LECTURE III. 



THE SUN'S COORDINATES IN TERMS OF THE TIME. 



To obtain the Moon's coordinates in terms of the time from the equa- 

 tions found in Lecture II., we must substitute in the expressions for the 

 forces the developments of the Sun's coordinates which we now proceed 

 to give. 



Employing as coordinates /', ff, of the last lecture, we have seen that 

 the Sun's motion may be regarded as purely elliptical, so that 



a' _l+e'cos(6'-n f ') 

 t j ~ 'Y-e' a - 



e'-iff' = n't - BT' + 2e' sin (n't - w') + - e'* sin 2 (n't - CT') + . . . 

 in which we have written for convenience n't in place of n't 

 The quantities that enter the equations are 



COS, 



r 1 ) sin ' 



sin 



r 1 sin 



Making the substitutions we find without difficulty 

 ft)' = ! + | e/2 + 3e/ cos (n't - w') + 1 e'* cos 2 (n't 



