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preceflion caufed by the moon, with refped: to the 
ecliptic ; which may be done by refolving the mo- 
tion of the earth’s pole, parallel to the plane of the 
lunar orbit, into two motions, one whereof is parallel 
to the plane of the ecliptic, and the other perpen- 
dicular thereto, and which varies the inclination of 
the earth’s axe to the ecliptic. This is what we fhall 
determine in the following Problem. 
Problem VIII. 
20. Having given , the motion of the pole P of the 
earth parallel to the plane of the lunar orbit , to 
find its motion parallel to the plane of the ecliptic. 
* C P, fig. 3. n° 1. & 11 2. is the femi-axe of 
the earth. The plane of the figure is the plane of 
the folfticial colure; C Z is the axe of the ecliptic, 
confequently perpendicular to C S ; s the folfticial 
point, and PCs the folfticial angle : P Z is parallel 
to C $ , and perpendicular to C Z \ and it is equal to 
the line C H o ^ fig. 2. The circumference /, /', /% / 3 , / 
is the circumference deferibed by the pole, /, of the 
lunar orbit ; L, L\ U, L 3 is the fe&ion of the cone 
C 7 , l P l 3 l prolonged, by the plane that is tangen- 
tial at the pole of the earth, P. 
Let /° be any place of the pole of the moon’s orbit, 
tf upon the point P be erected PR , perpendicular 
to the plane P C i°, this perpendicular will be the di- 
rection of the motion of the earth’s pole, parallel to 
* The lines which are in the plane which touches the earth’s 
pole /, are ieparately reprefented in fg. 2. » Q - 3. 
i the 
