[ 4°S 3 
The point E, in confequence of thefe two motions 
together, E e and E e, circulates neither in the cir- 
cumference E g^E <^E of the equator, nor in the 
circumference E P E P 1 E of the fun’s declination.. 
But if we form the redtangle E e e g E, the diagonal 
E e will be the elementary arc of the circumference 
E e' q E E wherein the point E will circulate ; and 
the angle e E e 1 , equal to the angle Qc <7, equal to 
the angle P' C />', will be the angle whereby the pole 
P is elevated, and the pole P depreffed, below the 
circle of declination, by moving in the circumference 
P' p' Qjq P p P', whofe plane is perpendicular to the 
plane of delination ; and the point p is the true 
place of the pole at the end of the inflant d t , and 
the fmall arc P' p> expreffes the inftantaneous varia- 
tion of the place of the earth’s pole. Which was to. 
be found. 
Corollary I. 
8. The fimilar fe&ors e E e\ q, or P' C p' y 
whofe three fides of the one are each parallel to the 
three fides of the other, give this proportion, E e : 
e e or E g : : C P' : P' p‘ = ~ x C P' = (by the 
Lj 6 
preceding Prob.) to ——7 — x C P — — x a. But 
r & ' mat m 
by Problem III. fx — ^ ( 7 — 2a> ) ; therefore P P ~ 
3 i* a n v xadt — Avuadt, making A 
i J )(fflx( i — 2a) 
3 $ a a 
s 3 x m x ( i — 2a) 
CoRQL* 
