[ 3 8 7 ] 
The inftantaneous motion of the pole, which is P' p\ 
or Pp, fig. 2. rfi.&rfi*. may be refolved into 
two, P R and P M, perpendicular to each other, and 
both to the earth’s axe. The former caufes the pole 
P to move parallel to the ecliptic T © vr, and alters 
the place of the folftice & , and confequently alfo that 
of the equino&ial points T and ; the latter, which 
is according to P alters the inclination of the 
earth’s axe to the ecliptic. 
To have the motion of the pole parallel to the 
ecliptic, or, which is the fame, the motion of the 
node r, or the preceffion, in the fame time that the 
fun paffes from the equinox r to the folftice $ , take 
the integral of the lines P R , fuppofing P R gene- 
rally to exprefs the inftantaneous preceffion for any 
declination of the fun S. 
And to have the alteration of the inclination in the 
fame time that the fun is paffing from r to take 
the fum, or the integral of the lines P M y fuppofing 
P M generally to exprefs the inftantaneous alteration 
of the inclination of the earth’s axe to the ecliptic for 
any given declination of the fun. 
The fum of the lines PR is always the fame, and 
has the fame fign, or the fame direction, during every 
quarter of the fun’s revolution, whether he moves 
from t to 5, or from s to tfs, or from as to vy, or 
from yp to t ; fo that the preceffion anfwering to any 
one quarter of the fun’s revolution about the earth, 
or to three months, being known, that multiplied by 
4, will be the annual preceffion ; by 8 will give it for 
two years ; by 16 for 4 years, &c. 
C c c 2 Likewife 
* Fig, 2. is explained at the beginning of Preb. 5. 
t 
