58 A NEW METHOD OF DETERMINING 
‘When the numerical value of (#7) has been found from this equation we trans- 
form it into another in which both the angles involved are mean anomalies. For this 
purpose we compute the values of the -/ functions depending on the eccentricity, ¢, of 
the disturbed body just as has been done for the disturbing body. The values of the 
(0) (1) 
J functions can be checked by means of the values of J,,, J,,., given in ENGEL- 
MAN’S edition of the Abhandlungen von Friedrich Wilhelm Bessel, Erster Band, seite 
103-109, or by equations (30),. 
Thus by means of the equation 
(m-+1) a (m—1) en (un) 
TN hr =< hd A 
(m) (0) (1) 
we are enabled to find -J,, if J), J), are known. 
It must be noted that the argument of BrssEL’s table is 2.5, or 2.hd, or he. 
Go) 
Thus if it is sought to find the value of -/,,, we enter the table with 2.2 or 2e as the 
argument. 
When we need the functions for h from h =—1toh=4, we must find the 
4 a 4 HO 2 (—2) 
yalues of a se» ad es ates the een and — td. 
(1) 
The values of 3. J. 
bo 
(0) (3) 
and J, we take from the table. ‘To. find J. - we have 
oy z 
e 
oy 
oe (1) 2 Fe 
a ne 4.5) 4g 
(4) 2 of 1 7° 
Pe ae eae le 46 1 45 | 
(2) 
For J... we have 
as 
(2) (0) 1 (1) 
SI og SS td eae) et 
385 385 3 85 
(2) 
And for J, we have 
z 
(2) O 7 
I, — J, ale 
z z mo 
