THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OP SCIENCE. 



[FOURTH SERIES.] 



AUGUST 1856. 



X. On a modified Form of the second Fundamental Theorem in 

 the Mechanical Theory of Heat. By R. Clausius*. 



IN my memoir '' On the Moving Force of Heat, and the Laws 

 which can be deduced therefrom f/' I have shown that the 

 theorem of the equivalence of heat and work, and Carnot's 

 theorem, are not mutually exclusive, but that, by a small modi- 

 fication of the latter, which does not affect its principal part, they 

 can be brought into accordance. With the exception of this 

 indispensable change, I allowed the theorem of Carnot to retain 

 its original form, my chief object then being, by the application 

 of the two theorems to special cases, to arrive at conclusions 

 which, according as they involved known or unknown properties 

 of bodies, might suitably serve as proofs of the truth of the 

 theorems, or as examples of their fecundit3^ 



This form, however, although it may suffice for the deduction 

 of the equations which depend upon the theorem, is incomplete, 

 because we cannot recognize therein, with sufficient clearness, 

 the real nature of the theorem, and its connexion with the first 

 fundamental theorem. The modified form in the following pages 

 will, I think, better fulfil this demand, and in its applications 

 will be found very convenient. 



Before proceeding to the examination of the second theorem, 

 I may be allowed a few remarks on the first theorem, so far as this 

 is necessary for the supervision of the whole. It is true that I 



* The present memoir appeai-ed in Poggendorif's Annalen, vol. xciii. 

 p. 481, and was referred to by the author in a letter lately published in 

 this Magazine ; it is also employed to a considerable extent in a memoir 

 on the steam-engine by the same author, a translation of which will shortly 

 appear. 



t Phil. Mag. vol. ii. pp. 1, 102. 

 Phil. Mag. S. 4. Vol, 12. No. 77. Aug. 1856. G 



