1 80 On the Second Axiom of the Mechanical Theory of Heat. 



that present in the system, we can write : — 



8q=:Sh + SL 



= S2mcT + 3L 



=SmcST+SL. 



Replacing herein SL by its value from (33), we obtain 



8q = X2mc8T + T22mcS log i 



= T(22mcS log T + 22mc $ log i) 



=T22mcSlog(Ti), 



or, otherwise written, 



8q = T8Z2mc\og{Ti). ..... (35) 



This equation corresponds to equation (59) in my memoir 

 " On some convenient Forms of the fundamental Equations of 

 the Mechanical Theory of Heat"*. If, namely, we multiply 

 both sides of the preceding equation by A (the caloric equivalent 

 of the work) , and then^ for ABq (which represents in heat-measure 

 the communicated vis viva) put £Q, and introduce the quantity 

 S with the signification 



S=AS2mclog(Ti), (36) 



the preceding equation is changed into 



SQ=TSS (37) 



The quantity S here is that which I have named the entropy of 

 the body. 



In the last equation the sign of variation may be replaced by 

 the sign of differentiation, since, of the two processes previously 

 considered together (the variation during a stationary motion, 

 and the transition from one stationary motion to another), to dis- 

 tinguish which two signs were necessary, the former does not 

 here come into consideration. Dividing, moreover, the equation 

 by T, it reads :— 



Supposing this equation integrated for a circular process, and 

 considering at the same time that S has the same value at the 

 end of the circular process as at the beginning, we obtain 



'^ = . (38) 



This is the equation which I first published f, in 1854, as an 

 expression of the second axiom of the mechanical theory of heat 



* Pogg. Ann. vol. cxxv. p. 353; Ahhandlungen iiber die mechanische 

 Warmetheorie, vol. ii. p. 1. 



t Pogg. Ann. vol. xciii. p. 353; Ahhandl. iiber die mech. Warme- 

 theorie, vol. i. p. 127. 



J ! 



