﻿334 
  Mr. 
  G. 
  W. 
  Walker 
  on 
  

  

  of 
  the 
  orbit 
  of 
  a 
  particle, 
  having 
  electric 
  inertia, 
  round 
  a 
  

   fixed 
  centre 
  which 
  is 
  at 
  rest 
  in 
  space. 
  

  

  Let 
  v 
  = 
  resultant 
  velocity 
  at 
  any 
  point 
  o£ 
  the 
  orbit. 
  

   p 
  = 
  radius 
  of 
  curvature. 
  

   r= 
  radius 
  vector. 
  

   p 
  = 
  perpendicular 
  on 
  tangent. 
  

   fx/r 
  2 
  = 
  attraction 
  to 
  the 
  centre. 
  

   m 
  1 
  = 
  Ion 
  gitudinal 
  inertia 
  = 
  m 
  (l 
  + 
  kiV 
  2 
  \c 
  2 
  ) 
  . 
  

   m 
  2 
  = 
  transverse 
  inertia 
  = 
  m 
  (l 
  + 
  k 
  2 
  v 
  2 
  /c 
  2 
  ) 
  neglecting 
  

   squares 
  of 
  v 
  2 
  /c 
  2 
  . 
  

  

  The 
  orbit 
  is 
  plane, 
  and 
  resolving 
  along 
  and 
  perpendicular 
  

   to 
  the 
  path 
  we 
  get 
  

  

  dv 
  a 
  dr 
  ,_ 
  

  

  ds 
  r 
  2 
  ' 
  ds' 
  

  

  ft,E 
  

  

  r 
  2 
  ' 
  r 
  

  

  and 
  m 
  2 
  v 
  2 
  /p= 
  4-~ 
  ( 
  2 
  ) 
  

  

  Integrating 
  (1) 
  we 
  get 
  

  

  where 
  a 
  is 
  a 
  constant. 
  

  

  From 
  (2) 
  m 
  (v 
  2 
  + 
  k^/c 
  2 
  ) 
  — 
  ^f 
  ~ 
  *, 
  since 
  P 
  = 
  r 
  j-- 
  

   Let 
  u 
  = 
  l/r 
  and 
  ?/ 
  = 
  l/a, 
  

  

  .\ 
  m 
  (v 
  2 
  + 
  ^Jc^/c 
  2 
  ) 
  = 
  2/j,u—fiu 
  , 
  

  

  and 
  m^ 
  + 
  hv^), 
  ^g, 
  

  

  