﻿-p, 
  fjuee 
  aa 
  coco 
  

  

  *2— 
  "273 
  

  

  62 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  The 
  complete 
  value 
  of 
  the 
  second 
  component 
  force 
  resolved 
  

   along- 
  r 
  is, 
  then, 
  denoting 
  for 
  brevity 
  S 
  = 
  sin 
  (cot 
  + 
  6) 
  ; 
  

   S' 
  = 
  sin(o)'* 
  + 
  0'); 
  = 
  cos 
  (cot 
  -{-6); 
  C' 
  = 
  cos 
  (co't 
  + 
  6 
  r 
  )\ 
  

  

  fcC 
  cos 
  a 
  -f 
  SS'l 
  [r 
  2 
  - 
  a* 
  S 
  - 
  a?/C 
  -f 
  a'z& 
  sin 
  « 
  

   WyC'W#S'cosa][l 
  + 
  u]~*r 
  (23) 
  

  

  Average 
  Values 
  of 
  the 
  Forces. 
  

  

  To 
  obtain 
  the 
  average 
  force 
  of 
  the 
  charge 
  e 
  1 
  upon 
  e, 
  each 
  

   describing 
  circular 
  orbits 
  in 
  any 
  fixed 
  position, 
  the 
  first 
  

   component 
  (18) 
  and 
  the 
  second 
  (23) 
  will 
  be 
  averaged 
  

   separately 
  over 
  a 
  long 
  time. 
  

  

  -, 
  _ 
  ffiy* 
  ^ 
  _ 
  .Ciy* 
  

  

  -T 
  1 
  — 
  (•* 
  • 
  -F 
  2 
  — 
  7*36 
  • 
  

  

  jo^ 
  = 
  T 
  j 
  ^=T 
  

  

  The 
  values 
  of 
  these 
  integrals 
  depend 
  upon 
  the 
  assumptions 
  

   made 
  concerning 
  the 
  relative 
  angular 
  velocities, 
  co 
  and 
  co\ 
  of 
  

   the 
  two 
  electrons. 
  If 
  the 
  angular 
  velocities 
  are 
  the 
  same, 
  or 
  

   some 
  exact 
  multiple 
  of 
  each 
  other, 
  there 
  is 
  a 
  particular 
  solu- 
  

   tion 
  for 
  that 
  case. 
  When 
  two 
  atoms 
  unite 
  to 
  form 
  a 
  molecule 
  

   there 
  is 
  a 
  tendency 
  to 
  synchronize 
  the 
  periods 
  of 
  revolution 
  

   in 
  their 
  orbits 
  if 
  they 
  are 
  not 
  very 
  different 
  originally, 
  and 
  

   on 
  this 
  account 
  the 
  solution 
  when 
  the 
  angular 
  velocities 
  are 
  

   exactly 
  equal 
  takes 
  on 
  an 
  added 
  importance. 
  The 
  average 
  

   forces 
  in 
  the 
  general 
  position 
  of 
  the 
  orbits 
  become 
  involved 
  

   expressions 
  when 
  higher 
  powers 
  of 
  u 
  are 
  considered, 
  and 
  for 
  

   this 
  reason 
  are 
  not 
  so 
  useful, 
  but 
  since 
  they 
  have 
  been 
  ob- 
  

   tained 
  for 
  the 
  particular 
  case 
  of 
  equal 
  angular 
  velocities, 
  and 
  

   including 
  the 
  first, 
  but 
  not 
  the 
  second 
  and 
  higher 
  powers 
  of 
  

   w, 
  and 
  will 
  be 
  useful 
  in 
  certain 
  instances, 
  they 
  are 
  given 
  here. 
  

   The 
  first 
  component 
  is 
  

  

  ^=-T^r[ 
  r2 
  -i> 
  ¥ 
  + 
  l&( 
  Gcosr 
  t 
  +Rsinr 
  r)} 
  • 
  < 
  24 
  ) 
  

  

  where 
  

  

  F 
  = 
  a\x 
  2 
  + 
  y 
  2 
  ) 
  + 
  a'Y 
  + 
  a' 
  2 
  (z 
  sin 
  x 
  + 
  x 
  sin 
  a) 
  2 
  , 
  

  

  Q 
  = 
  r 
  2 
  + 
  y 
  2 
  + 
  (r 
  2 
  + 
  2x 
  2 
  ) 
  cos 
  a 
  + 
  2xz 
  sin 
  «, 
  

  

  H 
  = 
  — 
  2,vy 
  f 
  2<ry 
  cos 
  « 
  + 
  2yz 
  sin 
  «. 
  

  

  