THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
745 
Then since 7 x'=Pp — Qqe N ' therefore 
dza' 1 
dN’~ x /-1 
Qq, and similarly 
dm' _ Qq d/c' _ Pq did _ Pcq 
dP'~ — dN'—~y/-V riQV ,— v /-r 
when IV'=0. 
Also after differentiation when A r =0, =—=cos ^+_/), /c=K=sin \{i-\~j) 
In order to find djjdt we must, as before, perform <£(fV, e) on W. Then take the 
same notation as before for the W’s and w’s with suffixes. 
Sloiv 
semi-diurnal term. 
r,dm' 
=Ts dW= 
m 7 Qq 
y-i 
and " 
1 7 
2y-i- CT 
Q 
also <p(e)e zw ' 
-0— 2fi — 1 
V-1 
Hence 
<r 2 t 
8 ? n 
c ' VVl - 2v /^I 
-73— — TTT .— 
and 
4£„-: 
V 
sf, 
<£(iV, e)W I =CT 7 «:F 1 sin 2f x . 
Sidereal semi-diurnal term. 
dw n g 3 / d/d cfe'\ 2nrV . 
jw= 2 * k \” , AN'+ K m’r - 7 = 1 ^ 2 +^?) 
and since <£(e)W n =0, therefore 
e) W h = 2ct 3 k 3 F sin 2f 
2cy 3 /c 3 
, - I'" 
semi-diurnal term. 
By symmetry 
</>(iV, e)W in =sTK 7 F 2 sin 2f 3 
>S7oir diurnal term. 
d 
dW- 
dm 
rL®' V=3A f+^fr -q^=pKQq-7zPq) 
€ ) w i == "“2 v/ —-T (3<y ~ ct°/c(ct 3 —3/c 2 ) 
(^(A 7 , e)Wj— •—ct 5 k-(ct — 3k 2 )G l sin g x 
and 
