284 PROFESSOR WILLIAM THOMSON ON THE 
Equation (14) will consequently become 
Ep P 
an %{ ae 5 | . 
= ees Sst 
a result peculiar to the dynamical theory; and equation (16), 
(25), 
which agrees with the result of § 53 of my former paper. 
If V be taken to denote the volume of the gas at the temperature 0°, under 
unity of pressure, (25) becomes 
iE? V 
Kl ake) 
(26). 
52. All the conclusions obtained by Ciaustus, with reference to air or gases, 
are obtained immediately from these equations, by taking 
E 
peri Ta 
which will make 2! =0, and by assuming, as he does, that N, thus found to be 
independent of the density of the gas, is also independent of its temperature. 
53. As a last application of the two fundamental equations of the theory, let 
the medium, with reference to which M and N are defined, consist of a weight 
1—« of a certain substance in one state, and a weight x in another state at 
the same temperature, containing more latent heat. To avoid circumlocution 
and to fix the ideas, in what follows, we may suppose the former state to be 
liquid, and the latter gaseous; but the investigation, as will be seen, is equally 
applicable to the case of a solid in contact with the same substance in the liquid 
or gaseous form. 
54. The volume and temperature of the whole medium being, as before, de- 
noted respectively by v and ¢; we shall have 
A (l-2)+y2%=v : : 3 ‘ ] (27), 
if \ and ¥ be the volumes of unity of weight of the substance in the liquid and 
the gaseous states respectively; and p, the pressure, may be considered as a_ 
function of 7, depending solely on the nature of the substance. To express M and 
N for this mixed medium, let L denote the latent heat of a unit of weight of the 
vapour ; ¢ the specific heat of the liquid; and / the specific heat of the vapour 
when kept in a state of saturation. We shall have 
dx 
Mdv=L Fe dv 
! 
Ndt=c(1—«)dt+h rdt+LS at. 

