﻿64 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  Taking 
  the 
  average 
  value 
  of 
  the 
  sum 
  of 
  these 
  forces 
  in- 
  

   tegrated 
  between 
  the 
  limits 
  and 
  go 
  , 
  we 
  have 
  

  

  Hence 
  F 
  = 
  i 
  ] 
  (f 
  8 
  + 
  F 
  4 
  V*=0. 
  

  

  These 
  forces 
  will 
  be 
  considered 
  ngain 
  when 
  obtaining 
  an 
  

   expression 
  for 
  the 
  moments 
  of 
  the 
  forces 
  within 
  an 
  atom. 
  

  

  Case 
  where 
  the 
  Two 
  Axes 
  of 
  Rotation 
  are 
  Parallel. 
  

  

  When 
  the 
  axes 
  of 
  rotation 
  and 
  the 
  planes 
  of 
  the 
  orbits 
  of 
  

   the 
  two 
  electrons, 
  or 
  electrical 
  charges 
  under 
  consideration, 
  

   are 
  parallel, 
  there 
  is 
  no 
  component 
  of 
  the 
  third 
  and 
  fourth 
  

   forces 
  perpendicular 
  to 
  the 
  plane, 
  since 
  these 
  forces 
  are 
  

   parallel 
  to 
  the 
  acceleration 
  and 
  velocity 
  of 
  the 
  second 
  

   charge, 
  each 
  of 
  which 
  lies 
  in 
  the 
  plane 
  of 
  its 
  orbit. 
  A 
  

   small 
  displacement 
  from 
  parallelism 
  brings 
  to 
  bear 
  forces 
  

   tending 
  to 
  restore 
  the 
  planes 
  to 
  parallelism 
  and 
  producing 
  at 
  

   the 
  same 
  time 
  a 
  gyroscopic 
  motion. 
  When 
  the 
  atoms, 
  of 
  which 
  

   the 
  two 
  electrons 
  now 
  being 
  considered 
  are 
  constituents, 
  are 
  

   in 
  equilibrium 
  with 
  each 
  other 
  forming 
  a 
  molecule, 
  the 
  

   first 
  and 
  second 
  component 
  forces 
  on 
  the 
  average 
  balance 
  

   each 
  other, 
  and 
  it 
  is 
  thought 
  that 
  the 
  control 
  of 
  the 
  position 
  

   of 
  the 
  plane 
  and 
  axis 
  in 
  this 
  situation 
  is 
  by 
  the 
  third 
  and 
  

   fourth 
  components. 
  These, 
  as 
  just 
  mentioned, 
  tend 
  to 
  bring 
  

   the 
  axes 
  into 
  parallelism, 
  and 
  hold 
  them 
  parallel. 
  

  

  From 
  these 
  considerations 
  it 
  is 
  thought 
  that 
  the 
  case 
  of 
  

   parallel 
  axes 
  of 
  rotation 
  is 
  most 
  important. 
  A 
  very 
  great 
  

   simplification 
  is 
  introduced 
  in 
  the 
  general 
  equations 
  by 
  

   making 
  this 
  supposition, 
  and 
  it 
  has 
  been 
  possible, 
  by 
  first 
  

   working 
  out 
  special 
  cases 
  and 
  later 
  generalizing 
  the 
  formulas, 
  

   to 
  obtain 
  a 
  complete 
  solution 
  to 
  any 
  desired 
  power 
  of 
  u, 
  as 
  

   the 
  law 
  of 
  the 
  series 
  has 
  been 
  determined. 
  

  

  In 
  the 
  case 
  of 
  parallel 
  axes 
  of 
  rotation 
  the 
  angle 
  a 
  is 
  zero, 
  

   and 
  by 
  assuming 
  that 
  the 
  centre 
  of 
  the 
  second 
  orbit 
  is 
  situated 
  

   in 
  the 
  i-k, 
  that 
  is, 
  the 
  x-z 
  plane, 
  none 
  of 
  the 
  generality 
  of 
  

   treatment 
  is 
  lost. 
  With 
  these 
  substitutions 
  the 
  value 
  of 
  u 
  

   in 
  (12) 
  becomes, 
  putting 
  6' 
  — 
  = 
  y, 
  

  

  u= 
  ^ 
  — 
  fltfS 
  + 
  a'tfS' 
  — 
  aa' 
  cosy 
  . 
  . 
  . 
  (26) 
  

  

  and 
  the 
  value 
  of 
  q 
  . 
  q' 
  in 
  (21) 
  reduces 
  to 
  a 
  constant 
  value 
  if 
  

   the 
  angular 
  velocities 
  co 
  and 
  &/ 
  are 
  equal. 
  

  

  q.q' 
  = 
  a«VcosY 
  (27) 
  

  

  