﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  57 
  

  

  other, 
  would 
  be 
  such 
  that 
  each 
  electron 
  in 
  the 
  one 
  stands 
  

   half-way 
  between 
  those 
  in 
  the 
  other 
  atom; 
  while 
  in 
  the 
  

   stable 
  position 
  of 
  the 
  two 
  atoms 
  at 
  an 
  angle 
  of 
  latitude 
  

   6b° 
  50', 
  they 
  stand 
  exactly 
  in 
  phase 
  with 
  each 
  other. 
  

  

  The 
  fact 
  that 
  the 
  approximate 
  equations 
  (45) 
  and 
  (46) 
  are 
  

   independent 
  of 
  this 
  phase 
  angle 
  has 
  an 
  important 
  significance. 
  

   It 
  means 
  that 
  one 
  ring 
  of 
  electrons 
  may 
  advance 
  ahead 
  of 
  

   or 
  become 
  retarded 
  behind 
  the 
  other 
  without 
  altering 
  the 
  

   approximate 
  positions 
  of 
  the 
  atoms 
  relatively 
  to 
  each 
  other. 
  

   If 
  the 
  transmission 
  of 
  the 
  force 
  from 
  the 
  one 
  atom 
  to 
  the 
  

   other 
  requires 
  a 
  certain 
  time, 
  instead 
  of 
  being 
  instantaneously 
  

   transmitted 
  as 
  these 
  equations 
  assume, 
  the 
  electrons 
  in 
  the 
  

   rings 
  would 
  occupy 
  a 
  different 
  phase 
  position 
  according 
  to 
  

   the 
  time 
  of 
  transmission 
  ; 
  but 
  it* 
  the 
  equilibrium 
  position 
  is 
  

   independent 
  of 
  the 
  phase 
  relation, 
  it 
  is 
  not 
  unreasonable 
  to 
  

   suppose 
  that 
  approximately 
  the 
  same 
  positions 
  would 
  be 
  

   obtained 
  had 
  the 
  more 
  complex 
  equations 
  involving 
  trans- 
  

   mission 
  at 
  the 
  velocity 
  of 
  light 
  been 
  employed. 
  

  

  Atoms 
  at 
  a 
  great 
  distance 
  from 
  each 
  other. 
  

  

  "When 
  the 
  distance 
  between 
  the 
  atoms 
  is 
  very 
  great, 
  as 
  in 
  

   astronomical 
  problems, 
  the 
  equations 
  are 
  very 
  much 
  simplified. 
  

   It 
  is 
  shown 
  that 
  the 
  electrostatic 
  forces 
  give 
  a 
  zero 
  resultant 
  

   between 
  two 
  atoms, 
  if 
  those 
  terms 
  only 
  are 
  admitted 
  whicii 
  

   give 
  the 
  law 
  of 
  the 
  inverse 
  square 
  of 
  the 
  distance 
  ; 
  but 
  

   that 
  the 
  second 
  component 
  force, 
  due 
  to 
  the 
  motion 
  of 
  the 
  

   electrons, 
  gives 
  a 
  term 
  varying 
  as 
  the 
  inverse 
  square 
  of 
  

   the 
  distance, 
  provided 
  only 
  that 
  the 
  angular 
  velocities 
  of 
  the 
  

   electrons 
  are 
  assumed 
  to 
  be 
  equal. 
  For 
  incommensurable 
  

   velocities 
  the 
  principal 
  term 
  of 
  the 
  force 
  varies 
  as 
  the 
  

   inverse 
  fourth 
  power 
  of 
  the 
  distance. 
  Equation 
  (65) 
  gives 
  

   the 
  complete 
  expression 
  for 
  the 
  force 
  between 
  two 
  electrons 
  

   varying 
  as 
  the 
  inverse 
  square 
  of 
  the 
  distance, 
  revolving 
  in 
  

   true 
  circles 
  inclined 
  at 
  any 
  angle, 
  a, 
  to 
  each 
  other, 
  and 
  at 
  

   great 
  distances 
  apart, 
  if 
  the 
  rotation 
  is 
  synchronous. 
  It 
  is 
  

   seen 
  that 
  the 
  force 
  may 
  be 
  an 
  attraction 
  or 
  a 
  repulsion 
  

   according 
  to 
  the 
  sign 
  of 
  cos 
  y. 
  If 
  this 
  force 
  is 
  summed 
  for 
  

   every 
  combination 
  of 
  electrons 
  in 
  two 
  masses 
  of 
  matter, 
  the 
  

   result 
  appears 
  to 
  be 
  zero. 
  This 
  summation 
  is 
  difficult 
  to 
  

   make, 
  however, 
  for 
  it 
  must 
  be 
  done 
  with 
  such 
  accuracy 
  that 
  

   it 
  is 
  correct 
  to 
  almost 
  one 
  part 
  in 
  10 
  36 
  . 
  This 
  number 
  is 
  the 
  

   approximate 
  ratio 
  of 
  the 
  total 
  unbalanced 
  force 
  between 
  all 
  

   the 
  electrons 
  in 
  a 
  gram 
  of 
  matter 
  to 
  the 
  very 
  small 
  gravi- 
  

   tational 
  attraction 
  between 
  them. 
  It 
  is 
  also 
  difficult 
  to 
  

   show 
  that 
  if 
  there 
  were 
  any 
  residual 
  force, 
  it 
  would 
  be 
  an 
  

   attraction 
  and 
  not 
  a 
  repulsion. 
  The 
  true 
  motion 
  of 
  the 
  

  

  