1006 Dr. Dorothy Wrinch on the 



Motions which are restricted to half the Plane, including 

 one Periodic Orbit. 



We have now considered the cases when 



0< 2^00*0! — h 2 < 1. 



We have considered in detail the boundary case 



2 JUL cos 6 Y — /*! 2 == 0, 



in which motion is restricted to the line = 0. 

 The particular features of the case 



2/jb cos 0i — A 2 = 0, h 2 = 2fju cos 0, 



also call for attention. Here the motion is restricted to the 

 positive side of the plane, given by 



Referring to the equation 



we get in this case 



r = 0, r = Ux ; 



so that the radial velocity is constant. Griven then an 

 outward radial velocity initially, the carve touches the lines 

 + 7r/2 alternately, and the distance at any time from the 

 origin of a particle describing it is given by 



r-r x = Ui(«-*0 



if it is projected from r ± with radial velocity Ui at fa. 

 If ?'•=— Ui, the particle approaches the doublet with 

 constant radial velocity along a wave path which alternately 

 grazes 6= +7r/2. 



The equation to the orbit if f = Ui>0 results from the 

 equation 



-duludO = drlrdd = Vi/rd = "' / —\^ =_ 

 ' Uy/2/i \/cos0 



duldd = ~- / v'cosfl 



in the form 



Hiu 0/2 =!«!.(+, 1A/2), 



u — u 



V-2 



