[ 4°6 ] 
Corollary II. 
<>. If, inftead of the terreftrial lpheroid, we fup-* 
poled only a fingle ring, it would be found in like 
manner, that the pole P of fuch ring would fhift its 
place during the inftant d t y by running through the 
arc P' p> = — x CP' = -x a. But then we fhould 
E e m 
take the value of u as in Coroll, of Prob. III. which is 
~ x a v u. Therefore we fhall have P' f = u -~ — 
s J m 
5 S a j 
x a =— *vua at. 
s'xm 
To apply, then, the formula of the preced. Coroll. 
cl 
it will fuffice to make in that Coroll. — i. for 
i — la 
then the formula of Ccroll. I. becomes the fame with 
that juft now found in this Coroll. 
This will be of ufe hereafter for applying the for- 
mulae of the motion of the nodes of the terreftrial 
equator to the mo don of the nodes of a moon or fa- 
tellite of a planet. 
Corollary IIL 
io. It fhould be well obferved in the preceding 
Corcll. that the diredion P' p' of the pole P is ever 
parallel to the diredion E e of the point E of the 
equator, fmee they are both perpendicular to the plane 
of the circle of the fun’s declination, and the di- 
redion P' p' goes on the lame fide as the diredion Ee 
of the point E y which is placed on the fame fide of 
the 
