LECTUBE XIV. 



THE LATITUDE AND THE MOTION OF THE NODE. 



LET ITS first treat this problem on the supposition that the latitude is 

 so small that its square may be neglected. The equation of motion, taken 

 from Lecture II. , may be written 



E-Mr. \n 



1 + ,-,- . f ~. 3 COS (a) \, 



E + Mr /J 



where z r sin (latitude) and the cube of s is omitted ; or neglecting the 

 parallactic terms 



The value of jii/r 3 may be considered known by the operations which have 

 determined the motion in an orbit coinciding with the ecliptic ; that is to say, 



J = J |~1 + 1 a, 3 + 3a 2 cos 2$ + (| a 2 2 + 3aJ cos 4i/T| , 

 r a \_ & \& / j 



where a, has the definition of Lectures IV, V; or numerically, taking 



n n' = 1 , 



= 1-17150,8 + -02523,0 cos 2t + '00025,15 cos 4t. 

 And 



^ = n' s = -00653,6. 



Hence 



j%= - is [1-17803,9 + -02523,0 cos 2* +-00025,15 cos 4A 



