410 Mr. J.J. Waterston on a Law of Liquid Expansion 
generating liquids, to the molecular condition of the liquids, where 
the dynamic condition of the chemical element is constrained by 
the cohesive force; and the struggle in which this dynamic force 
is gradually subdued by the increase of temperature is, as now 
ascertained, represented by one quantitative relation throughout, 
that seems to indicate a certain simplicity in the ultimate recon- 
dite principle on which molecular force is based. 
We know that the physics of gases conform to the physics of 
media that consist of perfectly free elastic projectiles*. Their 
free concourse and perfectly elastic recoil determines the resolu- 
tion of their vis viva into the six rectangular directions of space ; 
and it is this number that probably fixes the ratio of the propor- 
tionate increment of density in a saturated vapour to the corre- 
sponding proportionate increment of temperature reckoned from 
the fixed limit g. But the absolute increment of density corre- 
sponding to constant increment of temperature differs in different 
vapours, being ruled by a gradient, the sixth root of which has a 
constant ratio to the index of density of the generating liquid 
expressed as a function of the temperature. 
The next step that seems within reach, if we had a few more 
observations to work from, is the discovery of the relation which 
no doubt exists between the increase of volume and decrease of 
latent heat or capillarity regarded as the integral of cohesion. 
The density and the capillarity both diminish as the temperature 
rises. (See Note H.) If there is a simple law of quantitative rela- 
tion between them, its discovery would supply all that is now 
wanting to bring the dynamical theory of heat to bear upon the 
molecular physics of liquids. 
Notes. 
Note A. § 1.—The title of the paper is ‘‘On a General Law of 
Density in Saturated Vapours,”’ illustrated by Chart No. 2. Inthe 
Philosophical Transactions for 1852 there is a paper with the same 
title, illustrated by a Chart No.1. (This paper was originally sent to 
the British Association.) In Chart No. 1 the sixth root of density 
is laid off as ordinate to the square root of the temperature reckoned 
from the zero of gaseous tension. In Chart No. 2 the sixth root of 
density is laid off as ordinate to the temperatures simply. In Chart 
No. ] the lines appear straight at the upper part of their course, but 
with an increasing flexure at the lower part of the range convex to 
axis of temperature. Also there is no relation of harmony apparent 
betweenthem. In No. 2 Chart (of which a tracing is to be found in 
the archives of the Royal Society for 1852-53) the lines are straight 
* See paper “On the Physics of Media that consist of perfectly elastic 
ery in a state of Motion,” in the archives of the Royal Society, 
