Prof. Challis on a Theory of Molecular Forces. 91 
or, differently expressed, 
V=msin 6 sin (2 +e) +my sin 6 cos 6 sin (725 ), 
p and q, and by consequence vy, being in general functions of m 
as well as X, and depending also on the magnitude of the atom. 
If the last expression be applied to the velocity along the first 
hemispherical surface, y=0, the velocity impressed by the waves 
incident on that surface being Wsin@. For waves having large 
values of X and large excursions of the particles, such as those 
which came under consideration in the Theory of Gravity, the 
factor 4=0, because, on account of the small size of the atom, 
there is no sensible difference between the velocities along the 
surfaces of the first and second hemispheres, excepting that 
which was shown to be proportional to a and to be due to the 
varying momentum of the fluid which passes the plane separating 
the two hemispheres. On the other hand, for waves whose par- 
ticles perform excursions very small compared to the diameter of 
an atom, g must be very small, because the fluid in contact with 
the second hemisphere is disturbed but to a small extent, and the 
varying momentum just spoken of has very little effect. In this 
case we have very nearly 
V=W sin 0(1+ pcos 8). 
Now it is evident that V and W must have the same sign, and 
consequently that 1+ cos @ does not change sign. Hence the 
limiting value of @ is the are whose cosine is — a which, if w be 
a very large positive quantity, exceeds but little a Thus the 
conditions assumed in the mathematical theory of heat are 
satisfied by supposing y to be very large and ¢ to be very small; 
and the fulfilment of these conditions accounts for the great 
energy of calorific repulsion. For as the fluid in contact with 
the second hemispherical surface is nearly undisturbed, the 
pressure on the other is not counteracted by opposite pressure ; 
and as the total effective pressure on the first surface varies nearly 
as the square of the radius of the atom, while the quantity of 
inert matter of the atom varies as the cube of its radius, it follows 
that the expression for the acceleration contains the radius of the 
atom in the denominator. Hence atoms of very small size, act- 
ing upon each other by the intervention of waves of which the 
excursions are very small, mutually repel with a very great force ; 
and at the same time, as was shown in the Theory of Heat, the 
