[ 12 ] 
als. So that if 0 and P Stand for the folidities of 
the oblate and prolate Spheroids, and S } s, for the 
two fpheres S : 0 : P : s -x- are in the continued 
proportion of m : n. And S : P, or 0 : s : : m z : n z . 
As S : s : : m 3 : ?P. 
Or we may with Sir Ifaac Newton conceive of the 
geneSis of thefe folids as follows, i . Let the fphere 
APBQ be uniformly compreifed in the direction of 
its axis P till that axis is diminished to pq, and 
the fphere changed into the oblate Spheroid. 2. Let 
this Spheroid be equally compreSTed in the direction 
of that diameter of its equator, which is perpendicu- 
lar to pq and AB , or to the plane of the figure j and 
it will degenerate into the prolate Spheroid, whofe 
poles are A and B. ?. Let this laft be compreSTed in 
the direction of its axis AB , till it is changed into 
the fphere apbq ; and, in each of thefe compreSlions, 
the Solid Space, which the body contains will be di- 
mini (bed in the ratio of m to n. 
Now, as the determination of the earth’s figure de- 
pends not only upon that of the ratio of the centri- 
fugal force, by which a body tends to recede from 
the axis of rotation to the power of gravity > but 
likewife, upon the decrement of gravitation arising 
from the body’s being in that rotation actually re- 
moved to a greater distance fiom the centre: it is 
not enough, that we know, from the experiments 
with pendulums, the centrifugal iorce at the equator 
to be about - 2 j-g of the force of gravity. We need, 
farther, two diftinCt propositions ; one to determine 
the attractive force of a Spheroid at its pole ; and the 
other to determine its attraction at the equator. 
The firfb of thefe we have in Princip . lib. i. prop. 
9 1 * 
