14 A NEW METHOD OF DETERMINING 
: : 4 
In this expression for ce 
of the disturbed body; y. is a constant and of the order of the square of the eccen- 
tricity of the disturbing body. 
In the method here followed the circumference in case of the disturbed body will 
2 . ° 
) »% Y and 9, are functions of the eccentric anomaly 
be divided into a certain number of equal parts with respect to the mean anomaly, g. 
. : 2 2 360° 360° 
The various values of g will then be 0°, = Bs a6 5 8b ene —1. - : 
nm 
For each numerical value of g, the corresponding value of ¢ is found from 
g =e&—esine. 
Before substituting the numerical values of cos <¢, sins, for the n divisions of the cir- 
cumference, the expressions for 7, 71, 9, will be put in a form most convenient for 
computation. 
Let 
asin la) 20 g — 2ak cos (II — XK ) (3) 
p.cos P = 2a cos ¢' k, sin (II — K,), 
and 
HSjeom le |) 
See ) 
yi =f.cos F; J 
we find 
By =fsin f= 2a. cos p. cos 9’. k, cos (11 — K,). sine + pcos P. cos e — ep. cos P 
yi =f COS i= (24? —psin P). cose — 2x. cos p.ksin (Il — K). sine + ep.sin P. 
And from these equations we find, since 
f.sin (#— P) = f.sin F'cos P —f cos FP’. sin P 
J .cos(#— P) = feos #’.cos P + fsin F’. sin P, 
f.sin(#— P) = [2a. cos ¢?. cos 9’. k, cos (11 — Kj). cos P 
+ 2a.cos ¢.k sin(I—). sin P]. sin e + [ _ 202% sin P| . COS E—EP 
f. cos (#’— P) = [2a. cos. cos 9’. k, cos (Il — K,).sin P 
/ 
. — ° é 
— 2a.cos ~.k sin ((I—FK). cos P]. sine + 2a". .cos P. Gos é. 
