514 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
tion of the nucleus, and the density at the point in the canal. This equation may 
be written as follows, after the substitution of the above values, and it being remem- 
bered that 6 and &> are constant for the canal, 
dp=§{dV sin^^.rdr), 
V being a function of r, 6 and a. On integration this gives 
P~P'=^y^ §dV-\-ct^ sin^6 §rdr, 
P standing for the pressure on an unit of surface of the stratum of the nucleus having 
the radius r, and P# the pressure at the centre. With the angular velocity «i, all other 
things remaining as before, 
P"— P'"=^ sin^^^y^ ^rdr. 
But when 6 becomes its value at the parallel of mean pressure, 
P' = n— sin^^i^y^ §rdr, 
P'" = n— ^ V— «i sin^ ^ ^rdr, 
n representing the constant pressure on the stratum in question, and r' the value of 
r at the parallel of mean pressure. If a, be that angular velocity which would cause 
the surface of the nucleus to coincide with that of the shell P"=n, we shall obtain by 
combining the foregoing expressions and neglecting the difference between r and /, 
P=n-l-(a^ — af)(sin^^— sin^^i)^y^ ^rdr (1.) 
For the pressure Pj at the shell’s inner surface, we shall have 
Pj = ni-}-(a^— ai)(sin^ sin^^i)^y^ (2.) 
Ti and Hi representing respectively the radius and pressure at the surface stratum of 
the nucleus. If IT, be not negative, this expression will be always positive with 
respect to some portion of the shell’s inner surface ; for when a 7 os, the greatest 
pressure is at the equator, and ^ 7 ; when a A the greatest pressure is at the 
poles, and consequently 0 
3. The determination of 6^ may be thus easily effected. Let the equations of the 
generating ellipses of the surfaces of the nucleus and shell be respectively 
Ay^+Blz'^=AlBl 
A,, B, and A 2 , B representing respectively the less and greater axes of these surfaces. 
The volumes contained within these surfaces being equal, we have A,B^=A 2 B 2 , and 
hence at the parallels of mean pressure, where x=x' and z—z', 
B?Al-B^Af 
