Orbits in the Field of a Doublet. 1009 



At the same time, the variation of can be obtained 

 from the equations 



sin 0/2 = \/ 1] ^j-sn [4>, y'^YJ 

 r = n sec ( v2m((f) - fa)), 



or if the relation between and t is more convenient, from 

 the equation 



t - t x = (n 2 / s/ 2fim) tan ( ^2m (<j> - fa)) . 



These equations can be deduced from the relation 



U/V = rdd/dr 



as before. The path therefore, in general, waves backwards 

 and forwards between #=+a a finite number of times 

 (which may be zero), and has the asymptote 



= Q , p = (-du/d0) u = Q , 

 given by 



sin 0J2 = ^/!5±A m (fr + ,r/2 •Si). 



A typical orbit is appended in fig. 4. 



JFis. 4. 



There is, however, one particular case. If 



hi — 2//, cos #i = 2fi, 



then u — ir and the transverse velocity disappears when the 

 line = ir is reached. Unless therefore the particle goes off 

 Phil. May. Ser. 6. Vol. 43. No. 257. May 1922. 3 T 



