90 Prof. Challis on a Theory of Molecular Forces. 
To these preliminary remarks I beg to add the expression of 
my conviction, that theoretical physics can advance only in such 
a course as that above indicated, and that progress will be made 
in proportion as the difficulties which attend the application of 
partial differential equations to physical questions are overcome. 
I do not consider the following theory to be free from such 
difficulties. 
1. It is an evident consequence of the hypothesis that sub- 
stances consist of discrete atoms, that neighbouring atoms are 
mutually repellent, for they could not otherwise remain i posi- 
tions of equilibrium. This action is the repulsion of heat. It 
will not be necessary to show here in what manner such repul- 
sion results from the dynamical action of undulations of the 
eether, because I have discussed this question in the Mathema- 
tical Theory of Heat contained in the Philosophical Magazine for 
March 1859, and at present I have nothing better to offer on 
this part of the subject. There are, however, some mathematical 
considerations, relating equally to repulsive and attractive action, 
which may now be appropriately introduced. 
In an article on Attractive Forces, contained in the Philoso- 
phical Magazine for last November, I have investigated the pres- 
sure at any point of the surface of a given atom, due to the 
incidence of a given series of waves, on the assumption that, for 
the case in which the excursions of the particles of the ether are 
large compared to the diameter of the atom, the velocity V along 
the surface of the hemisphere on which the waves are incident is 
W sin @, and along the surface of the other hemisphere, 
W sind—q. oe sin 8 cos @. 
In this expression, W is put for m sin (2ze + e), the velocity 
of the etherial particles ; 6 is the angle which the radius to the 
point considered makes with the radius drawn in the direction 
contrary to that of incidence ; and gis a certain constant. These 
values of the velocity were deduced in the Philosophical Maga- 
zine for December, from a particular solution of the general par- 
tial differential equation to terms of the first order, of which P, 
or Nap. log p, is the principal variable, viz. 
Gre een i i el ae 
de" Naat + aye + ae) 
The following is a more general value of V satisfying the same 
solution : 
V=Wsin 0+ (uw—qo* ) sin @ cos 0; 
