OF GASES AT CONSTANT VOLUME. 
979 
still lower ; the line for 78° to 100° beino’ lowest. At low densities all these lines 
tend to converge, as if the specific heat was then nnafiected by the difference of 
range. 
As liquid is present at p = 0'124 from 6° to 8° C., it is to be concluded that in the 
neighbourhood of these temperatures most of the fall between 6°’39 and 35° is 
accomplished. We can refer to Part II. for a point about 16° C. The full curve 
of the diagram, Part II., gives the specific heat at this density, and knowing the weight 
(11'0416 grms.) affording this density we calculate zs and so get the point marked 
j2ll • This is a very reliable point, and as will be seen it carries back with uniformity 
the course of the line at the upper temperatures. 
The line for p = 0d24 is given by the following equation ;— 
zT~a (100 (100 — (100 - tf, 
where a = 0-003915 ; h = — 0-00000139 ; c = 0-0000000375. 
If these numbers are multiplied by the latent heat of steam and divided by W, 
i.e. by 536-5/11-042 = 48-56, we get, by differentiating with respect to an equation 
for the specific heat in terms of temperature at the density 0-124 ;— 
Cb = a + 26 (100 — 0 + 3c (100 - tf. 
where 
a= 0-19020000, 
h = - 0-00006750, 
c= 0-00000182. 
Th is, of course, is plotted, virtually, by the inclination of the curve upon the plate, 
the ordinates all being supposed as lengthened in the ratio 1 to 48-56. 
The line above this, p = 0-1800, shows a rapid upward curvature below 35°; liquid 
in fact was present up to 18°-5. Nothing being accurately known as to the specific 
heat of the saturated vapour, we cannot safely assume anything as to the course cf 
events between the 13° and 35° points. A theoretical point obtained from the curve 
of Part II., at the initial temperature 15°, lies on the prolongation of the experiments 
at the upper temperature. It is not, however, marked upon the dotted line, as it 
cannot be relied upon, except it be sho\vn that the variation with temperature of the 
specific heat of the saturated vapour is at the same rate as that of the superheated 
vapour. 
The following equation, of similar form to the last, gives the inclination of this line 
with fair accuracy :— 
a = 0-2056 - 2 X 0-0000819 (100 — t) + S X 0-00000133 (100 - tf. 
The specific heat is directly given by this for the density 0-180. 
6 I 2 
