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LXIX. On Clansius' Theorem for Irreversible Cycles, and on 

 the Increase of Entropy. By Prof. W. McF. Orr, M, A .* 



1. T7R0M the remarks with which Professor Planck, in 

 JO the January number of this Magazine, and in 

 private communications, has honoured my paper which ap- 

 peared in that of October, I conclude that on the points to 

 which he refers, although there has been a little mutual 

 misconception, there is in reality not much difference between 

 our views : this conclusion affords me much pleasure. 



I quite agree with Prof. Planck that his definition of re- 

 versibility has a practical bearing; it appeared necessary, 

 however, for me to point out that he uses the term in a 

 different sense from the other writers whom I ventured to 

 criticise, as of course the meaning of Clausius' Theorem for 

 Irreversible Cycles and its mode of proof must to some extent 

 depend on the meaning of the word ** Irreversible." 



My statement that Prof. Planck gives one definition of 

 " reversibility " but uses another was based on a slight mis- 

 conception which I regret. I understood him to state f that 

 the change from one state (A) to another (B) is reversible if, 

 and only if, it is possible starting from B to obtain A, and 

 leave all the materials and machines used in the same con- 

 dition exactly (at A) as before their application {at B). I have 

 since learnt from him, however, that the words here italicized 

 should be replaced by u as when the system was in the state A 

 in the first instance" This being so, my accusation must be 

 withdrawn; and Prof. Planck's argument does not seem open 

 to any serious objection on the ground of logic. 1 must 

 confess, however, that I have found it just a little obscure : 

 for instance, in § 124 and elsewhere it seems necessary to 

 imply an appeal to the First Law in order to show that the 

 change considered would really be completely reversed. 



In contesting my statement that " Under ordinary circum- 

 stances, however, no body can expand without producing a 

 change of density in some other body," Prof. Planck has not 

 attached sufficient importance to the words " under ordinary 

 circumstances/' which I used designedly. 



I note with gratification that Prof. Planck agrees that in 

 some cases of violent motion of a gas the usual definition of 

 Entropy is inapplicable : I had drawn the contrary conclusion 

 from his book. I should like, however, to see him go so far as 

 to admit that this definition applies only to equilibrium states. 



* Communicated by the Author. 



t Vorlesungen iiber Thermodynamic ; or Ogg's translation, Arts. 109, 



