Prof. Challis on a Theory of Molecular Forces. 101 
ProsiEoM III. To find the law of density in the interior of the 
earth. 
This question is here considered for the purpose of testing the 
formula just obtained for the relation between the pressure and 
the density in solids and fluids, which is in a great degree hypo- 
thetical. To adapt the formula to the circumstances of the earth, 
supposed to be of homogeneous material throughout its interior, 
let 
p=(5-1); 
5 being the density of primitive rock, as granite, at the surface. 
Then, as is well known, this equation gives for the law of den- 
sity in the earth’s interior, the form being supposed spherical, 
p _ sin Qr 
aes Or? 
D 
p being the density at the distance r from the centre, D the 
density at the centre, and Q a certain constant. If c¢ be the 
earth’s radius, M its mass, and g the usual measure of gravity 
at the surface, the value of the constant Q is given by the 
equation 
9_. 2mgc*o* 
o> Mi? * 
Now since the assumed relation between p and p takes into 
account the effect of heat in the earth’s interior, the constant k? 
has the same value for the whole of the mass, supposed to be of 
uniform material. Hence its value may be found experimentally 
by determining the compressibility of primitive rock at the 
earth’s surface, or, what is equivalent, ascertaining the velocity 
with which it transmits sound. (See on this subject an article 
“On the Ellipticity of the Planets,” which I communicated to 
the Philosophical Magazine for September 1831, p. 200.) If 
this velocity be called V, by a known process we shall have 
a id 
i ges 7 
Hence supposing the mean density of the earth to be né, we 
obtain for calculating Qe the equation 
1 3gc 
DM ae 
The value of n deduced from the law of density is 2°42. I am 
not acquainted with any experimental determination of the value 
of V for primitive rock. In art. 114 of the “ Treatise on Sound” 
in the Encyclopedia Metropolitana, experiments which appear to 
be trustworthy are adduced which give for the velocity of sound 
