DETERMINATION OF ELLIPTIC ORBITS. 133 



V. 



Corrections of the geocentric distances. 



Components of @. 



(This equation will generally be most easily solved by repeated 

 substitutions.) 



2 A<? 3 = C 3 - 



VI. 



Successive corrections. 



A<? 2 , Ag 3 are to be added as corrections to q l9 q 2 , q s . With the 

 new values thus obtained the computation by equations III^ III 2 , III S 

 are to be recommenced. Two courses are now open : 



(a) The work may be carried on exactly as before to the deter- 

 mination of new corrections for q lt q 2 , q s . 



(b) The computations by equations III', III", III'", and IV may be 

 omitted, and the old values of a l} b lt c l} a z , etc., G, and L may be 

 used with the new residuals a, /3, y to get new corrections for q lt q z , 

 q% by the equations 



where Dq 2 denotes the former correction of q 2 . (More generally, at 

 any stage of the work, Dq 2 will represent the sum of all the corrections 

 of q z which have been made since the last computation of a lt b l} etc.) 



So far as any general rule can be given, it is advised to recompute 

 a v 6 15 etc., and G once, perhaps after the second corrections of q lt q 2 , 

 <7 3 , unless the assumed values represent a fair approximation. Whether 

 L is also to be recomputed, depends on its magnitude, and on that of 

 the correction of <? 2J which remains to be made. In the later stages 

 of the work, when the corrections are small, the terms containing L 

 may be neglected altogether. 



The corrections of q lt q 2 , q 3 should be repeated until the equations 



a = /3 = y = 



