of experiments on the pendulum. 
9 1 
have a = c 2 3 and d = .385c, and c = z.6d : but this is a much 
greater increase of density than is likely to exist on a large 
scale : so that c must probably in all cases be considerably 
greater than this. 
C. The greatest elevation of the general surface above the 
sphere will be - , on the supposition that the mutual attrac- 
tion of the elevated parts may safely be neglected. 
The fluxion of the elevation is as the fluxion of the arc 
and as the deviation d conjointly ; it will therefore be ex- 
pressed by TT— —r-r?- Now the fluxion of — — — — , 
1 J (i+bb — 2 b$x) § y'P +bb — 2 bcx) 
7 r 1 ^ 
is — — 7-7 , consequently the fluent of the elevation 
2 (i+bb — 20fx) f 1 J 
— - : and while cx varies from 1 to —1, this 
1 2 bcx} * 7 
will be — - , . . . 
>v/(i +bb — 2 b$x) 
fluent will vary from to ~~ b , the difference being a 
, or simply — , since c is 
1 
1 +b 
a ^ c 2 — c) ^ 
2 — C ■ 
2C • 
an extremely small fraction. This quantity comprehends 
indeed the depression on the remoter side of the sphere., 
which would be required to supply matter for the elevation ; 
but it is obvious that such a depression must be wholly 
inconsiderable. 
D. The diminution of gravity to the centre at the highest 
point is -Id—, while the increase from the attraction of the 
disturbing mass is nearly -d-, which is greater in the propor- 
tion that half the radius bears to c. 
E. The increase of gravity, at the point of greatest devia- 
tion, is to the deviation itself, or its sine d, as \/q to 1. 
For the deviation is the measure of the horizontal attrac- 
tion of the disturbing mass, which is to its vertical attraction 
