C 432 ] 
Problem XII. 
34.. To find the precefiion caufed by the moon t during 
the time of a femi-revolution of the pole of the 
lunar orbit about the pole of the ecliptic ; that is , in 
about years t or pf x T, as T = 1 year. 
By Art. 21. we have found this precefiion = 
— x - — x(i— f x — ). 
2 2acc v Jf J 
By Art. 30. B = x ^ x : Subftituting this 
value in the preceding formula , it becomes ^=?x -x 
JL * 2 r 
f ff I , 
— x — X -- 7 r £ x (1 
2 <2 f f 170 
'a 
x x ) 
7J'J' 
f . 
But - is the ratio of the fine of 66 deg. 32 min. to 
the radius, = . 
10000000 
L is the ratio of the fine of 8 f deg. to the radius, 
c 
the angle l c z, whereby the pole of the lunar orbit is 
diftant from the pole of the ecliptic, being, at all 
times, about y degrees. Therefore^ = ~ 99 . ^LP^ 7 . m 
c IOOOOOOO 
*; is the ratio of the fine of f deg. to the fine of 8y 
, _ 87if57 
degrees, = — - — 1 . 
6 99 <>m 7 
3 
Therefore 
