THE ELEMENTS OP THE ORBIT OP A SATELLITE. 
737 
For the moment let I= \i, then since ns= Pp — Qqe N , and since P— cos I, Q— sin I, 
therefore drsjdl =—k, and therefore dzs^/dl — — izs’K. 
Hence (see slow semi-diurnal terms) 
^ K =P 3 Qp^+P 2 (^-3Q 2 )p d qe N -3PQ(P 2 -Q z )pYe^+Q 2 {SP 2 -Q 2 )pq s e 3N -PQYe^ 
c/V= same with — N' for N 
Hence 
Wl =[P 6 ^y + P i (P*-BQ*)yq 2 J r -* , + 9P 2 Q 2 (P 2 — QYpYe* N - N,) 
+ <F(3P 3 - Q' 2 )y q 6 e^- N,) + P 2 Q Q q s e i(N - N,) ] 
^) Wi= - r P*(^_ 3 Q 3 )V 2 + 18 P 2 0 s (P 3 -(? 3 )W 
+ 3Q i (SP*-QfpqS+iP !s Q et - 
• V _ 
< /.(e)w 1 = 
Adding 
e -gi 
2^7-1 
4 P Q Q 0 y 7 q +4 P\P 2 -3 Q 2 )Yq S + 3 6P*Q\P 2 - Q 2 )Yq 5 
+ iQ i {3P’— Q-ypq’+iPtQ* ^ 
— 1 8 P 2 Q 2 (P 2 —Q' 2 )Yq S ( P 2 —q 2 ) — $ 4 (3P 3 — Q 2 ) 2 pq° (3p 2 —(f) — 4 : P 2 Q r pq r ] 
Then let 
^i=l[ 4 P 6 Qy-P 4 (P 3 - 3 g 2 ) 3 p 4 (p 3 - 3 ^)- 18 P^ 3 (P 3 -^)W(p 2 ”/) 
-(R(3P 3 - Q 3 )Y(3p 3 ~7) ~ 4P 2 Q7 6 ] . (50) 
and we have 
<£(2V, e)W 1 =2(^ 1 G 1 sin gl sin j ...... (51) 
Sidereal diurnal terms (n). 
W 2 = G[t««:(to-W — KK) Ts'k' izs'zs' — K k')c~ S -f- 73k(zSTS —‘ Kk) Ts'K (tS* eg' - K K )e g ] . (52) 
Here the epoch is wanting, so that </>(iV, e) = <f>(N). 
