M. Poisson on the Caloric of Gases and Vapours. S29 



of jy, f>, and fi ; or, because those variables are connected by 

 the preceding equation, simply a function of /» and p. Thus 

 we shall have qz=J'(^p, p) ; 



f being a function whose form it will be required to deter- 

 mine. 



The specific heat of this gramme of gas is the quantity which 

 must be communicated to it to raise its temperature 9 one de- 

 gree ; and it will be very nearly -— ^ But we may consider 



this specific heat under two different points of view, — first, in 

 allowing the gas to dilate under an invariable pressure, — and 

 secondly, in keeping the volume constant whilst the tempera- 

 ture and pressure augment together. Hence we shall have in 

 virtue of the first equation 



df «j dp a;) 



d( ~~ l+a^'f71~~ r+ a. 6 



It results, therefore, if we put c for the specific caloric when the 

 pressure is constant, and c^ when the volume is constant, that 

 c =^- ~1 "g 1 



'' dp \ -J^ a. 6 J 



whicli, if we put - = hi give 



It is evident, a priori, that this ratio k ought always to ex- 

 ceed unity ; for the heat must necessarily be greater to raise 

 the temperature a certain quantity when the gas dilates, than 

 when the density is invariable. Experiment however is the 

 only way of obtaining the value of A-, and of discovering to us 

 in what manner it depends o\\ p and p. Following the expe- 

 riments of MM. Gay-Lussac and Welter, cited in the Meca- 

 jiique Celeste, book 12. p. 97, this quantity is sensibly constant 

 for the same gas ; and for dry atmospheric air its value is 

 k=\'31n. Now supposing k independent ofy; and p, the in- 

 tegral of equation (3) is 



♦ This is a very simple case of the integration of partial clifTcrcntials. 



Eiiniinatinff — in the course of integration instead of -— would have 

 rf f dp 



\fhich is rather closer to the subject and somewhat more easily obtained 

 than M. Poisson's, though in other respects virtually the same. — J- H. 

 Vol. G2. No. 307. Nov. 1823. T l' ./Ix^i^g 



