Xnmerical Calculation of the Jacobian Elliiisoids. ^3 



By appljàng (33), it can bo proved that this value of z^ is correct to 

 the seventh decimal figure, so that the approximation is sufficient, 

 if the accuracy required for //s, s's, /^, etc. be that attainable by 

 the use of seven-figure logarithms. Now (37) gives the same 

 values of « and ß as shown above, and (41) gives 



U = 0-09485085. 

 As the last example, take 7^=0 '(3, to which corresponds 



h, = 0-000000004064856. 

 The first approximation for z^ as given l)y (17) is 



z, = 11-047. 

 B}^ means of (33), we find that the second approximation is 



z, = 11-0505, 



and that the third is 



z, = 11-0505035, 



which can be proved to be correct to the sixth decimal. 

 From (23) and (41), we find respectively 



.Q = 0-0005114177, 

 and /2 = 0-0005114175. 



10. To compare the result with that obtained by Darwin' \ 

 Table II was calculated thus: — 



In Darwin's method, the auxiliary quantity to which arbitrary 

 values are attributed is an angle r which is defined in our notation 



by 



COS/' = p^, 



or cosr = -^A^'A = A^oiMl. C43) 



From the computed values of ,oi=cosr, the value of Ji corresponding 

 to an assigned value of r was first interpolated, a correction was 

 added, when necessary, to this value of h so as to satisfy (43) 

 accurately, and then, Ijy tlie usual method, the corresponding 

 values of Oj, J^, Oi and -| i? were interpolated from Table I. The 



1) G. H. Darwin, /. c. 



