96 M. R. Clausius on a modified Form of the second 



satisfy the following coudition, 



rf/1 dQ\_lfl dQ\ 

 rf/\f * dv)^dv\T' dt)' 



If we compare this result with the before-mentioned equation 

 established by Clapeyron, we shall at once see the relation which 

 exists between the function T, here introduced, and that used by 

 Clapeyron, denoted by C, and known as Carnet^s function, which 

 I have also used in former memoirs. This relation may be ex- 

 pressed thus : 



dT 



dt A , 



T = c (^^) 



We proceed now to the consideration of non-reversible circular 

 processes. 



In the proof of the previous theorem, that in any compound 

 reversible process the algebraical sum of all the transformations 

 must be zero, it was first shown that the sum could not be 

 negative, and afterwards that it could not be positive, for if so it 

 would only be necessary to reverse the process in order to obtain 

 a negative sum. The first part of this proof remains unchanged 

 even when the process is not reversible ; the second part, how- 

 ever, cannot be applied in such a case. Hence we obtain the 

 following theorem, which applies generally to all circular pro- 

 cesses, those that are reversible forming the limit : — 



The algebraical sum of all transformations occurring in a circular 

 process can only be positive. 



