﻿42 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  z-&x\s 
  being 
  coincident 
  with 
  the 
  axis 
  of 
  rotation 
  of 
  e. 
  a 
  is 
  

   the 
  angle 
  between 
  the 
  directions 
  of 
  the 
  axes. 
  

  

  Since 
  the 
  instantaneous 
  values 
  of 
  the 
  four 
  component 
  

   forces 
  each 
  act 
  in 
  different 
  directions, 
  they 
  are 
  resolved 
  in 
  

   each 
  instance 
  along 
  three 
  selected 
  rectangular 
  axes. 
  The 
  

   atom, 
  in 
  which 
  the 
  electron, 
  e, 
  describes 
  a 
  circular 
  orbit, 
  may 
  

   be 
  considered 
  to 
  have 
  an 
  equator, 
  poles, 
  meridians 
  and 
  circles 
  

   of 
  latitudes. 
  The 
  selected 
  axes 
  are, 
  first, 
  along 
  the 
  line 
  

   joining 
  the 
  centres 
  of 
  the 
  orbits, 
  00 
  / 
  ; 
  second, 
  perpendicular 
  

   to 
  00 
  / 
  in 
  the 
  plane 
  of 
  the 
  meridian 
  of 
  e 
  ; 
  and 
  third, 
  perpen- 
  

   dicular 
  to 
  each 
  of 
  these 
  directions 
  along 
  the 
  circle 
  of 
  latitude. 
  

   The 
  complete 
  expression 
  for 
  the 
  instantaneous 
  force 
  due 
  to 
  

   the 
  first 
  component 
  is 
  given 
  by 
  (18), 
  and 
  due 
  to 
  the 
  second 
  

   component 
  by 
  (23). 
  These 
  forces 
  are 
  then 
  averaged 
  over 
  a 
  

   long 
  period 
  of 
  time, 
  and 
  the 
  resulting 
  expressions 
  give 
  the 
  

   attraction 
  or 
  repulsion, 
  as 
  the 
  case 
  may 
  be, 
  along 
  the 
  line 
  

   OCK 
  joining 
  the 
  centres 
  of 
  the 
  orbits, 
  which 
  the 
  two 
  electrons 
  

   contribute 
  toward 
  the 
  force 
  between 
  the 
  atoms. 
  

  

  When 
  the 
  average 
  is 
  taken, 
  different 
  results 
  are 
  obtained 
  

   according 
  to 
  the 
  assumption 
  made 
  as 
  to 
  the 
  relative 
  angular 
  

   velocities 
  of 
  rotation 
  of 
  the 
  electrons 
  in 
  the 
  two 
  orbits. 
  

   When 
  these 
  velocities 
  are 
  equal 
  to 
  each 
  other, 
  there 
  is 
  a 
  

   particular 
  solution 
  which 
  does 
  not 
  obtain 
  when 
  they 
  are 
  

   incommensurable. 
  When 
  two 
  aioms 
  are 
  in 
  equilibrium 
  with 
  

   each 
  other 
  forming 
  a 
  molecule, 
  it 
  has 
  been 
  shown 
  that 
  if 
  their 
  

   electrons 
  are 
  displaced 
  a 
  little 
  from 
  a 
  fixed 
  phase 
  relation, 
  the 
  

   moment 
  of 
  the 
  forces 
  tends 
  to 
  return 
  them 
  to 
  their 
  original 
  

   phase 
  relation, 
  and 
  they 
  are 
  again 
  in 
  phase 
  equilibrium. 
  It 
  

   is 
  considered 
  that, 
  if 
  the 
  periods 
  of 
  revolution 
  are 
  nearly 
  the 
  

   same, 
  they 
  will 
  become 
  synchronized 
  during 
  the 
  process 
  of 
  

   forming 
  a 
  stable 
  molecule. 
  This 
  emphasizes 
  the 
  importance 
  

   of 
  obtaining 
  the 
  solution 
  of 
  the 
  equations 
  on 
  the 
  assumption 
  

   of 
  equal 
  angular 
  velocities 
  ; 
  and, 
  while 
  the 
  work 
  has 
  not 
  been 
  

   entirely 
  restricted 
  to 
  this 
  hypothesis, 
  the 
  chief 
  results 
  as 
  

   applied 
  to 
  stable 
  molecules 
  are 
  based 
  upon 
  this 
  assumption. 
  

   With 
  this 
  understanding, 
  the 
  average 
  force 
  along 
  the 
  line 
  00' 
  

   between 
  the 
  two 
  electrons 
  due 
  to 
  the 
  first 
  component 
  is 
  given 
  

   by 
  (24), 
  and 
  due 
  to 
  the 
  second 
  component 
  by 
  (25). 
  

  

  The 
  third 
  and 
  fourth 
  components 
  of 
  the 
  force, 
  (3) 
  and 
  (4), 
  

   have 
  not 
  been 
  mentioned 
  because 
  it 
  is 
  shown 
  generally, 
  

   page 
  63, 
  that, 
  while 
  their 
  instantaneous 
  values 
  are 
  not 
  zero 
  

   individually, 
  their 
  sum 
  is 
  always 
  zero 
  when 
  averaged 
  over 
  a 
  

   long 
  time. 
  These 
  components 
  contribute 
  nothing, 
  therefore, 
  

   to 
  the 
  translational 
  force 
  between 
  two 
  atoms, 
  and 
  the 
  whole 
  

   force 
  is 
  obtained 
  from 
  the 
  first 
  and 
  second 
  components. 
  

   They 
  do, 
  however, 
  contribute 
  much 
  toward 
  the 
  internal 
  

  

  