800 
MR. G-. H. DARWIN ON THE SECULAR CHANGES IN 
Therefore 
Again 
and 
1 dL-, \ b 
=g; 
l_dLJ\ __ b 
Zi dt ] g & a:i —k 3 ' \Z a dt J g ^ K i~ • 
d 2 
v H"b/^o b To a v 
k 2 + /3 
=«fe> by (219) 
Therefore the equation for £ is 
(220) 
—D 4 £=2/c 1 (k: 1 + k: ; ,) 77 1 + the same with 2 for 1 
gb 
Hence 
Therefore 
—A£. — 
gb t g Kj —« 2 /C 2 — /C 1 
1 dL{ 
LJ dt J g ^/c 1 — k* \LJ dt J g & H — ^2 
1 dL' 
= -g; 
( 221 ) 
The same results may he obtained by means of the equations for D b y, Dbp 
Terms depending on d. 
These may he written down by symmetry. 
— d is symmetrical with g. Therefore by symmetry with (221) 
a 
and by symmetry with (220) 
1 dLJ\ _ l a / 1 dL<J\ _, a 
LJ ~di ( \Z? "dTA -Cl («i-* a ) ’ 
/I 
\Z X dt ] 
= —d- 
/£-, —/Co 
1 dZ 2 \ _^ a 
-^2 dt J a fCy Key 
. ( 222 ) 
(223) 
This completes the consideration of the effects on the constants of integration 
L y , L. 2 , Ly, L.-J of all the small terms. 
Then collecting results from (205-8, 210-13, 215-18, 220-23), 
