24] IN A PARTICULAR CASE. 187 



If this be converted into numbers by substituting the value of m = 0'0748013, 

 we find 



.9-1-00399,91722,8, 



which differs from the true value in the eighth place of decimals. 



*M 



If we take m= and develop the value of g in powers of m. we 



1 m 



find 



3 57 123 1925 25667 268309 

 ' > 



2048 24576 



and substituting the value of 



iii = 0-08084,89030,52, 

 we find gr = 1-00399,91591,1, 



which is considerably nearer the truth than the value found from the series 

 in powers of m. 



The numerical values of the successive terms of the series for g 1, 

 in terms of powers of m and of m respectively, are given in the following 

 comparative table : 



111 powers of m. In powers of m. 



m~ '00419,64258,6 nr '00490,24088,4 



m 3 - 11,77117,9 m 3 - 94,13416,4 



m 4 - 6,67712,1 m 4 4,10574,2 



m 5 - 1,12023,4 m 5 - ,32469,2 



m 6 - ,14203,4 m 6 ,02916,8 



m 7 - ,01479,0 m 7 - ,00102,7 



00399,91722,8 '00399,91591,1 



This shews that the development in powers of m is much more advantageous 

 than that in powers of m. 



The same thing likewise holds good with respect to the value of c, 

 which determines the motion of the perigee. 



The following is a similar table, shewing the numerical values of the 

 successive terms of Delaunay's series for 1 c in powers of m, and of the 

 terms of the corresponding series in powers of m : 



242 



