286 APPENDIX. 



absolute values of S greater than 0.03, and for values of x considerably greater 

 than 90, the terms here given woitld not be sufficient. In such cases the 

 method of 37 and the following articles should be used. 

 Example. For HALLEY S cornet^ 



logtf = 8.5099324, and t = 63&quot;.43592, we have 



by table II ff , w = 99 36 55&quot;.91 



and by table Va, A = -f 417.45 1st cor. + 22 30&quot;.63 



#= + 3.111 2d cor. -f 32&quot;.57 



v = 99 59 59&quot;.ll 



which, rigorously, should be 100; so that d is in this case too great. 

 Inversely, we find, for v= 100, 



v = 100 00&quot;.00 



4 = 4-426.78 1st cor. 23 0&quot;.83 



B = + 0.297 2d cor. 3&quot;.ll 



w= 9936 56&quot;.06 



which agrees nearly with the preceding value. The change of the table to the 

 present form has been made under the supervision of D ARREST. 



39. 



When table Ha is used instead of BARKER S table, to is the value of v, which 

 corresponds to the argument 



at 



40. 



If we put 



l 



E 

 j-^t 



1-jA+O 



-i 



the formulas for computing the true anomaly and radius vector are 



tan i v = E, y tan w 



