ÖFVERSIQT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1 "JOO, N:0 1). 1069 



to tind tliem, a necessary result indeed, there being no such 

 orbits for this value of i(. 



Hence, in the points L^ and X-, there are periodic Solu- 

 tions only for small values of i-i. It is then advicable to ex- 

 pand I in powers of /.i. From (16) we obtain now for one root 



(18) I- = — 6.75 ,« — 116.9375 ibl- 

 and for the other 



(19) Z2 = — 1 + 5.75 ^i + 116.9375 ^<2 



For each value of X we get a corresponding value of A: B, 

 and the general integral has the form 

 i 4 



(20) 



§ = ^4 



e ' 



the values of Ai and Bi being connected through 



Four of the coefficients Ai and Bi are arbitrary. I will 

 regard B^, B^, B^ and B^ as those arbitrary constants. The 

 corresponding values of Ai are then obtained through (21). 



Now let Xy and l^, be two conjugated purely imaginary 

 roots, and put 



.^- = - ^^ 



so that »'j and V2 are real. It is then 



d^iJ 



oa- 0«- 



Ö2ß 



3a9ö 2V1 + f^V2\f 



3a^ öa" 



V-1, 



where v^ 



Öfversigt af K. Vet.-Akad. Förh. 1900. Arg. 57. N:o 9. 



