THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
797 
Therefore 
Again 
( 1 
1 
^ 1 
a'b /q + a. 
/I 
a'b Kot* 
u 
dt y a 
(«i~«a) 2 /q + «’ 
u 
dt ]~ 
(/q — /Co) 3 ATj + « 
2 i _ 5±4; i=2i . 
b + 
a'b 
k 2 + /3 
A 1 + « Sl -^ + /3V Sl_ b 
(Vi + ZxitCi) b ) r (209) 
Also 
Kl ’+* s )"‘ -ub & —iab/f,))! 
( 210 ) 
Therefore the equation for £ is 
7 rD 4 £=(K- 1 -]-/< 2 )(') 7 1 + 2 /cg£ 1 ) + 2 «: 1 T 7 1 + the same with 2 for 1 
a'b 
Therefore 
h-AL=: 
r, 
a'b t a 2/c 1 (/c 1 2 — k 2 ) 
ft 
Therefore 
(' c i + ^) + 2«i — 2 /Ci(/Ci + k 2 ) 
2/Cj I 
2/1 O 2 I O 
7 v /C-p — K 2 AtCyj j 
-f&C. 
i-rr+fc 
K i- K i\ *i-*s/ 
r 2 
(/q — /c 2 ) 2 (/q — /Co ) 2 
/ 1 
a'b 
/i 
dA s '\ 
a'b 
1 
3 
(«i-* 3 r 
w 
dt / a 
(/Ci-/c 2 ) 2 
( 211 ) 
The same results might have been obtained from the equations to D hj, DSp 
Terms depending on the variation of b. 
By symmetry with ( 211 ) 
n dL\ _ b'a / 1 clLf _ _ b'a 
\Z X clt )b (aTi —^ 2 ) 2 ’ dt /b (« 1 —Ko) 2 
( 212 ) 
By symmetry with ( 210 ), and putting 
(*2+/3) 
1 ZZ/X _ b'a /c 2 + a 
.Z^ dt J /Cp | _ ££ 
— (#Co + a) for (Kq-b/3) and — (fq-J-a) for 
/i_ = 
\X 2 ' clt j b 
b'a /q + « 
(/q — /q) 2 /c 2 + a 
(213) 
We now come to a different class of terms, viz. : those depending on y, g, 8 , cl. 
MDCCCLXXX. 5 K 
