DETERMINATION OF ELLIPTIC ORBITS. 135 



VIII. 



For the second hypothesis. 



-L = 0057613A;(/o 2 /> 3 ) (aberration-constant after Struve.) 

 Pz ) log (-0057613A;) = 5-99610 



A log TI = log TI - log ( TI cic. - 



T = 



calc. 



A log ( Tl T 3 ) = A log TI + A log r 3 

 A log = A log T! A log r 3 



T 3 



A log 4, = -4, A log 



A log B l = A log ( Tl T 8 ) - ^-Wi? 8 - A log - 1 



These corrections are to be added to the logarithms of A I} A 3 , 

 B v B 2 , B 3 , in equations III 1} III 2 , III 3 , and the corrected equations 

 used to correct the values of q lt q 2 , q%, until the residuals a, /3, y 

 vanish. The new values of A ly A z must satisfy the relation 

 A l -\-A 3 = l ) and the corrections Alog-^j, AlogJ. 3 must be adjusted, 

 if necessary, for this end. 



Third hypothesis. 



A second correction of equations III 1 , III 2 , III 3 may be obtained in 

 the same manner as the first, but this will rarely be necessary. 



IX. 



Determination of the ellipse. 

 It is supposed that the values of 



72' 



73 



** 



have been computed by equations III^ III 2 , III 3 with the greatest 

 exactness, so as to make the residuals a, /8, y vanish, and that the 

 two formulae for each of the quantities 1 , s 2 , s 3 give sensibly the same 

 value. 



