467] 
371 
467. 
EXPEESSIONS FOE PLANA’S e, y IN TEEMS OF THE ELLIPTIC e, y. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxv. (1864—1860), 
pp. 265—271.] 
The coefficient of sin cnt in Plana’s expression for the true longitude v (see 
Plana, t. 1. p. 574), putting therein E' = e = e!, that is, neglecting the terms which 
depend on the variation of the solar excentricity, is 
= e 
+ e 3 
+ <? 5 
+ e 7 
+ ef 
+ 
+ ë'f 
+ ef 
+ e 3 7 4 
+ ef 
( 9 4- 3 _ 75 m 3 _ 6659, m 4 _ 4884375 
V L -T 2 m ^4 ni 2 5o 36ÏÏ64 
(_ 1 _l7 m 2_319 5 m 3_45 T 3_5_9^7 m 4) 
( &+m> 2 ) 
( 5921 N 
\1612B0/ 
(“ 2 - If m ‘ Z + W(f + “Iff 1 W4 ) 
( H-m™ + 1 ffPm 2 ) 
(- tH) 
(- S + Ml m + IM! ™ 2 ) 
(HM) 
( _ ■&) 
w 5 _ 65756819 
147456 
m 6 ) 
+ ee‘ (<- V + I =)-9m» + (-^“ + -W=)-^m> 
+(- tof -m=)~ to#* «*) 
+ ((- i||§i - ¥ =) - afM 1 ™ ! ) 
+ «V ( ( TO - HI =) + ™ ! ) 
+ ee" ( ( « - 2 §F=>- W ™ ! ) 
+ e& 4 (— A 3 / 1 m2 ) 
+ ee' ! 6*(- ft )• 
47—2