98 Prof. Challis on a Theory of Molecular Forces, 
between the atoms of a gas, would allow any diffusive action 
operating on the atoms of another gas, to take effect in the 
space occupied by the former, and all collision between the two 
sets of atoms would be prevented by the proper repulsions of 
the individual atoms. It is evident that the force by which the 
atoms in motion are diffused, must act on the atoms of the 
medium in which the diffusion takes place ; but this action only 
produces a slight alteration of the density of the latter, without 
affecting its state of equilibrium. 
In applying the general expression for the velocity (V) of the 
zether along the surface of an atom, to account for the repulsive 
force of gases, it must in general be supposed that each of the 
constants » and qg has a sensible value, and consequently that 
both the hemispherical surfaces of the atom are pressed by the 
incident series of waves, the pressure on that which directly 
receives the waves predominating. This may account for the 
comparatively small repulsive action of a gaseous body which is 
at no part extremely rare, such as the earth’s atmosphere, at the 
upper boundary of which the force of the earth’s gravity im- 
poses a limit on its rarefaction. But the repulsion will assume 
a different character in a gaseous substance of very large extent 
and great tenuity, such as was the coma of Donati’s comet, 
which produced no sensible refraction of the light from stars, 
whatever were the direction and length of the path of the light 
through it. In this case the dimensions of R and D are greatly 
extended; becomes large and g very small for waves of the 
second order, and their action on any atom approximates to that 
of the repulsion of the first order, extending but little beyond 
the hemispherical surface on which they are directly meident, 
while at the same time the action varies but slowly with distance. 
This will account for the enormous development of repulsive 
action in the extremely attenuated tails of comets. 
6. The foregoing theory of molecular forces admits also of 
application to the following physical problems. 
Prostem I. To account for the difference of elasticity of 
different simple gases. 
The theory allows of no other difference between simple gases 
than a difference in the magnitudes of the component atoms. 
Take a portion of one gas bounded by a spherical surface, and 
containing a certain number (7) of atoms, and a portion of the 
other gas, bounded by an equal spherical surface, and containing 
the same number of atoms similarly arranged. Let R be the 
radius of an atom of the former, and r the radius of an atom of 
the other, and suppose R to be greater than 7. Now by the 
theory, the elasticities of the gases depend on the waves accom- 
panied by condensations which are reflected from the atoms ; and 
