[ 420 ] 
For this reafon, the motion according to P M mufl 
produce an ofcillution of the eai th's axis, whofe period 
is the time of an entire revolution of the pole of the 
lunar orbit about the pole of the ecliptic. 
Problem IX. 
21. To find the quantity cfi the precefiion caufied hy the 
moon with regard to the ecliptic j that is , the arc 
parallel to the ecliptic , run through by the earth's 
pole P, during the time of a femi-r evolution 1 l 1 P 
of the pole 1 of the lunar orbit. 
Let there be drawn the lines N K, 1° K perpen- 
dicular to the axe of the earth C P, and parallel to 
the lines NP , 1 ° P, fig. 3. no 1 . & n° 1. 
The triangles PR M, P N L° , K N 1° are right- 
angled and fimilar ; for the three fides of the firil are 
perpendicular to the three fides of the fecond, and 
the three fides of the fecond are parallel to the three 
fides of the third. 
Still retaining the foregoing denominations, let 
z l — Z N = z- } P Z == g, as in fig. 2. the 
line C II-, CZ=f -, ClovCl° = C. 
We dial 1 have N P = V xx. — zz ; NP — g — Z; 
NK 
f 
a 
x£ 
Zj or - - x g-\-z i when the point /* 
a 
lies on the other fide of /’ ; P R = - xg — z> or'-x 
a a 
when the point l n is on the other fide of /'. 
Tire triangle C l K is here fimilar to the triangle 
whofe three iidts are reprefentcd by the letters afi\ r, 
fince 
