MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
207 
10. The coefficient of the term which gives the precession (First Series, Art. 26.) 
now becomes for the heterogeneous spheroid 
(7) ( } ” 
(A) (since (y 2 ) = y 2 , (Art. 1 .), 
(A), 
(7i) + 7a 
1 
i +h r h 
72 
- h 0 + L + s) q q 5 A, 
(since ^ = - r 1 , ) (First Series, Art. 25.), 
x y 2 Q ~ ^ 
i + 
q a - 
4^1 A. 
If P denote the precession for the homogeneous shell considered in the preceding 
memoir, or (which has been shown to be the same thing) for the homogeneous 
spheroid of which the ellipticity = g, 
P = £l^2 A 
(First Series, Art. 26.) 
and therefore if P' denote the precession for the heterogeneous shell, 
P'=H i + 
-P; 
1 + -S 
q b — 1 . 
and if P 2 denote the precession which would exist if the earth were homogeneous, i. e. 
that of a homogeneous spheroid whose ellipticity = £ A , 
P = P, 
and therefore 
P' = 4 
rr-^-- 1 
1 + 
1 + 
and 
q b — 1 
•-J-Pj. (since a = J?(y- i)) ; 
P, - P'=< 
0-i) 
1 + 
q b — 1 
= 0-4) 
1 — 
Pi- 
1 + 
q b — 1 . 
Since y cannot be greater than unity except when the earth’s crust is very thin (Art. 2.), 
or q = 1 nearly, this expression for Pi — P' is essentially positive, and therefore P' 
is always less than P^ 
