464] 
NOTE ON PLANA’s LUNAR THEORY. 
359 
which is 
a 4 (dii s dii 
— *- 3 (l +7 2 ) 7 hj- + - j- 
cra, \du u dv 
aP 
da 
dv 
— ~ A“ (1+7 2 )'* (1 + s 2 ) ^2 J Udv (destroyed by term infra) 
+ (1 + 2 J Udv)f(e, <y) Q'e cos (cv — J ?*dv) 
— X* (1 + 7 2 ) 1 j(l + s/)' 1 - £ (! + «*)” f | 
— (1 + 7 2 )^ (1 + s, 2 ) 2 j Udv 
+ ^A 2 (l+7 2 ) f (1 + s 2 )~- 2 J Udv (destroyed by term supra) 
+ (1 + 2 J Udv)f(e, 7) P7 2 (1 + 8*)© ; 
or, putting u = - (w 7 + Sw), this becomes 
cl 
+ 2 / +8 “) = £ x5 (1 + (te + 5 
dii . s dii 
dv 
TT /dw, dSw 
(* + * 
— A* (1 + 7)* (1 + s 2 ) * 2 J Udv 
+ (1 + 2 J Udv) f(e, 7) Q'e cos (cv — J zrdv) 
-A!(1+7 2 )" |(1 + s /) ~ (1 + s 2 ) 
+ (1 + 2 J Udv) f(e, 7) P7 2 (1 + sf) ©, 
agreeing with the Formula II. p. 265, except that in Plana’s last term, instead of 
the factor f(e, 7) (= A ;i (1 + 7 2 ) a ), we have the factor A“(l + 7 2 )^. That is, the last 
term, as given by Plana, should be divided by 1 + 7 2 . And this error is introduced