ÖFVERSIGT AP K. VETENSK.-AKAD. FÖRHANDLINGAR 1000, N:0 J). 1077 



For such values of (7, which are a little greater than this 

 minimum value (33), tlie limiting curve consists of two ellipse- 

 like branches surrounding the points L^ and i-, the equation 

 of which are 



fjin d-P d-P 



(35) c7-3(l+rt=^%« + 5S^-f + 25ji?1- 



In comparing this ellipse with the ellipse (25) we find that 

 the axis of the ellipse are in the same direction as the axes of 

 the ellipse (25). We find thence, that the periodic curves d 

 Surround the ellipses, which constitute the limiting curve for 

 values of C somewhat greater than 3(1 + [.i). 



Meanwhile it is also to be observed, that when 6'<3(l+.«)j 

 when there is no limiting curve, there are, nevertheless, periodic 

 curves namely the family e of orbits. 



M. BuRRAU has first observed that the existance of a limit- 

 ing curve is not a necessary condition for the appearance of 

 periodic orbits. 



The period of a revolution of the little mass m in it& 

 orbit may easily be found. 



Designing the time of a revolution in any curve of the 

 family d with r^ and in a curve of the family e with x-, we 

 have genei'ally 



^= — , 



V 



whereas the time T of revolution of m^ or m^ around the centre 

 of gravity is given through the equation 



j. '2Tt 



It is hence generally 



(36) T; = yL±J!^.T. 



V 



If we Substitute in this equation the values of v correspond- 

 ing to the cases cZ and e, we find the following approximate 

 values for the periods. 



