﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  43 
  

  

  moments 
  of 
  the 
  force, 
  determining 
  the 
  relative 
  positions 
  of 
  

   the 
  axes 
  of 
  rotation, 
  and 
  the 
  phase 
  positions 
  of 
  the 
  electrons 
  

   in 
  their 
  orbits 
  for 
  equilibrium. 
  If 
  the 
  axes 
  of 
  the 
  two 
  orbits 
  

   are 
  not 
  parallel 
  to 
  each 
  other, 
  the 
  forces 
  due 
  to 
  the 
  third 
  and 
  

   fourth 
  components 
  have 
  a 
  tendency 
  to 
  alter 
  the 
  direction 
  of 
  

   the 
  axis 
  of 
  rotation, 
  since 
  these 
  forces 
  act 
  parallel 
  to 
  the 
  

   acceleration 
  and 
  the 
  velocity 
  V)f 
  the 
  second 
  charge, 
  that 
  is, 
  in 
  

   a 
  plane 
  parallel 
  to 
  the 
  orbit 
  of 
  e'. 
  If 
  the 
  planes 
  are 
  exactly 
  

   parallel, 
  on 
  the 
  other 
  hand, 
  there 
  is 
  no 
  component 
  of 
  these 
  

   forces 
  perpendicular 
  to 
  the 
  common 
  planes, 
  and, 
  con- 
  

   sequently, 
  no 
  tendency 
  to 
  alter 
  the 
  direction 
  of 
  the 
  axes. 
  

   This 
  is, 
  therefore, 
  the 
  stable 
  condition. 
  If 
  the 
  axis 
  of 
  

   rotation 
  is 
  slightly 
  disturbed, 
  there 
  are 
  forces 
  tending 
  to 
  

   return 
  it 
  to 
  parallelism, 
  and 
  at 
  the 
  same 
  time 
  giving 
  the 
  

   whole 
  system 
  all 
  the 
  effects 
  of 
  a 
  gyroscopic 
  motion. 
  The 
  

   gyroscopic 
  motion 
  of 
  the 
  whole 
  atom 
  must, 
  however, 
  be 
  of 
  a 
  

   peculiarly 
  modified 
  character 
  because 
  of 
  the 
  flexibility 
  of 
  the 
  

   rings 
  of 
  electrons 
  not 
  being 
  exactly 
  the 
  same 
  as 
  if 
  the 
  ring 
  

   were 
  a 
  rigid 
  body. 
  

  

  In 
  this 
  discussion 
  the 
  first 
  and 
  second 
  components 
  of 
  the 
  

   force 
  have 
  been 
  omitted 
  from 
  consideration 
  because, 
  when 
  

   the 
  two 
  atoms 
  have 
  come 
  to 
  positions 
  of 
  equilibrium 
  forming 
  

   a 
  molecule, 
  the 
  average 
  translational 
  force 
  is 
  zero 
  in 
  this 
  

   position, 
  the 
  first 
  and 
  second 
  components 
  exactly 
  balancing 
  

   each 
  other 
  ; 
  and, 
  although 
  their 
  instantaneous 
  values 
  do 
  not 
  

   balance, 
  it 
  is 
  thought 
  that 
  their 
  joint 
  effect 
  in 
  determining 
  

   the 
  direction 
  of 
  the 
  axis 
  is 
  negligible 
  in 
  comparison 
  with 
  that 
  

   due 
  to 
  the 
  third 
  and 
  fourth 
  components. 
  

  

  The 
  quantity 
  "w" 
  (12), 
  which 
  is 
  the 
  chief 
  part 
  of 
  the 
  

   variable 
  distance, 
  R, 
  between 
  the 
  electrons, 
  enters 
  the 
  

   instantaneous 
  values 
  of 
  the 
  forces 
  (L8) 
  and 
  (23) 
  as 
  an 
  

   infinite 
  series. 
  The 
  first 
  power 
  of 
  u 
  only 
  has 
  been 
  included 
  

   in 
  the 
  average 
  equations 
  (24) 
  and 
  (25), 
  and 
  these 
  expressions 
  

   are 
  even 
  then 
  too 
  complex 
  to 
  be 
  of 
  much 
  value. 
  The 
  approx- 
  

   imation 
  is 
  better 
  the 
  larger 
  the 
  value 
  of 
  r. 
  In 
  the 
  molecules, 
  

   it 
  is 
  considered, 
  for 
  the 
  reasons 
  given 
  above, 
  that 
  the 
  axes 
  of 
  

   the 
  atoms 
  are 
  approximately 
  parallel 
  to 
  each 
  other. 
  The 
  

   introduction 
  of 
  this 
  assumption 
  greatly 
  simplifies 
  the 
  

   expressions 
  for 
  the 
  forces. 
  The 
  value 
  of 
  u 
  becomes 
  (26), 
  and 
  

   the 
  product 
  of 
  the 
  vector 
  velocities 
  of 
  the 
  electrons 
  which 
  

   enters 
  into 
  the 
  second 
  component 
  (2) 
  becomes 
  a 
  constant 
  (27) 
  

   independent 
  of 
  the 
  time. 
  The 
  instantaneous 
  value 
  of 
  the 
  

   first 
  component 
  force 
  becomes 
  (28), 
  and 
  it 
  is 
  now 
  easy 
  to 
  

   derive 
  the 
  average 
  value 
  of 
  the 
  second 
  component 
  from 
  the 
  

   first 
  component 
  because 
  of 
  the 
  constancy 
  of 
  the 
  product 
  of 
  

   these 
  velocities. 
  The 
  first 
  component 
  multiplied 
  by 
  the 
  

  

  