Elastic Force, Density, and Temperature in Gases. 55 



Mr. Joule*, Professor TV. Thomson, and myself f have all found 

 a certain but small change of temperature ; and I have also, in 

 the paper to which the present is a sequel, investigated the law 

 of the change, which, I believe, is the true law for the instanta- 

 neous result. 



This law is as follows : — 



Let v be the volume of a gas when the pressure is p and the 

 density p } 

 ri be the volume of a gas when the pressure is p' and the 

 density p 1 



after an expansion ; and since the mass is the same, we have 

 v .p^v 1 . p'. 

 Also let S be the rarefaction or negative condensation ; and 

 since the change of temperature is small, we have by Boyle's law, 



p = icp, p' = fcp'' f 

 then 



P' 



- p' 



and it was found by the experiments that if co L was the number 

 of Fahrenheit's degrees through which the temperature fell for 

 an expansion unity or for 8 = 1, and co the degrees it fell for an 

 expansion 8, then 



a) /8\ 3 



or 



co = co x . h s ; 



and the experiments gave the value of the constant, 



Wl =0°-2077. 



From this formula the ratio of the specific heats was deduced 

 to be 



specific heat of air under a constant pressure _ c 

 specific heat of air with a constant volume '"" d 



+ 2359(1 +ad)' 



where a= 73^, and 6= degrees of Fahrenheit's scale above the 



freezing temperature. 



In the paper to which the present is a sequel, I stated that I 



* Phil. Trans, for 1853, and Phil. Mag. for September 1853, p. 230. 

 t Phil. Mag, for September 1853, p. 161. 



