450 
Proceedings of the Royal Society 
1862 ; and it is also shown that by the formula a conclusion was 
anticipated, which M, Kegnault has deduced from his experiments, 
viz., that “ the elastic force of a vapour does not increase {ndefi7iitely 
with the temperature^ hut converges toioards a limit luhich it cannot 
exceedP (“ Relation des Experiences,” vol. ii. page 647.) 
The second division of the paper is occupied chiefly with a com- 
parison between the actual values of the pressures of saturation of 
the vapours of various fluids, and the values which those pressures 
would have if the vapours were perfectly gaseous. In the first of 
the papers already referred to, read to the Royal Society of Edin- 
burgh, and published in their Transactions in 1850, the author 
proved from the principles of thermodynamics that the ^Hotal heat'' 
of evaporation of a perfectly gaseous vapour must be represented in 
dynamical units by the expression 
J dt^ 
where 5 is a constant to be found by experiment, c the specific heat 
of the vapour at constant pressure, and J the dynamical equivalent 
of an unit of heat, t being the absolute temperature as before. In a 
paper read to the Royal Society of Edinburgh in 1855, but not pub- 
lished, the same formula was shown to express, in dynamical units, 
the total heat of gasefication of any substance under any constant 
pressure, when the final absolute temperature is t. In the present 
paper the author equates that expression to another expression for 
the total heat of evaporation, from the absolute zero, at a given 
absolute temperature t, as follows : — 
J/) -f- Jc't -- J r cdt + t ^ (v- v") ; 
0 
dt 
in which v and v" are the volumes of unity of weight of the sub- 
stance in the gaseous and liquid states respectively, under the 
pressure p, and at the absolute temperature t. Then putting for v 
its value in the perfectly gaseous state — namely, 
J(c' — c^t 
V = J 
p 
where c is the specific heat of the gas at constant volume, and ne- 
glecting V as very small in comparison with f, there is found, by in- 
tegration, the following value of the hyperbolic logarithm of the 
