158 
MR. MACQUORN RANK1NE ON THERMO-DYNAMICS. 
[Remarks .) — The existence of a necessary relation between the density, pressure, 
and temperature of a vapour and its liquid in contact, and the latent heat of evapo- 
ration, was first shown by Carnot. If for r—x in the preceding 1 equation be substi- 
tuted, according to Professor Thomson’s notation, -, J being “ Joule’s equivalent” 
and (Jj “ Carnot’s function,” the equation is transformed into that deduced by Messrs. 
Clausius and Thomson from the combination of Carnot’s theory with the law of the 
mechanical convertibility of heat. 
(38.) Corollary . — The volume occupied by unity of weight of vapour at saturation 
may be computed from its latent heat of evaporation by means of the inverse for- 
mula, — 
L 
(60.) 
the latent heat, L, being of course always stated in units of motive power. 
The want of satisfactory experiments on the density of vapours of any kind, has 
hitherto prevented the use of the direct formula (59.). 
It is otherwise, however, with the inverse formula (60.), at all events in the case of 
steam ; for, so far as we are yet able to judge, the experiments of M. Regnault have 
determined the latent heat of evaporation of water with accuracy throughout a long 
range of temperature. 
M. Clausius, applying to those experimental data a formula founded on the suppo- 
sition of Mayer (that is to say, similar to the above, with the exception that x is 
supposed =0), has calculated the densities of steam at certain temperatures, so as to 
show how much they exceed the densities calculated from the pressures and tempe- 
ratures, on the supposition that steam is a perfect gas. From these calculations he 
concludes, that either the supposition of Mayer is erroneous, or steam deviates very 
much, at high densities, from the condition of a perfect gas. 
In the following table, the value of x is supposed to be 2°T Centigrade ; and use 
has been made of the formula for calculating the pressure of steam and other vapours 
at saturation, first published in the Edinburgh New Philosophical Journal for July 
1849, viz. — 
logP=«-^-J. (61.) 
This table exhibits, side by side, the volume in cubic feet occupied by one pound 
avoirdupois of steam, at every twentieth Centigrade degree from — 20° to +260° 
(that is, from —4° to +500° Fahrenheit): — first, as extracted from a table for com- 
puting the power of steam-engines, in the Transactions of the Royal Society of Edin- 
burgh, vol. xx., which was calculated on the supposition that steam is a perfect gas ; 
and secondly, as computed by equation (60.) from the latent heat of steam as deter- 
mined by M. Regnault. The excess of the former quantity above the latter is also 
given in each case, with its ratio to the second value of the volume. 
