[ 421 ] 
But it is demonftrated by Sir Ifaac Newton, and 
by other authors, that the force of all the particles, 
or of all the matter in the whole fpheroid A P ap, to 
turn it about its center, is equal to fth of the force 
of a quantity of matter, placed at A, equal to the 
excefs of the matter in the whole fpheroid above 
that in the infcribed fphere, whofe axis is P p. Now 
this excefs (afiuming the ratio of 7r to i , to exprefs 
that of the area of a circle to the fquare of the radius) 
will be truly reprefented by OPxOA : 
OP : 
and, confequently, the force of all the matter in the 
whole earth, by|i^X-— — X 
AK OK 4T 
TT” O A r 'Q A X 15 x OPxOA 1 - 
-OP\ 
ILet, therefore, this quantity be now fubftituted for 
p 
F , in the general formula writing, at the fame 
and 
n 
in the place of their 
time, jxOA 2 xOP, 
equals c and n ; by which means we have (here) 
F 3 it O A 1 — OP* AK x OK D 1 
v ' ^ — o A^ — * ^ ut t “ e g lven 
= k 5 and let the angle 
' 2 TT X 
3 " 
X 
O A 1 
o A 1 — O P 1 
OA 1 
ncf 
quantity %rr 
E A e reprefent the horary alteration of the pofition 
of the terreftrial equator, arifmg from the force F 
(here determined), and let the arch Ee be the re- 
grefs of the equinoctial point E, correfponding there- 
to: then, in the triangle EAe (confidered as fpheri- 
cal) it will be fin. e : fin. AE (: : fin. EAf : fin. E<?) 
:: EA< : Ee = k 
AK x OK 
= k X 
iin. £ 
fin. A E x cof. AH x fin. A H 
, fin. A E 
X r~ X 
fin. E 
But in 
OA 1 iin. E 
the triangle EH A, right-angled at A (where HA is 
fuppofed 
