[ 424 J 
Problem X. 
22. T'o fnd the quantity of the nutation , or of the 
variation of the inclination of the earth's axe to the 
ecliptic, caufed hy the moon during the femi -revolution 
1 1‘ l 2 of the pole of the lunar orbit . 
The fpace run through in an inftant d t by the 
pole of the earth, parallel to the plane of the lunar 
aa 
orbit, being, by Art. ly. = B b x — xdt, the inftan- 
irr 
tancous nutation for any one place 1° of the lunar or- 
bit will be, by Prob. VIII. = Bbx ° a ’ ' PM 
xd tx DD 
irr PR 
(by the denomination of the preceding Problem) 
z 
aa nT 
B bx — x — x — ■ ■■■ - ■ . — . 
2 rr 2 7r V-jcx — zz 
V XX — 
.32; 
a c 
r 
aa nT' 
x — x — x 
z 
b 
= £x~ 
r 
b . 
Putting inftead of —its 
r 
2 7T V XX — 33 
yy . ^ 
value, which was found to be — — , we fhall have 
a c 
B x — x ttfgz^dz i and when the point 
2tt X 2 C C 
l a is on the other fide with regard to we fliall have 
J] x — !L — xff — gzxdz. 
2 7T X 2 C C 
Taking therefore the nutation for the two points 
together, /°, placed on either fide of /‘, we have 
B* 
