

Notices respecting New Books. 309 



of a portion of the system of which the entropy and absolute 

 temperature are and r. 



Assuming, however, the formula for a single mass, consider a 

 system of two masses m v m 2 of the same substance with entropies 

 (p v </> 2 and at absolute temperatures t x , r 2 respectively; and let 

 these masses be respectively expanded and compressed adiabati- 

 cally to the temperature r and then respectively compressed and 

 expanded isothermally to the pressure^: the system is now in 

 equilibrium, and, if r is taken such that no energy is lost or gained 

 by the system and that the heat lost by the one mass is equal 

 to that gained by the other, it is in that state of equilibrium 

 which the system would finally attain in isolation. If, then, (j> is 

 the final entropy of the system, the heats lost and gained are 

 m i 7 ( ( Pi~ ( P) an ^ W V (0~~02)> whence <f>=(m l (p 1 + 'm 2 <j) 2 ) /(m 1 + m 2 ), 

 which does not satisfy the proposed formula except for r x =r 2 or 



Entropy being thus considered a debatable subject, it is surpri- 

 sing to see it postulated in the Introduction as an evident property 

 of a substance and to find it treated as such without debate or 

 explanation till the last chapter. In Maxwell's opinion, " it is to be 

 feared that we shall have to be taught thermodynamics for several 

 generations before we can expect beginners to receive as axiomatic 

 the theory of entropy." 



The account given of thermodynamic motivity and dissipation of 

 energy is good and clear, and it is properly remarked that Clausius' 

 theorem of the tendency of the entropy of the universe to a maxi- 

 mum is only a restatement in terms of entropy of Lord Kelvin's 

 dissipation theorem published thirteen years earlier. 



Though the book, therefore, does not seem quite to fulfil the pro- 

 mise of the Preface, it will doubtless prove a useful mathematical 

 introduction to the subject, which it does not pretend to treat 

 experimentally, the few experiments that are referred to being- 

 mentioned only briefly and without detail. 



Its arrangement seems capable of improvement. Thus, it is not 

 broken up into articles and its equations are numbered consecu- 

 tively from first to last, so that references are tedious : the theorem 

 of the dependence on pressure of the temperature of the maximum 

 density of water is placed where it seems to be dependent on 

 thermodynamical considerations, while that of the equality of the 

 ratios of the principal specific heats and of the principal elasti- 

 cities is actually proved by such considerations, of which it is 

 absolutely independent — as is obvious, since it was known to 

 Laplace : and two general equations of very great importance, 

 (216) and (217), are deduced only incidentally to prove that the 

 principal specitie heats of superheated vapours are approximately 

 functions of temperature only. 



There is some looseness of expression: thus the word 'perfect 

 is used as equivalent to efficient, which leads to the solecisms 

 more perfect and equally perfect ; the dyne, centimetre, and erg are 

 called French units : the dynamical equivalent of heat is said to be 



