmann himself. That 

 of M. Szily proposes to establish the same conclusion upon no 

 other assumption than the fundamental principle of the con- 

 servation of energy. 



To M. Szily's argument I have to offer the following objec- 

 tion. He says (p. 29) : — " In a definite passage out of (fo^o) 

 into (ftfi) the quantity of energy is a certain function of the 

 time. The passage, however, from the same initial to the same 

 final state, by the same path, can, with respect to time, be 

 executed quite arbitrarily ; consequently Se is a different func- 

 tion of the time, according to the velocity of the importation 

 of energy. By suitably selecting this velocity, any indefi- 

 nitely small value whatever may be assigned to I Bedt. Let 



i 



$€dt=t$Q,:' 



Upon this I have to remark that Se is in this sense a different 

 function of the time according to the velocity of the importa- 

 tion of energy — that it is a function, not of the absolute time, 

 but of the proportion of the whole time which has elapsed ; so 



that l Sedt or Set is a quantity which varies as t. On the 



other hand, SQ being, as already stated, absolutely independent 

 of tj t$Q likewise varies as t. Unless therefore SQ = Se, for which 



* Communicated by the Author. 

 Phil Mag. S. 5. Vol. 1. No. 5. May 1876. 2 C 



