AND ITS CONNECTION WITH THE THEORY OF HEAT. 427 
as the heat is less; but their sum, so far as elasticity of volume is concerned, is a 
function of the density only. 
That is to say, as in equation (12) of my paper on the laws of the elasticity of 
solids (Cambridge and Dublin Mathematical Journal, February 1851), let the total 
coefficient of elasticity of volume be denoted thus 
= Ith (Cy Cn G,) oa ee a (1) 
C,, C,, C,, being the coefficients of rigidity round the three axes of elasticity, and 
J a coefficient of fluid elasticity ; then 
; i a 
Fg Vee 
. 
: 
| 
i (1 C.) 
$ Cp Cn 0,) =- (1-40, ) ays) 
Vie 








For the present, we have to take into consideration that portion only of the 
expansive pressure which depends on density and heat jointly, and is the means 
_ of mutually converting heat and expansive power ; that is to say, the pressure at 
the boundaries of the atomic atmospheres; which I shall denote by 
p=F (V, Q) 
Pressures, throughout this paper, are supposed to be measured by units of 
weight upon unity of area; densities, by the weight of unity of volume. 
(3.) Determination of the External Pressure of an Atomic Atmosphere.—Let a 
body be composed of equal and similar atomic nuclei, arranged in any symmetrical 
- manner, and enveloped by an atmosphere, the parts of which are subject to attrac- 
tive and repulsive forces, exercised by each other, and by the nuclei. Let it further 
__ besupposed, that this atmosphere, at each point, has an elastic pressure proportional 
to the density at that point, multiplied by a specific coefficient depending on the 
nature of the substance, which I shali denote by 4. (This coefficient was denoted 
_ by 6 in previous papers). 
Let ¢ and p’ denote the density and pressure of the atomic atmosphere at any 
point ; then 
p=he 
® d® d® 
PT da) dg” eee 
of the molecular attractions and repulsions, which I have made explicitly negative, 
attractions being supposed to predominate. The property of the surfaces called 
_ the boundaries of the atoms is this 
d@ do de® 
(7) = (7), = Ge), = 
