210 
PROCEEDINGS OP SOCIETIES. 
G. Johnstone Stoney, A. M., read the following—• 
NOTES ON THE MOLECULAR CONSTITUTION OE MATTER. NO. I. 
The extraordinary power of the general method in Mechanics which we 
owe to the genins of Lagrange has tempted several mathematicians to 
try its strength in studying the unknown forces which enter into the 
molecular constitution of matter. In the applications of this method 
which have been hitherto made, as well as in other mathematical inves¬ 
tigations into molecular forces,*' the body under consideration has been 
supposed in its usual condition to consist of molecules:— 
1°. At rest— 
2°. Resembling one another, and similarly placed, each acting on its 
neighbours within a certain range— 
3°. By forces adequately represented by functions multiplying the 
masses of the attracted and attracting molecules— 
And which are such that the action on any one molecule may be repre¬ 
sented by integrals extended through the sphere of action. In order that 
these integrations may be legitimate, it is necessary— 
4°. That the sphere of action round each molecule include an immense 
number of other molecules, no one of which contributes more than an 
infinitesimal part to the total action on the central one; and— 
5°. That the contributions from any two consecutive molecules be 
almost undistinguishable either in direction or amount, f 
These hypotheses involve some remarkable results, the examination 
of which will enable us to limit the area of our search in prosecuting 
the study of molecular physics. 
1°. Conceive a medium of uniform density within a closed space, and 
possessing a constitution fulfilling the conditions required by these hy- 
* See Cauchy : “ Sur 1’ equilibre et le mouvement d’un Systeme de points materials 
sollicites par des forces d’ attraction ou de repulsion mutuelle.”—Conchy’s Exercises de 
Mathematiques , tom. iii., p. 202 ; and “De la Pression ou Tension dans un Systeme de 
points materiels.”— lb., p. 224. Navier : “ Sur les lois du mouvement des fluides.”— 
Memoires de VInstitute tom. vi., p. 389 ; and “Sur les lois de l’equilibre et du mouve¬ 
ment des corps solides elastiques.”— lb., tom. vii., p. 375. Poisson : “ Sur les equations 
generates de 1’equilibre et du mouvement des corps solides elastiques et des fluides.”— 
Journal de VEcole Polytechnique, Cahier xx., p. 1. Hacghton : “ On the Equilibrium 
and Motion of Solid and Fluid Bodies.”— Trans. Royal Irish Academy , vol. xxi., part 2. 
Jellett : “ On the Equilibrium and Motion of an Elastic Solid.”— lb., vol. xii., part 3. 
f The last two hypotheses, which must be insisted on if the method of integration be 
adopted, exclude many continuous functions; thus, using F to denote the mutual action 
of two molecules, and r for the interval between them, if the law of force be such that 
r 2 F becomes infinite for r — 0, the central elements of the integral will contribute unduly 
to it, so that such a value as— 
F= ^{ 1 ~ A Al7^ &c }’ 
where y is the coefficient of gravity, A , B, &c., constants, and a a line of fixed length, 
is not admissible if the method of integration be retained; yet this law, and others like 
it, would, it is evident, lead to several of the most obvious properties of matter. 
