303 Notices respecting New Books. 



forms of the thermodynamic relations, each of which is patent on a 

 glance at the corresponding infinitesimal cycle. 



In his investigation of these general expressions, the author 

 prefers not to avail himself directly of the fact that infinitesimal 

 changes of entropy and intrinsic energy are perfect differentials, 

 and so, according to Lord Kelvin's simple plan, to apply the corre- 

 sponding criteria forthwith, this method savouring of mathematics 

 only : he follows Clausius' original lead instead, without, however, 

 Clausius' elaboration, and, taking an infinitesimal cycle composed 

 of two pairs of thermal lines of any different types, he sums up the 

 heat absorbed all round the cycle and also the changes of entropy, 

 and equates the former sum to the area of the cycle and the latter 

 to zero, this lengthier process being chosen as being of a more 

 distinctly physical character than the other. In the second of 

 these calculations the criterion of a perfect differential is of course 

 necessarily arrived at, since the process of determining the cri- 

 terion is essentially that of the method pursued ; attention might 

 therefore with advantage have been called to the mathematical 

 character of this resulting equation, more especially as after 

 reading Chap. XV., wherein is given Lord Kelvin's method, a 

 student will not be likely to have recourse to the other. Advan- 

 tageous, too, would be the omission in this calculation of the signs 

 of integration, which are finally discarded as quite unnecessary 

 and are not even introduced into the other calculation on p. 42. 



With respect to irreversibility, it is pointed out that there may 

 be processes which, though not actually reversible, are, so far as the 

 working substance is concerned, in one direction equivalent to pro- 

 cesses that are reversible, in which case the changes of entropy 

 that occur in the working substance itself during such processes 

 (termed conditionally irreversible, in contradistinction to intrinsi- 

 cally irreversible processes which have no such equivalents) depend 

 only on its initial and final states. But we are not really helped 

 by these considerations — which are not new — since it is the actual 

 sources &c. and the actual variations of entropy with which we 

 are really concerned. 



The proposed enlargement of the definition of entropy which is 

 to help with the treatment of irreversibility greatly needs defence. 

 It is ushered in with an objection to the definition of the entropy 

 of a body or system as the sum of the entropies of its parts, 

 " which seems to me as unwarrantable as to define the temperature 

 of a body or system as the sum of the temperatures of its parts" so 

 that to speak of entropy per unit mass " seems to me as un- 

 warrantable as to speak of temperature per unit mass " ; though no 

 reason whatever is given or even hinted for likening entropy to 

 temperature rather than to such another physical property as 

 energy or volume. Such a definition of entropy is then desired 

 as will make the entropy of any system whatever invariable when 

 no heat passes into or out of it ; and the author considers that he 

 has obtained such a definition — which satisfies also his previous 

 objection — in the formula 2 . rmy/X . rm, where m is the mass 





