﻿Mdlecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  65 
  

  

  The 
  instantaneous 
  force 
  F 
  1} 
  resolved 
  along 
  the 
  vector 
  r, 
  

   becomes 
  from 
  (18) 
  

  

  F 
  1= 
  = 
  — 
  ^-3 
  Tr 
  8 
  — 
  aarS 
  + 
  a'^S'l 
  Tl 
  + 
  wl 
  "r. 
  . 
  (28) 
  

  

  When 
  the 
  angular 
  velocities 
  are 
  equal, 
  the 
  second 
  component 
  

   force 
  (2) 
  is 
  easily 
  expressed 
  in 
  terms 
  of 
  the 
  first 
  component, 
  

   and 
  we 
  have 
  

  

  = 
  _ 
  Fl 
  ^!<^ 
  = 
  _ 
  Wcos7) 
  . 
  (29) 
  

  

  6 
  

  

  where 
  = 
  velocity 
  of 
  light, 
  and 
  

  

  o_ 
  9 
  _^. 
  #' 
  _ 
  / 
  _ 
  ^® 
  

  

  c 
  c 
  c 
  c 
  

  

  Because 
  of 
  this 
  relation 
  the 
  second 
  component 
  force 
  resolved 
  

   along 
  any 
  desired 
  direction 
  and 
  averaged 
  over 
  a 
  long 
  period 
  

   is 
  easily 
  found 
  from 
  the 
  first 
  component. 
  

  

  The 
  Perpendicular 
  Component 
  of 
  F 
  x 
  . 
  

  

  To 
  find 
  the 
  force 
  resolved 
  along 
  the 
  perpendicular 
  to 
  r 
  in 
  

   the 
  meridian 
  plane 
  and 
  in 
  the 
  direction 
  towards 
  the 
  axis 
  of 
  

   rotation, 
  it 
  is 
  seen 
  that 
  the 
  vector 
  j'xr 
  lakes 
  the 
  direction 
  

   of 
  this 
  perpendicular. 
  By 
  (7) 
  we 
  have 
  in 
  this 
  case 
  

  

  r 
  = 
  xi 
  + 
  zk 
  (30) 
  

  

  Hence 
  jxv 
  = 
  zi 
  — 
  xk 
  (31) 
  

  

  The 
  cosine 
  of 
  the 
  angle 
  between 
  the 
  vector 
  R, 
  along 
  which 
  

   the 
  force 
  acts, 
  and 
  the 
  vector 
  j 
  x 
  r, 
  along 
  which 
  we 
  desire 
  to 
  

   resolve 
  the 
  force, 
  is 
  

  

  -7iP=4[>' 
  s 
  '-<4 
  • 
  • 
  • 
  < 
  32 
  > 
  

  

  The 
  first 
  component 
  force 
  resolved 
  along 
  j 
  x 
  r 
  is, 
  therefore, 
  

  

  F 
  x 
  = 
  -i^-rp-l'a'S'— 
  aS 
  K 
  where 
  sin 
  \= 
  -. 
  . 
  (33) 
  

   Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  Xo. 
  151. 
  July 
  1913. 
  F 
  

  

  