Prof. Challis on a Theory of Molecular Forces. 99 
by hydrodynamics, the reflected condensations, the incident 
waves being the same, vary as the radii of the atoms. Hence 
the condensations at the same distances from the centres of the 
atoms are proportional to the squares of the radii. Hence also 
the resultant condensations from all the atoms at points P simi- 
larly situated with respect to the two spherical spaces, vary as 
the squares of the radii. Let now the number of atoms in that 
space which contains the smaller atoms be increased till it con- 
tains the same quantity of matter as the other space. Then the 
' Rs 
number of the smaller atoms will be 3 , and the resultant con- 
densation at P of the waves propagated from them will be in- 
creased in the same ratio. Hence the ratio of the resultant con- 
densations due to the smaller atoms to the resultant condensations 
Seri iyf 
similarly due to the larger atoms will be = x wen or %. And 
as, according to the theory, the forces which tend to produce 
motions of translation of the atoms, to which the pressures 
which counteract the expansions of the gases may be assumed to 
be proportional, vary as the squares of the condensations or velo- 
cities of the incident waves, it follows that the pressures of equal 
weights of two simple gases contained in equal spaces vary inversely 
as the squares of the radii of their atoms. Hence the elasticity 
of a simple gas is greater the smaller its atoms. 
Prostem II. To find the relation between pressure and density 
in different substances. 
This question, which is the special subject of a communication 
to the Philosophical Magazine for June 1859, is introduced here 
for the purpose of answering it more completely by the applica- 
tion of the theory of molecular forces contained in the present 
communication. I see no reason to modify the argument by 
which the effective acceleration of an atom, due to the action of 
the surrounding atoms, may be expressed by the function 
Ap 
“AR, 
Ap being the increment of density corresponding to the linear 
increment Az in the direction perpendicular to a surface of equal 
density, and therefore in the direction of the molecular accelera- 
tion. But it is to be observed that the factor H was obtained 
on the hypothesis that the sphere of molecular activity is not 
altered by change of density. According to the theory now 
advanced, it appears that, while upon an increase of density the 
action of the atoms in a given elementary space upon an atom 
at a given distance is increased in the same proportion, the sphere 
of molecular activity is diminished in that proportion, the linear 
H 2 
