ÖFVERSiaT AF K. VETENSK.-AKAD. FÖRHANDLINGAR lOOO, N:0 1). 1()B8 



Indeed, if such an orbit exists, when only the first powers 

 of S and iq be retained, there exists also a corresponding peri- 

 odic orbit, when all powers of these quantities are taicen into 

 consideration. On the contrary one can not be sure, that all 

 periodic orbits corresponding to ß7iite values of ^ and i] will 

 also occur, when these quantities are infinitesimal. 



If we retain then only the first power of § and iq in (5) it 

 is obvious, that, in order that ^ and iq may remain small quan- 

 tities, we must have 



(6) 



da dh 



From these equations the position of the point (a, b) is 

 determined. 



The Solution of these equations may be very simply obtained 

 in the following manner. 



It is 



2 



Qt={a-r,y- + b'' 



(a + r^f + 52 , 



and thence 



?2 



da 



di2 a — r^ dQ a + r^ 



(7) 



or 



~~ dh ~ dq^ Q, dg^ q^ " 

 From these equations it follows, that it is either 



dn_dn_^ 



dQi ~ dQ^~ ' 



(8) O 



« — ?'j a + 7\ 



Q1Q2 



?i Q2 



h_ b_ 



Qi ' Q2 



The equations (7) may be written 



Qi ^2 



(r, + r^) = — 



b 

 QiQ-2 



