42 A NEW METHOD OF DETERMINING 
Thus we have, between the mean and the eccentric anomaly, the relations 
(h—1) ; 
gl — wh. i y | 
ea ae (20) 
y= 7 Um 2 | 
Tn the application of these relations, since 
: (7) ; 
Dy ape SIPs» e aie 
the expression for /’ is changed from 
F=4333 §Gt/c) -v—1 Gi, 8s) yy 
into 
= ISS Ei,e) Vl @H,a)) oS Pee 
The other value of /” is 
F=433 $3 ((4,4,c)) —v—1((Gh,s)) y'. 2. 
A comparison of these two values gives 
Oo Ry ee) aaa a UO 9) 
((4, 0) == 2) IPSs (47,6) = 2.5, Su (4, 7, €) (21) 
In transforming from the series indicated by (7, 7’, c) into that of ((z, /’, c)), it is 
evident that h’ is constant in each individual case, and 7 is the variable. 
Thus we find, beginning with 7’ = h’, 
y (WW) iil (—(Wt—=1) 
) : 
(Gl! .e)) = Me shine (G50, @) Se = 3 din (2, h’—1, c) + ete. 
h h 
eel Gi—(-+-1)) 
— ial ite Siu @ (fe IL, Cc) + ete. 
