OF THE PARAFFraS AND THEIR MONOHALOGEN DERIVATIVES. 
5 
Hence, neglecting the square of Ifp . dpvjdv, we have 
([') d-pvidv) .(2). 
Equation (1) is quite general, but the assumption that 1/p . dpvjdv is small, limits 
(2) to gases. 
To find the value of the last factor, I have determined experimentally the vapour 
densities of the gases at various pressures, and plotted a curve connecting pin and v, 
the slope of which, at any point, gives the value of dpvjdv at that point. 
It is, of course, of no consequence what units are used, as the dimensions of 
Ijp . dpvjdv are those of a number. 
The formula can be put in various forms, but that given above seems to lead most 
directly to the required result. It is not, however, easy to determine the correction 
very accurately, for the variation of pv is not rapid, and a small error in the density 
observations, or in the drawing of the curve, may make a considerable change in the 
slope of the curve. For most of the gases that I have used, the correction is from 
one to two per cent, of the whole value of y. 
WuLLNER, Strecker, and others used the uncorrected formula, and, though they 
worked on gases with low boiling j^oints, their results would be quite appreciably 
raised by the correction. 
If there is any impurity present in the gas, p wiU be the specific gravity of the 
mixture. In the case of Marsh Gas and Ethane, this was got by calculation from the 
analysis of the gas, and in the case of the rest of the compounds by direct 
experiment. 
The result is the ratio of the specific heats of the mixture, and requires a further 
correction if the y of the impurity is not the same as that of the gas under 
investigation. 
A formula for effecting this may be obtained in the following way, the gas being- 
assumed perfect as the correction is small :— 
Let 
T = the total kinetic energy of translation of all the molecules in unit mass of 
the gas. 
T^, T 2 , &c,, the same for each of the components. 
P, the pressure of the mixture. 
Pi, P 2 , &c., the partial pressures of the components. 
8T, the increment of T ; for a rise of temperature, Sd. 
y8ST, the increment of the internal energy of the molecules; for a rise of tem¬ 
perature, h6. 
Cp, the specific heat of the mixture at constant pressure. 
C„, „ „ „ ,, „ volume. 
