[ 4i5 ] 
Problem VII. 
14. To find the alteration of the inclination of the 
earth's axe to the ecliptic , during the fun's pajfage 
from the equinox to the folflice , or from the foU 
fiice to the next equinox ; which is the fame, only 
affeSled with a contrary fign , as has been feen in 
Prob. V. 
By Art. 8. we have a P p — A Vu x a d t ; and by 
Trob. V. the inflantaneous variation of the inclination 
of the earth’s axe to the ecliptic is A V u x a d t x 
PM 
■pp 
= A V u x a d t x 
$ D 
W‘ 
becaufe of the fimilar 
triangles '•P pM, P D — (taking the denominations 
r /T7Twrr 7 * r % dCD S D Arr 
of Prob.Vi.) AV uxar. — x — — -= x — -~-~AFuy 
2tt CD x ffijD P D 
du 
aT rdCD __ 
X — = ~AV U 
CD x PD 
r x 
uu 
-AVy 
ar a 2 x 
■ — x - 
u u 
X u d u , whofe integral is i A rx — xuu-, and when 
2 7T 
the funis at the point $, we have 1 : u :: r : a, and 
a = r u ; therefore the preceding integral is then 
T 
Ax x a a. Which was to be found. 
2 irr 
Remark. 
1 5. When the motion of the node is not infenfible, 
you are to take the value of d t of the Remark that 
follows 
