37 
These are the more important points I have been enabled to make 
out regarding this genus as established by Forbes, and, taking into con- 
sideration the close approximation, almost amounting to identity in form, 
which exists between these and the Sertularia, their mode of growth, as 
far as we can judge, and place of occurrence, being so similar,—so much 
so that a superficial examination would lead one to pronounce them iden- 
tical,—I think we are justified in considering these rather Sertularian 
Polypidoms than Polyzoan Czenecia,—a view of the genus which, I am 
convinced, further research among living forms will eventually prove 
to be the correct one. 
G. Jounstone Stoney, A. M., read the following— 
NOTES ON THE MOLECULAR CONSTITUTION OF MATTER. NO, I. 
Tue extraordinary power of the general method in Mechanics which we 
owe to the genius 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. 
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. 
* See Caucuy: “ Sur l’ équilibre et le mouvement d’un systéme de points matériels 
sollicités par des forces d’ attraction ou de repulsion mutuelle.”—Cauchy’s Exercises de 
Mathematiques, tom. iii., p. 202; and “De la Pression ou Tension dans un Systéme de 
points materiels."—7., p. 224. Naver: “‘ Sur les lois du mouvement des fluides.”— 
Memoires de ? Institut, tom. vi., p. 389; and ‘Sur les lois de l’équilibre et du mouve- 
ment des corps solides élastiques.”—J0., tom. vii., p. 375. Porsson: “‘ Sur les équations 
générales de l’équilibre et du mouvement des corps solides élastiques et des fluides.”— 
Journal de V Ecole Polytechnique, Cahier xx., p. 1. Haueuton: “ On the Equilibrium 
and Motion of Solid and Fluid Bodies.”—Trans. Royal Irish Academy, vol. xxi., part 2. 
JevLErT: “On the Equilibrium and Motion of an Elastic Solid.’”’—J0., vol. xxii., part 3. 
+ The last two hypotheses, which must be insisted on if the method of integration be 
