MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
195 
no continuous angular motion of the whole fluid mass can arise from this oscillatory 
motion, which may here, therefore, be also neglected. 
Hence, then, the angular motion of the fluid about the axis of y will be the same, 
to the required degree of approximation, whether the earth be heterogeneous or ho- 
mogeneous ; i. e. if, for the heterogeneous spheroid, we denote by (y 2 ) the quantity 
analogous to that in the homogeneous one denoted by y 2 (First Series, Art. 16.), we 
shall have 
I shall now proceed to determine the motion of the heterogeneous shell ; for which 
purpose we must find the values which the quantities Aj B 4 D 4 A 2 B 2 D 2 , &c. (First 
Series, Art. 5.) assume when the spheroid is heterogeneous ; or, adopting the notation 
of the last paragraph, we must find the values of (A : ) (A 2 ) (A 3 ) (A 4 ) (B 4 ) (B 2 ) (B 3 ) 
2. The moment of the disturbing force of the sun communicating a rotatory motion 
to the earth, considered as a heterogeneous spheroid*. 
(y 2 ) = 72- 
Motion of the Shell. 
(B 4 ) (D,) (D 2 ) (D 3 ) (D 4 ), and (y,). 
where = polar radius of the earth. 
s' = the ellipticity of that surface of equal density (§') of which the polar ra- 
dius is a'. 
Consequently, if a be the polar radius of the inner surface of the shell, this moment 
for the shell will be 
Also the moment of inertia of the shell 
And hence we have (First Series, Art. 19.) 
( 
sin 2 A, 
sin 2 A. 
* Airy’s Tracts, p. 207. Second Edition. 
2 c 2 
