346 
MR. J. P .JOULE AND PROFESSOR THOMSON ON THE 
Hence 
!«• [cr] 1 — <7 
H — * ’ i-M’ 
or, approximately, since a and [<r] are small fractions, 
p __ M 
l>] ^ ’ 
We have, therefore, 
[W] . 
[<r] — 1390’ 
and we infer that the densities of saturated steam in reality beat the same propor- 
tions to the densities assumed, according to the gaseous laws, as the numbers shown 
for different temperatures in the preceding Table bear to 1390. Thus we see that 
the assumed density must have been very nearly correct, about 30° Cent., but that 
the true density increases much more at the high temperatures and pressures than 
according to the gaseous laws, and consequently that steam appears to deviate from 
Boyle’s law in the same direction as carbonic acid, but to a much greater amount, 
which in fact it must do unless its coefficient of expansion is very much less, instead 
of being, as it probably is, somewhat greater than for air. Also, we infer that the 
specific gravity of steam at 100° Cent., instead of being only as was assumed, 
or about as it is generally supposed to be, must be as great as — Without 
using the preceding Table, we may determine the absolute density of saturated steam 
by means of a formula obtained as follows. Since we have seen the true value of W 
is nearly 1390, we must have, very approximately. 
1390E 
^“T+Ep 
and hence, according to the preceding expression for p in terms of the properties of 
steam, 
1 I T?_/\ ^ ^P 
^“I390e( 1 + E *)a£»’ 
or, within the degree of approximation to which we are going (omitting as we do 
fractions such as ^ of the quantity evaluated), 
(1 +E^) dp 
1390E.X dP 
an equation by which g><r, the mass of a cubic foot of steam in fraction of a pound, or r, 
its specific gravity (the value of £ being 63*887), may be calculated from observations 
such as those of Regnault on steam. Thus, using Mr. Rankine’s empirical formula 
for the pressure which represents M. Regnault’s observations correctly at all tem- 
peratures, and M. Regnault’s own formula for the latent heat ; and taking E= 
273 
we have 
e*= 
273 +/ 
1390 
^ ( (274-6 + o 2 + (274-e y + ^) 3 ) x ‘ 4342945 
(606-5 + 0-305 1) - (t + -00002* 2 + -00000032 3 )’ 
