100 Prof. Challis on a Theory of Molecular Forces. 
quantities on which the law of molecular action depends retain- 
ing the same ratios. It follows that the number of the given 
elementary spaces containing effective atoms is diminished in 
proportion as the density is increased, and consequently that the 
factor H is of the form >: the quantity os being given. It is 
here supposed that atoms situated in parts of the fluid which 
have different densities have the same specific heat, that is, are 
centres of waves of equal condensation. But though this is ap- 
proximately true in aériform bodies, it cannot be exactly true, 
because, while the waves reflected from a given atom are chiefly 
due to incident waves from extraneous sources, they are partly 
due to secondary incident waves originating at the surrounding 
atoms, and therefore partly depend on the density. Hence, the 
reflected waves from extraneous sources being supposed to be the 
same throughout the fluid mass, we ought in the place of K to 
put K(1 +a.f(p)), « being very small. Consequently if @ be 
the accelerative force which counteracts the molecular accelera- 
tion of a given atom, we shall have 
K A 
G= = (1+e-fe) oe 
and 
dp=GpAz= Ka +a .f(e) Ap, 
which is the law for gases. 
Exactly the same kind of reasoning applies to fluids and solids, 
excepting that in these the condensations of the waves propa- 
gated from a given atom appear to be determined as to quantity 
by the reflexions of successive orders of secondary waves from 
the surrounding atoms. It would be in accordance with hydro- 
dynamical principles to say that the dynamic effect of waves 
coming originally from extraneous sources (as the sun, the pla- 
nets, and stars) is by these reflexions multiplied in a certain pro- 
portion to the density of the substance. Also among the primary 
waves to which the secondary waves are owing may be reckoned 
the waves of the second order previously considered, the conden- 
sations of which are proportional to the same density. Without 
at present discussing this point at greater length, I shall assume 
as an hypothesis that the calorific repulsion of solids and fluids is 
fully taken into account by supposing that H=Kp. Consequently 
eae, ae and dp=GpAz=KpAp. 
Hence 
K 
p= gp +0. 
