Prof. Challis on a Theory of Molecular Forces. 93 
smal], the radius R of a molecule will be small, and as . is a 
D 
fixed ratio, D will also be comparatively small. Hence, as the 
condensation propagated from each atom varies inversely as the 
distance, it may be supposed that the resultant condensation and 
corresponding velocity of the ztherial particles at the distance D 
from the centre of the molecule, are so large that the excursions 
are large compared to the diameter of an atom. Thus the dynamic 
effect of the new order of waves will be an attraction towards the 
centre of the molecule. The mathematical investigation of the 
amount of this attraction will be the same as that I have given 
in the Theory of the Force of Gravity (Numbers of the Phil. Mag. 
for November and December 1859) ; and the expression for the 
acceleration of any atom will consequently be 
S7r?2gam? 
8xr? 
at a position where the maximuin velocity of the waves is m. It 
is here to be remarked that, as the value of X is much smaller 
for this class of waves than for those which were supposed to 
account for the force of gravity, this molecular attraction will be 
much more energetic, for the same value of m, than the attraction 
of gravity. 
It follows from this reasoning that the waves propagated from 
the atoms of a given molecule have no repulsive action at the 
distance D, their dynamic action having merged into that of the 
second order of waves. The atomic repulsion due to the part of 
the velocity which is unaccompanied by condensation, must vanish 
at a much less distance than D, on account of its varying in- 
versely as the fourth power of the distance. That due to the 
part of the velocity accompanied by condensation vanishes more 
slowly, but is at its origin comparatively feeble. In this manner 
the theory accounts for the small sphere of activity of the atomic 
repulsion. 
If we consider apart the dynamic action of the same molecule 
at distances much greater than D, the condition that the excur- 
sions of the particles of the medium are very large compared to 
the diameter of an atom, must at a certain distance cease to be 
satisfied ; the factor g will continually diminish, and the factor 
become significant, till the molecular attraction will be changed 
to molecular repulsion. But the amount of this repulsion, which 
will depend on the relative magnitudes of « and qg, may be very 
much less than the atomic repulsion, and vary much less rapidly 
with the distance. Also if we take a spherical space of radius RY, 
containing N molecules of N atoms, N being the same fixed 
number as before, and suppose the molecules to be of the form 
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