6(5 On the Second Law of Thermodynamics. 



And we have seen that 



hPfretX^. 



Therefore 

 that is, 



1 * v dv 



v av 



Substituting in (B), wo obtain 



8u=- x Zh + hF8r, 

 or 



and substituting in (A), we obtain 



an exact differential. 



2 2 



The expression — X log A 4- o^X+ o w is what Eankine de- 

 notes by <f) in his equation 



JdQ=Td<l). 



The value which we have obtained for </> is the same as that 

 obtained by Boltzmann in the memoir above referred to. But 

 his expression for SQ is 



_ 3\ 



2A 



VJll IVJL '-'V^ ■»►-» 



which is not easily to be reconciled with the expression we 

 have used. 



V. We have assumed hitherto that no alteration takes place in 

 X except as the equivalent of work done by or against the forces. 

 It is, however, conceivable that a change should take place in 

 X for one and the same configuration, especially if, in the ad- 

 justment of external pressure to maintain equilibrium, new 

 forces be brought into play. Boltzmann appears to contemplate 

 this case. We proceed to show that^ provided x be for each 



