201 



directed towards the centre and to be a function of r only, so that 

 it can be derixed from a potential and we shall ai)|)ly Gauss' 

 theoi-em for the integral of the normal component of the force over 

 a closed surface (force-current). 



The equations of motion thus have the form 





Mm .v/i 



,,«-1 



dV 



{h 



n) 



The motion takes place in a plane. In this plane we introduce 

 polar coordinates. Then the two first integrals can be written down 

 at once 



m 7-^ (f =z 

 By elimination of <f> we find for r 



2E 2V 



0' 



m r 



- \/Ar'' 4- 5r4-" — C^ 



(2) 



That r may oscillate along the trajectory between positive values, r 

 must have real and alternately positive and negative values. Therefore 

 the quantity from which the root has to be taken must always be 

 positive, between two values of r for which it is zero. The discus- 

 sion of the latter cases is to be found in appendix (1). There we 

 shall also consider the case n = 2 for which (J) has to be replaced by 



V =.it Mm log r 

 and (2) therefore by 



r = — y (tr^ — j3r' log r — 



(2^ 



where 



2E 

 a:= — , ^=2xM 



in 



0» 



The result of this discussion is 



14 



Proceedings Royal Acad. Amsterdam, Vol. XX. 



