﻿332 
  Mr. 
  G. 
  W. 
  Walker 
  on 
  

  

  Starting 
  thus 
  with 
  longitudinal 
  and 
  transverse 
  electric 
  

   inertia 
  given 
  by 
  m 
  1 
  and 
  m 
  2 
  as 
  functions 
  of 
  the 
  resultant 
  

   speed, 
  and 
  employing 
  what 
  I 
  hold 
  to 
  be 
  the 
  correct 
  pro- 
  

   cedure 
  in 
  forming 
  the 
  equations 
  of 
  motion, 
  viz., 
  resolving 
  

   along 
  and 
  perpendicular 
  to 
  the 
  resultant 
  direction 
  of 
  motion, 
  

   we 
  can 
  proceed 
  as 
  follows 
  : 
  — 
  

  

  Let 
  the 
  origin 
  be 
  the 
  sun 
  moving 
  in 
  space 
  with 
  com- 
  

   ponents 
  of 
  velocity 
  w, 
  v, 
  w, 
  which 
  are 
  constant, 
  and 
  let 
  

   #, 
  y, 
  z 
  be 
  the 
  co-ordinates 
  of 
  a 
  planet 
  relative 
  to 
  the 
  sun 
  

   and 
  referred 
  to 
  axes 
  through 
  the 
  sun. 
  The 
  components 
  of 
  

   relative 
  velocity 
  of 
  the 
  planet 
  are 
  

  

  a, 
  y, 
  z, 
  

  

  and 
  of 
  velocity 
  in 
  space 
  x 
  + 
  u, 
  # 
  + 
  v, 
  z 
  + 
  w, 
  with 
  resultant 
  

   say 
  V. 
  

  

  The 
  components 
  of 
  acceleration 
  are 
  

  

  x, 
  y, 
  z. 
  

  

  The 
  acceleration 
  along 
  the 
  resultant 
  direction 
  of 
  velocity 
  is 
  

  

  { 
  (x 
  + 
  u)x 
  + 
  (y 
  + 
  v)y 
  + 
  (z± 
  w)z}/Y. 
  

  

  and 
  if 
  the 
  components 
  of 
  force 
  are 
  X, 
  Y, 
  Z, 
  the 
  component 
  

   along 
  the 
  direction 
  of 
  V 
  is 
  

  

  {X(x 
  + 
  u)+Y(y 
  + 
  v)+Z(i 
  + 
  w)}/Y. 
  

   Hence 
  the 
  equation 
  

  

  JWi{ 
  (x 
  + 
  u)x 
  + 
  (y 
  + 
  v)y 
  -f 
  (z 
  + 
  w)z 
  } 
  

  

  = 
  X(x+u) 
  +Y(# 
  + 
  t;) 
  + 
  Z(i 
  + 
  u>) 
  

   = 
  S 
  say 
  (1) 
  

  

  Resolve 
  along 
  any 
  direction 
  X, 
  /x, 
  v, 
  at 
  right 
  angles 
  to 
  the 
  

   direction 
  of 
  V, 
  

  

  then 
  m 
  2 
  { 
  Xx 
  -\- 
  fiy 
  -t 
  v'z) 
  = 
  XX 
  + 
  Y/j, 
  + 
  Zv, 
  

  

  and 
  (x 
  + 
  u)\+ 
  (y 
  + 
  v)fi 
  + 
  (z 
  + 
  w)v 
  = 
  0. 
  

  

  Hence 
  ra 
  2 
  #=X4 
  (x 
  + 
  u)k, 
  

  

  m 
  2 
  y=Y+(y+v)k, 
  

  

  m 
  2 
  z 
  = 
  Z-\- 
  {z±w)k, 
  

   where 
  k 
  is 
  some 
  quantity 
  to 
  be 
  determined. 
  Multiply 
  these 
  

  

  