174 



become condensed. Hence the abstraction of the heat, 

 ~Y-pdv produces two effects; it cools the mass of air at con- 

 stant volume from temperature t to temperature t+df, and it 



condenses a bulk 



ds 



— dv 



of vapour. Hence, if L denote the latent heat of a cubic 

 foot of vapour of water at temperature f, and N the specific 

 heat of one pound of air in constant volume, we have 



1 ds 



^pdv=z'^X{—di)+L(v—~~dv,) 

 J \ s / 



if we suppose the mass of air considered to weigh 1 lb. (with 



or without the vapour, which will make but little difference 



on the whole weight). Hence 



dlog s 



JN + JLv — 



dv — dt 



— dt i? + JL 



ds 

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



s 



denoting the Napierian logarithm of s. 



d logs . 

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



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

 the Author demonstrated,* by experiments on air and by 

 dynamical reasoning, that 



3 dp /^ X 

 7 

 where p denotes the pressure of vapour at saturation at the 



temperature t, and — denotes the rate of the bulk of liquid 



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



approximately. 



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

 tions, Section II., Traasactions of the Epya} Society, Jime, 1851. 





