200 
MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
proper limits), we have the moment 
= 2 oo 1 s sin 2 (3 a 3 f(a ) sin 3 6 cos 2 6 cos 2 <p d <p dd, 
= £ sin 2 j3 a 5 // sin 3 0 cos 2 0 cos 2 <pd<p dO, 
_ ^2 g s j n 2 j3 a 5 . 
If be constant, 2 f (a) = a 2 ; and this expression becomes the same as that pre- 
viously obtained (First Series, Art. 23.) for the homogeneous spheroid. 
The moment of inertia of the shell 
8 7t /*°i dr 5 
8 7T /*°i or® 7 
= W„ fs* 
(omitting terms involving s) 
where 
if {» («i) — «■ («) } 
(r) = f 
r d r l 
^ dr 
dr. 
Hence the accelerating force of rotation on the shell produced by the part of R now 
considered 
=( ,» )= sin2|3 , 
v ' 0 - (Oj) — 0 - (a) 2 r ’ 
or if 
__ g /( g ) g3 (g 5 - 1) # to** - m 
- cr (a,) — <r (o) 2 (? »-l) 8i n-P» 
2/(«K(? 5 - 1) 
(7(Oi) - <r(a) 
= A, 
(«") 
= A 
CO 6 . 
a(j»- i) sm 2 
— hy 1 sin 2 (3, 
(First Series, Art. 23.) 
which gives 
Oi) = h 7i 
6. We have now to consider that part of R which depends on the sun’s action. 
Let X', Y', Z' be the disturbing forces of the sun parallel to the axes of x, y, z 
respectively, the plane of x z being now so taken as to pass through the sun’s centre. 
Then if A be as heretofore the N. P. D. of the sun, we have (First Series, Art. 21.) 
X' = ^ x' sin A + A z' cos A, 
'i ' i 
y' = - 
Z' = yFx' cos A — A *' sin A, 
1 1 ‘ i 
