THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
807 
r= 1 
\k dtj2n 
r A ^\E 
\k dtj2n 
\k dt)2n 
\k dtJ2n 
III (SI 
sin 4f : 
7"' 
(sin 4f x — sin 2g x + sin 2g) + - 
T 
/ 
2g) + - sin 2g 
T 
sin 4f x 
(sin 4f a + sin 2g 1 — sin 2g) — 2 — sin 2g -f j sin 4f 
sin 4f x 
T / 
(sin 4f x + sin 2g : — sin 2g)-sin 2g 
, /\ Q 
£). 
!- 
sin 4f L 
(244) 
If the viscosity be small we have by (179), (227), and (230) 
x k dt)2nl-\ 
1 + f 
^ \7 dtj2n 1 —A, 
_/l dg \m 1 ~ t 
\n 1 — A 
H-^(f)‘ ' 
s= 
1 
7’ dt 2n 
1 —A 
1 — 9 A — -L— 
‘ * T 
k dt 2n 1 —A 
(245) 
I think no confusion will arise between the distinct uses made of the symbol g in (244) 
and (245); in the first it always must occur with a sine, in the second it never can do so. 
[If r be zero 
bG + aD =^i)("J( T >> 
and by (232), (237), (240) 
tC 
+b— (i+m) 
ah '- ba H-f)!( T fTc+n>> 
Therefore we have 
(bG + a D) (a-fb) -f a'b — b'a=0 
This was shown in (226) to be the criterion that the differential equations (224) 
should reduce to those of (71) and of (29) of “Precession,” when the solar influence 
is evanescent, and the above is the promised proof thereof.] 
5 l 2 
