1159 



For the solution of the equations (l) and (2) we started from the 

 approximations ') 



loga, = 9.5997740—10 e, = 0.00404164 



log a, = 9.8015496—10 e, = 0.00936330 



% a, =0.0042524 e, = 0.00059680 



% a, = 0.2494696 e, = 



The coefficients of Laplack corresponding to these values of a, 

 were derived from those given by Souiu.akt by the ap[)iioation of 

 the corrections necessary to reduce from Souillart's values of the 

 ratios of the mean distances to ours. Then with these coefficients 

 the Nevvcomb's operators occurring in the formulas (1) and the othei- 

 coefficients of these formulas were computed, and the values of n'i 

 were solved and from these the values of a/ were derived. The 

 coefficients of Laplace were then reduced to these new values of 

 a/, and a second approximation of ,a', was derived, which differed 

 only very little from the first. The corresponding values of a/ were 

 considered as final, and were used as the basis for an entirely new 

 computation of the Laplace coefficients. Then with these coefficients 

 we computed the operators necessary for the equations (2). These 

 equations (2) ai-e not, like (1), independent of each other, but must 

 be solved by successive approximations. The approximations, which 

 converged very rapidly, were continued until the ninth decimal 

 place of e, was no longer affected. The values of e^ thus derived 

 are the definitive ones. They were substituted in (1) instead of the 

 original approximations, but this did not produce any change in 

 the values of ,a',- and a,. 



The elements of the intermediary orbit are thus determined. The 

 different terms of f/'/ are given below. The terms marked "ackr 

 are the second and third of the formula (1), "x " is the fifth and 

 "sun" the fourth term. The effect of the last term is given for each 

 perturbing satellite separately. The quantities x and e/ are considered 

 to be of the first order, the masses and J, are of the second order. 

 A term containing the factor me'' is thus of the fourth order. We 

 found ') 



*) See Leiden, Annals XII, 1, pages 52 and 53. 



') The computations were made with two more decimals than are published 

 here. Consequently it may happen that the sum of the printed numbers differs 

 one unit in the last decimal place from the printed sum. 



75* 



