358 
NOTE ON PLANAS LUNAR THEORY. 
[4 6 4 
but, by an error which is implicitly corrected, the cr which multiplies (1 + s 2 ) - 2 J Udv 
is omitted. Hence the equation (6) becomes 
du dn — o-(l + s 2 )“$2 J Udvr 
(1 + 2 
d 2 Bu 
dv 2 
+ Sii] = —■ 
/ o’ a, 
Ÿ( e > 7) 
a- 
dv u 2 dv 
+ (1 + 2 J Udv)f(e, y) Q'e cos (cv — j’zjdv) 
-(1 + 2/mv)[/(e, 7 )(l+y)(l +s ;)-i-^+£ÿ} 
+ (1 + 2 J Udv) f(e, y) Py 2 (1 + s 2 )~^ (*), 
era. 
U, p. 265, 
in which equation 
dCL s dil - „ _, „ dO 
H 2 =-t-+- -T-, pp- 26, 24o, a 
aw m as w 2 dv x 3 (l+y 2 )= 
f (e, y) = A^(l+y 2 )" 1 , /(e, y) = X 3 (1 + y 2 ) 3 , p. 261. 
But retaining for greater convenience the function f(e, y) in two of the terms, 
we have 
(1+2 
d 2 Bu 
dv 2 
+ Bu 
a ^ 2 
era 
■V o /T „\4 (dii 5 dH era, -y-T-dw ... . a _ f Tr7 
-A 3 (l + y 2 ) 3 /^+- ^ <—P^ _cr(l + s 2 ) *2 Udv 
■, [du u ds x 3 (l+y 2 ) 2 dv v ' J 
+ (1 + 2 J Udv) f(e, y) Q'e cos (cv — J vrdv) 
- (1 + 2 j Udv) A 3 (1 + y 2 )^ j(l + S/ 2 )” f - ^ (1 + s 2 ) _i | 
+ (1 + 2 J Udv) f(e, y)Py 2 (l + 5 / 2 )- | @ 
= -^(l+yf(f + -S 
o-a / \du u ds ) 
-a U 
du 
dv 
Udv 
- — X 3 (1 + y 2 ) 3 (1 + s 2 ) - 2 [ 
a / J 
+ (1 + 2 J Udv) f(e, y) Q'e cos (cv — j vrdv) 
- (1 + 2 J Udv) X 3 (1 + y 2 ) 3 1(1 + «/)“* (1 + S *)-*J 
+ (1 + 2 J Udv)f(e, y) Py 2 (1 + s, 2 )" 1 0,