it>4 M. R. Clausius on the Moving Force of Heat, 



retaiuing the first and really essential portion of the assumption 

 of Carnot, and to apply it as a second maxim in connexion with 

 the fonner. It will be immediately seen that this procedure 

 receives manifold corroboration from its consequences. 



This assumption being made, we may regard the maximum 

 work which can be effected by the transmission of a unit of heat 

 from the body A at the temperature t to the body B at the tem- 

 perature T, as a function of t and t. The value of this function 

 must of course be so much smaller the smaller the difierence 

 / — T is; and nmst, when the latter becomes infinitely small ( = dt), 

 pass into the product of dt with a function of t alone. This 

 latter being our case at present, we may represent the work 

 under the form 



wherein C denotes a function of / only. 



To apply this result to the case of permanent gases, let us 

 once more turn to the process represented by fig. 2. During 

 the first expansion in that case the amount of heat, 



passed from A to the gas ; and during the first compression, the 

 following portion thereof was yielded to the body B, 



[(f)*i(S)»-i(S)"]". 



or 



(S)*-[i(S)-i(S)]"'- 



The latter quantity is therefore the amount of heat transmitted. 

 As, however, we can neglect the differential of the second order 

 in comparison with that of the first, we retain simply 



(S) 



dv. 



The quantity of work produced at the same time was 



V ' 



and from this we can construct the equation 

 ^dv .dt 



(S) 



dv 



