[ 4 °9 ] 
ecliptic, as when the fan was on the other fide in S, 
but with a contrary fign, or direction ; and the fum of 
the lines P M', from the folftice $ to will be the 
fame as the fum of the lines f M, from T to s, but 
with a contrary fign : fo that the angle of inclination 
of the earth’s axe to the plane of the ecliptic is con- 
tinually increafing from V to s, and then decreafing 
from to ^ 3 and as the diminution is equal to the 
increafe, the inclination becomes again the fame in 
as it was in T, having undergone an ofcillation 
whofe period is fix months. 
Whilft the fun paffes from £1 io v?, there are the 
fame motions of the pole, as whilft it was paffingfrom 
$ to 
Thus is the motion of the pole determined at 
every inftant, with refpedt to the ecliptic. Which 
was to be done. 
Problem VI.. 
12. To find the quantity of the precejjion , or, which 
is the fame , the arc of the parallel to the ecliptic 
run through by the pole of the earth P in the fipace of 
time the fun is pajjing from the equinox to the fiol- 
fiice , or from the folfiice to the equinox ; which 
may he taken for a quarter of the time of the fun's 
revolution about the earth ; the angle comprehended 
between the equinox and the enfuing folfiice differing 
but by an infinitely Jmall quantity from 90 degrees. 
Calling, as in Prob. I. the femi-axe C P, a ; fig * 2. 
?i° 1. & m 2. the fine of the angle P C S, or P C D , V ; 
and its cofine, or the fine of the fun’s declination, u : 
F f f Let 
