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MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
difference of ellipticities of these surfaces. It must therefore involve a factor of the 
order g. Secondly, the direction of the attraction of the whole shell on the fluid par- 
ticle (or of the fluid particle on the shell) will pass at a distance from the axis of y not 
exceeding 1 a quantity of the order s a. Consequently, the moment of this attraction 
will involve the factor s 2 ; and such being the case for every fluid particle, the moment 
of the whole attraction of the fluid on the shell will contain the factor s 2 . Thirdly, this 
moment must vanish with ( 3 , and must therefore contain (3 as a factor. It will con- 
sequently be not greater than quantities of the order s 2 ( 3 , and may be neglected. 
9. From the preceding results we obtain 
(A) = (Aj) + (A 2 ) + (A 3 ) + (A 4 ) (First Series, Art. 6.), 
= (1 + s) (A x + A 2 ) + h (A 3 + A 4 ) (l -f- 2^5). 
When the solid shell is very thin, A 3 and A 4 are respectively much larger than A 4 and 
A A 
A 2 , since A 3 = -_ 1 — , and A 4 = g5 (First Series, Arts. 21, 22.). In that case, 
therefore, the precession will depend almost entirely on A 3 and A 4 , and the introduc- 
tion of the factor 1 + ^ instead of unity will give a correction amounting to nearly 
j^th of the whole precession, or something less than -^-th of a second. For any but 
the most inconsiderable thickness of the solid shell, the correction will be much less. 
It may, therefore, be altogether neglected, as a quantity of the same order as the 
terms involving s 2 ( 3 . We shall then have 
(A) = ( 1 + s) (A 4 + A 2 ) + h (A 3 + A 4 ), 
= (1 + s) (Aj + A 2 ) + ^ (A 4 + A 2 ) (First Series, Arts. 21, 22.), 
= (l -f s + -- 5 - k _ q -) A (First Sei ' ies > Arts. 6, 21, 22.). 
Also 
(B) = (B 4 ) 4- (B 3 ), 
= (1 + s ) 4- h B 3 , 
= 0 + 5 + ^~ri) Bi, 
= (1 +S+-^— 
) ? V 2b - 
\ q — 1 
/ q 
Similarly 
(B') = (B 2 ) + (B 4 ), 
/ h 
\ — 1 
~ V + S + q>- l 
) V B ’; 
(DO-b + . + A 
) V- D ' 
