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VI. On a General Law of Density in Saturated Vapours. By J. J. Waterston, Vsq. 
Communicated by Lieut. -Col. Sabine, V.P. and Treas. 
Received June 19, 1851,— Read June 19, 1851. 
The relation between the pressure and temperature of vapours in contact with their 
generating liquids has been expressed by a variety of empirical formulae, which, 
although convenient for practical purposes, do not claim to represent any general 
law. Some years ago, while examining a mathematical theory of gases, I endeavoured 
to find out from the French Academy’s experiments, if the density of steam in con- 
tact with water followed any distinct law with reference to the temperature measured 
from the zero of gaseous tension. [By Rudberg’s experiments, confirmed by Magnus 
and Regnault, this zero is —461° in Fahr. scale, or — 273°'89 in the Centigrade 
scale. Temperatures reckoned from this zero I shall call G temperatures to save 
circumlocution?^ If t represents the G temperature, A the density of a gas or a 
vapour, and p its elastic force, the equation 
( 1 -) 
represents the well-known laws of Marriotte and of Dalton and Gay-Lussac. The 
function that expresses a general relation between p and t in vapours must include a 
more simple function, expressing a general relation between A and t. The proper 
course, therefore, seemed to be to tabulate the quotients ^ from the experiments of 
the Academy and to project them into a curve. Now, for reasons connected with 
the vis viva theory of gases, which represents the G temperature as a square quantity, 
I projected these densities as ordinates to the square root of the G temperatures as 
abscissw, and the curve traced out was of the parabolic kind, but of high power. 
To reduce this, because density is a cubic quantity, I tabulated their cube roots and 
set them off as ordinates to the same abscissae. The result was gratifying, for the 
familiar conic parabola made its appearance. To ascertain whether this curve was 
exactly the conic parabola, I tabulated the square root of these ordinates, correspond- 
ing with the sixth root of the densities, and laid them off as new ordinates to the 
same abscissie. The result is shown in the accompanying Chart, Plate VII., under 
the title French Academy's Steam. The observations are denoted by dots thus ®, and 
it will be remarked that they range with great precision in a straight line, any slight 
divergence being sometimes to the right and sometimes to the left ; precisely as 
might be expected from small errors of observation. Other series of experiments 
on steam were projected in a similar manner ; and it was found that although no two 
exactly agreed with each other, yet that each set ranged in a straight line nearly. 
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