the Disgregation of a Body. 31 



of T in question is the integral 



I 



which enters into the expression for -r- Z given by equation (5), 



but does not occur in the expression for F. I have also stated 



that in the case where -^= =0, as happens for the perfect gases, 



these two quantities may be regarded as equal. 



In an exposition of the mechanical theory of heat recently 

 published by M. Paul de Saint-Robert*, this talented author 

 expresses the opinion that the difference insisted on by me 



between the quantities F and -r Z does not exist. But I cannot 



agree with his reasoning, and in my opinion the simplifications 

 which he has introduced into the formulae, by means of this rea- 

 soning, are not generally admissible. 



M. de Saint-Robert supposes that if the free space afforded 

 to the body is very large, the body will be reduced at all tem- 

 peratures to the state of a perfect gas — that is to say, to a state 

 in which there is no internal work, and in which consequently 



we have -= =0. Under these circumstances, if, in equation (5), 



we take as the initial state one in which the volume v is very 

 great, we shall have 



T (rS) rfT=0 > w 



T X a 1/ «=»o 



and consequently equation (5) is reduced to 



Z=Z +aP4* (8) 



J v 



We thus arrive at the result that the quantity — Z is iden- 

 tical with the quantity F as denned by equation (6). 



But it will be seen that the accuracy of this conclusion de- 

 pends on the accuracy of M. de Saint-Robert's supposition. 

 This, therefore, is the point which specially demands our atten- 

 tion. 



M. de Saint-Robert says, at the end of his reflections on this 

 subject (p. 91 of his book), that he supposes that all natural 

 bodies can be caused by heat to pass into the state of perfect 



* Principes de Thermodynamique, par Paul de Saint-Robert. Turin, 1865. 



j" 



*/T, 



