concerning the Specific Heat of Gases. 459 



friends, and Professor Price pointed out to me a note in Janiin's 

 Cours de Physique, which appeared at first sight to assert the 

 equality of the two kinds of specific heat. The probable expla- 

 nation of it (vide infra) was suggested to me by Professor H. 

 Smith and Sir B. Brodie. 



At p. 491, vol. ii. of Jamin's book, there is a note on the ve- 

 locity of sound. If Y be the velocity calculated on the suppo- 

 sition that pressure is proportional to density, V a/1 + 6 the true 

 velocity, c the specific heat (or "capacity" as it is here called) 

 at constant pressure, and d at constant volume, the ordinary 

 theory accepts the equation 



1+0= ^T- 

 c 



In the note referred to, Jamin objects to this equation on the 

 ground that the old proof of it involved the assumption that the 

 temperature of a gas is lowered by free expansion. After de- 

 scribing the process which he considers to imply this error, he 

 says, — 



" Mais ce raisonnement est inexact. Quand un gaz se dilate, 



il est vrai qu' habituellement il se refroidit, mais c'est parce qu'il 



produit du travail, et s ; il arrive qu'on le dilate en le faisant 



penetrer dans un vase vide, il ne change plus de temperature 



(page 435). Les deux capacites sont done necessairement egales 



entre elles. Par consequent, ^equation (/3) est vraie, mais elle 



c 

 devient fausse si Pon y remplace 1 + 6 par — ." 



(The equation (J3) is velocity =V \/l + 6.) 



This note is objectionable in several respects. In the first 

 place, it is not a safe conclusion that a result is false because it 

 has been obtained by fallacious reasoning. Secondly, although 

 the reasoning objected to probably did contain, in the minds of 

 its first authors, the fallacy attributed to it, it is capable of being 

 so interpreted as not to contain it, Thirdly, the modern mecha- 

 nical theory of heat supplies a demonstration* of the equation 



* Let p, V, p, t, h be the pressure, volume, density, temperature, and 

 actual beat of a unit of mass of gas. Let E=AA be the energy which 



dh 

 would have to be spent in communicating the actual heat h, and let c'= -37 



be the real specific heat (or specific heat at constant volume), and c the 

 specific heat at constant pressure. Then assuming that pW=a+cct, we 

 shall have 



pdV+Vdp=ctdt (1) 



Suppose the gas to be compressed to volume V+c?V (d\ being negative), 

 then dp, dt being the increments of pressure and temperature, the incre- 

 ment of actual heat is c'dt, and the corresponding energy is Ac'dt. Now 



2H2 



