OF TEMPERATURE IN THE ATMOSPHERE. 129 



(with or without the vapour, which will make but little 

 difference on the whole weight). Hence 



JN + JL?; 



dlog s 



dv _ —dt 



^dt~~ /> + JL 



ds 

 where, for brevity, d log s is written in place of — , log s 



s 



denoting the Napierian logarithm of s. 



To find L and - — ^ , it is necessary to know the bulk 



of a pound of steam at different temperatures. Dr. Joule 

 and I have demonstrated "^^ by experiments on air and by 

 dynamical reasoning, that 



t dt\ 7/ 



7> 

 where p denotes the pressure of vapour at saturation at the 



temperature tj and - denotes the ratio of the bulk of liquid 



to vapour. Since - is very small, we have L=--^ 



approximately. 



It was shown also in the same Paper, that the density of 

 saturated vapour was to be obtained more accurately from 

 this equation, and Regnault's experiments on the latent 



or, since JN = -t- . _ (by an elementary thermodynamic formula for a 



perfect gas), 



dv _ I y— <^^ 

 V k—\ t ' 



whence, by integration, _=ir _ j 



This expresses the elevation of temperature experienced by a perfect gas 

 when compressed and not allowed to part with heat. 



* On the Thermal Effects of Fluids in Motion, Part II., Theoretical De- 

 ductions, Section II., Transactions of the Royal Society, June 1854. 



SER. III. VOL. II. K 



