ÖPVERSIGT AP K. VETENSK.-AKAD. FÖRHANDLINGAR 1 900, N:0 9. 1073 



Hence we have 



h = V3,i/. a . 



The excentricity is in value near to unity. The greatest 

 vallie of the quotient h : u is 



max.- = V0.12 = 0.35 



a 



If 1.1 designs the earth, hence 



^1 = 1: 320000 , 



then 



-= 0.00306 . 



a 



Is il the mäss of Jove, then the major axis is 19 times 

 the minor one. 



If we take the other root 



2) v'^=l — b.lb^i. 



then 



and we become; 



.2 — 64 848 ,, 



«2 = <H (/?;- + /?') 



Both axes remain finite for evanescent values of /u. The 

 major axis is the double of the minor one. 



Hence it is through any point sufficiently near to L^ or 

 L^ possible to draw two curves, corresponding to two difFerent 

 periodic solutions of the problem. It is to be observed, that 

 the values of the half-axes of the ellipses in the two cases 1) 

 and 2) are not directly comparable with another, ß^ being in- 

 deed dependent not only on the initial coordinates, but also on 

 the value of the root v^ that has, in the two cases, diflFerent 

 values. 



It is easy to express a and h directly as fonctions of the 

 initial coordinates. 



