﻿74 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  By 
  these 
  equations 
  it 
  becomes 
  evident 
  that 
  the 
  instantaneous 
  

   moment 
  of 
  the 
  force 
  exerted 
  by 
  one 
  electron 
  upon 
  another 
  

   cannot 
  at 
  all 
  times 
  vanish 
  for 
  any 
  phase-angle 
  y. 
  The 
  motion 
  

   of 
  each 
  electron 
  cannot, 
  therefore, 
  remain 
  perfectly 
  uniform 
  in 
  

   its 
  orbit, 
  but 
  must 
  be 
  subject 
  to 
  periodic 
  displacements 
  every 
  

   revolution. 
  These 
  displacements 
  must 
  be 
  small 
  because 
  of 
  

   the 
  interaction 
  of 
  the 
  adjacent 
  electrons 
  in 
  the 
  same 
  ring. 
  

   If 
  they 
  tend 
  to 
  approach 
  each 
  other, 
  an 
  opposing 
  force 
  is 
  

   produced 
  by 
  the 
  electrostatic 
  forces 
  between 
  them. 
  

  

  The 
  average 
  values 
  of 
  the 
  forces 
  on 
  one 
  electron 
  obtained 
  

   from 
  (53) 
  to 
  (56) 
  are 
  

  

  15a 
  V 
  , 
  3 
  5 
  7 
  2 
  3 
  T3 
  4/ 
  ' 
  , 
  9N 
  

  

  + 
  (Je*W(a 
  2 
  + 
  a' 
  2 
  ) 
  -| 
  x 
  4 
  aa' 
  \eos 
  7 
  ~| 
  *W 
  a 
  cos 
  2 
  7 
  + 
  . 
  . 
  ."] 
  | 
  ,(57) 
  

  

  TT^FjflS'cosy, 
  (58) 
  

  

  w 
  pee' 
  a' 
  v 
  2 
  sin 
  y 
  ( 
  , 
  ,1 
  2 
  , 
  ^ 
  1 
  3 
  2 
  2 
  r 
  ■*> 
  . 
  _ 
  , 
  ^ 
  

  

  F 
  3 
  = 
  ^< 
  L 
  l 
  + 
  ^. 
  ? 
  aacos 
  7 
  + 
  -.- 
  4 
  . 
  ? 
  [_-(a 
  2 
  + 
  a'0 
  

  

  — 
  aa! 
  x 
  2 
  cos 
  7 
  -f 
  a 
  V 
  2 
  cos 
  2 
  7 
  + 
  9 
  • 
  1 
  • 
  c 
  • 
  ~e 
  ~V 
  ( 
  ft2 
  "•" 
  a 
  '^ 
  aa 
  ' 
  cos 
  ^ 
  

  

  "1 
  13 
  5 
  7 
  2 
  4 
  r3^ 
  4 
  

  

  — 
  ?>x 
  2 
  a 
  2 
  a' 
  2 
  cos 
  2 
  7 
  + 
  aV 
  3 
  cos 
  3 
  7 
  -+ 
  « 
  • 
  t 
  • 
  ^ 
  • 
  o 
  • 
  --g 
  ~ir 
  ( 
  a2 
  + 
  a/2 
  

  

  — 
  2aa' 
  cos 
  y) 
  2 
  -f 
  3x 
  2 
  (a 
  2 
  + 
  a 
  2 
  )a 
  2 
  a 
  2 
  cos 
  2 
  7 
  

  

  — 
  6x 
  2 
  a 
  3 
  a' 
  3 
  cos 
  3 
  7 
  + 
  aV 
  4 
  cos 
  4 
  7I 
  + 
  . 
  . 
  A- 
  , 
  (59) 
  

  

  F 
  4 
  = 
  (60) 
  

  

  I£ 
  these 
  average 
  values 
  are 
  summed 
  for 
  every 
  electron 
  in 
  

   the 
  two 
  atoms, 
  the 
  process 
  in 
  general 
  becomes 
  involved. 
  In 
  

   the 
  case 
  of 
  two 
  atoms 
  with 
  a 
  single 
  ring 
  of 
  three 
  electrons 
  

   each, 
  it 
  has 
  been 
  shown 
  that 
  there 
  is 
  equilibrium 
  oE 
  the 
  

   average 
  moments 
  of 
  the 
  forces 
  when 
  the 
  electrons 
  are 
  exactly 
  

   in 
  phase, 
  making 
  7 
  = 
  0, 
  y—l27r, 
  7=! 
  2tt. 
  Tt 
  is 
  assumed 
  

   that 
  the 
  atoms 
  are 
  in 
  translational 
  equilibrium, 
  the 
  angle 
  of 
  

   latitude 
  being 
  65° 
  50', 
  and 
  distance 
  fi 
  2 
  v 
  2 
  = 
  7*075, 
  in 
  which 
  

   position 
  the 
  sum 
  of 
  the 
  moments 
  of 
  the 
  forces 
  is 
  zero. 
  For 
  a 
  

   small 
  displacement 
  on 
  either 
  side 
  of 
  this 
  position 
  the 
  sum 
  of 
  

   the 
  moments 
  tends 
  to 
  return 
  the 
  atoms 
  to 
  this 
  fixed 
  position, 
  

   making 
  7 
  = 
  0, 
  etc., 
  and 
  showing 
  stability. 
  When 
  the 
  two 
  

  

  