112 SOME METHODS OF COMPUTING THE RATIO OF 



The last values being taken from Table III. 



log. '^ = log. li ^ = 9.95367 log. ^J = 0.27043 



With these is obtained from (57) a computed value of log. q = 

 9.319, instead of the assumed value log. g = 9.265, indicating 

 that the assumed value log. g = 9.523 was too small by about 

 0.050. Taking, therefore, for a corrected value, log. p = 9.573, 

 and using the new values of ^^ and — Ij in (4) and (28), they 

 give log. ^ = 0.11546 and log. £^ = 9.74500. 



Second Approximation. 

 log. g 9.573 r 1.0548 TFT^l 9-2507 ^, 9.99768 



log. g' 9.317 r' 0.8993 pr^l 9.3070 j 9.99698 



log. g" 9.688 r" 0.7712 TFTFni S-S^SG ^, 9.98934 



From the latter are derived log. ^ =9.95354 log. g =0.27041, 

 which give a new computed value, log. p' = 9.3093, assumed log. 

 p'= 9.3170; and the corrected values log. f =0.11541, and 

 log. J = 9.74494, differing in the last decimal place from the pre- 

 vious values. 



In these two assumptions the elements have been assumed as 

 parabolic ; further correction may be made by using the more gen- 

 eral method (IV.). 



Third Approximation. 

 log. g 9.56436 r 1.05262 v' —v \\ I'l 53 log. sin.'' ^" 6.59134 



log. g' 9.30930 r' 0.90063 »" — v 13 44 49 log. sin.' g 6.63464 



log. 9" 9.67977 r" 0.77297 v" —v 24 56 42 log. sin.' ^' 7.21514 



log. y 0.0030007 log. ^^ 9.9535654 Computed log. g' 9.30893 



log. y 0.0106495 log. ^ 0.2704277 Assumed " 9.30930 



log. y" 0.0023236 



Whence the third approximation, taking into account the ec- 

 centricity of the orbit, gives log. 7 = 0.1154807 log. ~ 9.7449467; 



