IN PHYSICAL ASTRONOMY. 
379 
If n{l+2r 0 } = n and n 8 =^ a = a j 1 +-1 r 0 j 
If 2 e is the coefficient of sin (w (1 + k) t + £ — in the expression for the 
longitude, 
e (1 +/) =e(l + k — r 0 ) 
y = 1 - y r 0 + e 11 + k - L t 0 J cos (A (1 + *) t + 2 - arj 
e,f cos (n(l +k,)t + e — 
+ e /. 
. 7 ii, U- 7 . To/O" t 
6 p «/ 2 
r _ :>ij a\ b 6, cos(n(l - ^Lb sl )t + a-A 
1 6(io/ 3,0 12pa, 2 3,1 J \ V 4|^«, 2 7 / 
+ e// cos (1 +&/)! + £ — 
= 1 + y r 0 — e 11 + k — A r 0 | cos A? (1 + k) t + a — ®r | 
— e,/, cos (1 + i/) t + a — -nr^j 
i , to, a 3 , to, a® , 
= 1 + 6^ i “-TT l iv‘ s -‘ 
-e{l+ *£«„, 5 ’» 
6 3 ! 1 cos ( n ( 1 — a -~ b 3 A t + a — raA 
t-a ( 2 3,1 J V V 4j*a;» 3,1/ / 
6 [j, a/ 3 ’ 12 t- ( 
— e,f cos (1 + &,) t + e — ®, j 
If a < a t as before, and 
y = 1 + L 0 + e ( (1 +/') cos (n, (1 + £') t + a, — y ^ + e// cos (1 + &/) < + *« — ^ 
we find 
/;{(! + »/)•(!-sr„)-l}=^£. 4,., 
If Mi + 2r 0 } = 11 / and n / 2 = y J a, - a ; j 1 + y r /0 j 
