CONTINUOUS ELECTRIC CALORIMETRY. 
147 
not constant, but increases at higher temperatures, on account of the co-aggregation 
of the molecules, as represented by the increase of the product cp , where j) is the 
saturation-pressure. 
Similarly, we might suppose that the rate of variation of the total heat h of the 
liquid would be constant for ideal water, hut increases at higher temperatures for 
actual water on account of the existence of molecules of vapour in the liquid. The 
two phases in equilibrium at saturation-pressure may be regarded as a saturated 
solution of water in steam (the dissolved water being represented by the proportion 
of co-aggregated molecules cp/^XO), the liquid phase conversely as a saturated solution 
of steam in water. On the one hand, the total heat of the steam is reduced below 
its ideal value by the amount (n +1) cp, owing to the presence of dissolved molecules 
of water causing a diminution of volume c per unit mass of the solution ; on the other 
hand, the total heat of the liquid is increased by the presence of a certain proportion 
of dissolved molecules of steam, which may doubtless account for part of the thermal 
expansion of the liquid. When the temperature is raised, the properties of the two 
phases continue to approach each other, as the proportion of water in the steam and 
of steam in the water increases At the critical temperature the two solutions mix 
in all proportions. 
It is possible to estimate more or less perfectly the number of co-aggregated 
molecules present in steam at any temperature by observing the defect of volume 
from the ideal state ; or to deduce the value theoretically on certain assumptions 
from experiments by the Jotjle-Thomson method on the cooling effect of expansion 
through a porous plug or throttling aperture (‘ Roy. Soc. Proc.,’ 1900, vol. 67, p. 270). 
It is probable that the proportion of steam molecules present in the liquid is similarly 
related to its expansion, but there is no certain theoretical guide to the relation. 
The simplest hypothesis to make would be that the number of vapour molecules per 
unit volume of the liquid is the same as the number of molecules per unit volume of 
the saturated vapour at the same temperature. If we suppose the formation of 
vapour molecules in the interior of the liquid (specific volume w) to require the 
addition to the liquid of the latent heat corresponding to the same quantity of 
vapour (specific volume v) when formed outside the liquid (i.e., if we neglect the 
heat of solution of the vapour in the liquid), the total heat h of the liquid would 
require to be increased by an amount iv/(v — iv) of L to allow for the latent heat of 
the dissolved steam. It happens that this result, though obtained by a quite different 
line of reasoning, agrees with the expression given by Gray, and approximately 
represents the experiments of Regnault at high temperatures. We thus obtain the 
simple formula, 
h — s () t -f wL/{y — iv) .(16). 
On similar grounds it would be natural to suppose that the increase of the specific 
heat, as we approach the freezing-point, was due to the presence of a certain 
u 2 
