20 M . R. Clausius on the Moving Force of Heat. 



and heat of gases*, harmonizes very well with our present theory, 

 while it is not possible to reconcile it with the theory of Camot 

 as heretofore treated. 



In equation (116.) let Q=: const., we then obtain the following 

 equation between v and / : 



cdt + A.n^^dv=:0; .... (13.) 



V 



from which, when c is regarded as constant, we derive 



V • (a + t)= const. ; 



AT? /^ * 

 or, since according to equation (10a.), = -— I==A— 1, 



v*~*(fl + ^)= const. 



Let three corresponding values of v, / and p, be denoted by g^ 

 tQsmdpQ} we obtain from this igsWxs 



a + tQ \v/ ^ ^ 



By means of equation (I.) let the pressure p, first for v and 

 then for /, be introduced here, we thus obtain 



m-(B'- (-) 



fe-fe)" <«•' 



These are the relations which subsist between volume, tempe- 

 rature and pressure, when a quantity of gas is compressed, or is 

 suffered to expand in a holder impervious to heat. These equa- 

 tions agree completely with those developed by Poisson for the 

 same casef, the reason being that he also regarded k as constant. 



Finally, in equation (lib.) let /= const., the first member at 

 the right-hand side disappears, and we have remaining 



d(i=AU^-^dv; (17.) 



V 



from which follows 



Q= AR(a + /) log i; 4- const. ; 



or when the values of v, p, t and Q, at the commencement of 

 the experiment, are denoted by Vq,Pq, ^q and Qo, 



Q-Qo=AR(«.F/o)logf. . . . (18.) 



* Traiti de M^canique, 2nd edit. vol. ii. p. 646. 

 t Traits de M^canique, vol. ii. p. 647. 



