Prof. Clausius on the Internal Work of a Mass of Matter, 201 



of the Calculus of Variations, I maintain that that particular 

 surface is the composite one to which the foregoing reasoning 

 has conducted, and that the principle of discontinuity which the 

 reasoning involves must be recognized. An inference of this 

 importance invests the discussion of the problem with peculiar 

 interest. 



Cambridge, August 6, 1862. 



XXIX. On the Application of the Theorem of the Equivalence of 

 Transformations to the Internal Work of a mass of Matter. By 

 Professor R. Clausius. 



[[Concluded from p. 97.] 



§ 7. "\^7*E will now investigate the manner in which, from 

 ▼ t equation (II.), it is possible to arrive at the equa- 

 tion (I.) previously given in § 1, which equation must apply, 

 according to the fundamental theorem that I have already enun- 

 ciated, to every reversible circular process. 



When successive alterations of condition constitute a circular 

 process, the disgregation of the body is the same at the end of the 

 operation as it was at the beginning, and hence the following 

 equation must hold good : — 



pZ = (15) 



Equation (II.) is hereby transformed into 



'' Q +£*=P (16) 



j" 



In order that this equation may accord with equation (I.), namely, 



Jf=o, 



the following equation must be applicable to every reversible cir- 

 cular process : — 



Jy^ (IIL) 



It is this equation which leads to the consequences referred to 

 in the introduction as at Variance with commonly received views. 

 It can, in fact, be proved that, in order that this equation may 

 be true, it is at once necessary and sufficient to assume the fol- 

 lowing theorem : — 



The quantity of heat actually present in a body depends only on 

 its temperature, and not on the arrangement of its component 

 particles. 



It is at once evident that the assumption of this theorem suf- 



Phil. Mag. S. 4. Vol. 24. No. 1G0. Sept. 1862. P 



