THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
799 
Hence 
/ 1 clL^\ tc° / 1 dLn'\ AT-J T - CL 
\L{ dt J y ^'k 1 —k 2 \L( dt ) y ^ k x —k 2 
(216) 
Terms depending on §. 
These may be written down by symmetry. 
— S is symmetrical with y. Hence writing —(/q + a) for k. 2 -\-/3, and — (k 2 -\-u) for 
(/q-|-/3), we have by symmetry with (216) 
/ 1 dL-\ _g ATj + a 
\A^ dt )$ /q k% 
And by symmetry with (215) 
/ 1 dL(\ _g *q + « 
dt J g -■ /q /Cg 
1 clL, 
Lc, dt I s 
= —8 
K 0 + « 
(217) 
1 clL 2 \ g ~^ 
Lq (Lb J § fCy K g 
(218) 
Terms depending on g. 
Here 
S——gC, u=—grj, cr=0, a=0 
S =-g(J+ a7 ?) S=—gb 7] 
Si= g(*i— a )Vi ^i--—g h Vi 
S 2 , S 2 have similar forms with 2 for 1 
Clearly 
(*.'+|)s.=o 
(219) 
Thence 
-D%= 2 K 1 (/< 1 + Ko)(Ko + a )>h+ the same with 2 for 1 
1 A _ y «2+ a , y *1 + “ 
~A2 g =4r—- +4 
/q — K 0 K.C, — K-, 
K 1~ K 2 K \ — K 2 
h . j, b j, b 
, since t >l =z 1 - r y—, 43=%“'7 
V 2 + « 
+ 54 
5 K 2 
s 1 -'brs 1 =2 gKl % 
Therefore the equation for 2 is 
