174 
become condensed. Hence the abstraction of the heat, 
-i- pdv produces two effects ; it cools the mass of air at con- 
stant volume from temperature t to temperature t+dt, and it 
condenses a bulk 
5 
of vapour, Ifence, if L denote the latent heat of a cubic 
foot of vapour of water at temperature t, and N the specific 
heat of one pound of air in constant volume, we have 
1 fjo 
~pdv = N X (— dl)+L (v——dv,) 
J ^ s l 
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 
d loq s 
JN + JL v — — — 
dv __ — dt 
— dt P 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 
d logs 
— dt 
* 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 
t dt\ 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 = — 
1 7 J ’ t dt 
approximately. 
* On the Thermal Effects of Fluids in Motion, Part II., Theoretical Deduc- 
tions, Section II., Transactions of the Koyal Society, Juno, 1851. 
