C *9* ] 
nution of the Gravity from the Pole to the Equator is 
proportional to the Square of the Cofine of the Lath 
tude 5 or, which is the fame thing, that the Augmen- 
tation of Gravity from the Equator to the Eole is 
as the Square of the Sine of the Latitude , as Sir 
Ifaac Newton has demonftrated in his Hypothefis of 
a homogeneous Spheroid. 
XVIII. From the following Calculation it is eafy to 
conclude, that Sir Ifaac’ s Theorem, ( Trin . Math . 
L. III. Prop. XX.) which is this, that the Gravity in 
any T lace within is reciprocally as the Diftance 
from the Centre , cannot obtain here. For we may 
fee by the foregoing Exprefllon, that the Gravity in 
N cannot be to the Gravity in P as 1 to 1 +a, except 
when p— q — o, which happens only in Sir Ifaac’ $ 
homogeneous Spheroid. 
It was for want of confidering, that this Theorem 
was demonftrated by Sir Ifaac only in the Cafe of his 
homogeneous Spheroid, that feveral Geometricians 
have too haftily concluded, this Theorem might be 
apply'd to determine the Ratio of the Earth's Axes* 
and the Lengths of the Pendulum obferved in two 
Places of different Latitudes. Dr. Gregory is one of 
thofe who have fallen into this Miftake, in his Ele- 
ments of Aflronomy, Lib. III. Sed. 8. Prop. y2. And 
in the Ehilofophicai TranfaElions , N g 432. it is con- 
cluded, from the Proportion of Gravity at Jamaica 
to that at London , that the Diameter of the Equator 
muft exceed the Earth's Axis by 7-f^th Part, which 
Computation was founded on this 20th Propofition, 
Lib. III. of Sir Ifaac $ Trincipa } which is true only 
of his Spheroid. 
XIX, La 
