196 
MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
Let s be the ellipticity of the inner surface of the shell. If the earth were homo- 
geneous, and the ellipticity of the external surface were also = s, we should have 
— = ^ s sin 2 A (First Series, Art. 19.) ; 
r ' P ,ii*ip dal 
(a) a da l oi 
co p a \ ,da' b n , s co 
J. t 
and therefore 
Let us suppose this 
then 
= (!+*) 
/’■'i , d («'■’ s') , , 
J. e ~i^r ia 
j : 
a \ . da 15 , . 
p ’ tt d ° 
v da! 
— — L 
which for brevity may be written 
s g • 
If s' were constant and = e x , we should have 
^ = — - 1. 
In our actual case we may put 
S = r,-f - 1 ; 
we shall then have 
£ - 
V = 
Unless — a be very small it is manifest that li will be less than e 1} and therefore y 
less than unity. 
(«) 
The value of — gives 
CO ° 
(AJ = (1 + $) Aj 
(B x ) = (l +*)B la 
Similarly 
(First Series, Art. 19.). 
(DJ = (1 + s) D l5 
(A 2 ) = (1 + s) A 2 , 
(B 2 ) = C 1 + s) B 2 , 
(D 2 ) = (1 + -?) L 2 . 
3. The fluid pressure on the interior surface of the shell will be produced by the 
mutual attractions of the particles of the whole mass fluid and solid, the centrifugal 
