THE ELEMENTS OF THE ORBIT OF A SATELLITE. 8G1 
assign to i an average value, say I, and neglect the solar tidal friction in assigning a 
value to n. 
Then 
n=n o+l( l ~€) 
Let 
kn 0 -\-l = K, so that u = ~(k — £) 
Hence the last term in (303) is approximately equal to 
= — 7Lf2 n sec I 
dZ 
= 7 sec I 
I/i-Ai/I 
jAt ) 2« ! \f 
In the last term n has been written for (k — £)/ic. 
Now let 
K= 
3v(f3- 1 ) + 2^(p- 1 ) + Xr 1 
7kI2 0 sec I+“ 2 L> ?o(^ — ^ n ) 
Then 
,7 in., y 
n secr 
(304) 
This formula will now be applied to trace the changes in the eccentricity of the 
lunar orbit. 
The integration will be made over a series of “ periods ” which cover the same 
ground as those in the paper on “Precession;” and the numerical results of that 
paper will be used for assigning the values to n and I. 
kn 0 is equal to 1 / p , of that paper, and therefore k is 
First 'period of integration. 
From f=l to '88. 
I is taken as 22°. In “Precession” g was 4 - 0074, therefore kn 0 —'24954 and 
k=1 ’24954. Also Jcf2 0 =Jcn Q Il 0 /n 0 , and ^ 0 /n 0 =^l/27'S2. 
In computing for § 17 of “Precession” I found at the end of the period 
log nJn 0 ='lS971. 
Using these values I find 
/ \ 71 - 
, / 11 sec 1 
Sl0 W = ' 00G92 
Also 
K=-01980+¥i? 0 (1-£ U ) 
5 s 
MDCCCLXXX. 
