﻿58 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  electrons 
  in 
  the 
  molecules 
  must 
  depart 
  somewhat 
  from 
  a 
  

   circle, 
  as 
  has 
  been 
  shown 
  ; 
  and 
  whether 
  or 
  not 
  any 
  terms 
  

   may 
  be 
  found 
  due 
  to 
  the 
  gyroscopic 
  motions 
  of 
  the 
  atoms 
  

   that 
  will 
  give 
  rise 
  to 
  a 
  force 
  varying 
  as 
  the 
  inverse 
  square 
  

   of 
  the 
  distance 
  is 
  worth 
  investigating. 
  The 
  only 
  way 
  as 
  yet 
  

   found 
  to 
  obtain 
  terms 
  with 
  the 
  inverse 
  square 
  of 
  the 
  distance 
  

   is 
  by 
  the 
  assumption 
  of 
  synchronous 
  revolution 
  of 
  the 
  

   electrons 
  at 
  a 
  great 
  distance 
  apart. 
  The 
  probabilities 
  

   against 
  such 
  synchronous 
  motions 
  are 
  very 
  great, 
  but 
  it 
  is 
  

   different 
  at 
  molecular 
  distances 
  when 
  a 
  rigid 
  connexion 
  has 
  

   been 
  established 
  between 
  the 
  atoms 
  of 
  a 
  molecule. 
  

  

  Part 
  III. 
  

  

  Let 
  e 
  and 
  e' 
  denote 
  two 
  electrical 
  charges 
  moving 
  with 
  

   velocities 
  q 
  and 
  q\ 
  and 
  accelerations 
  q 
  and 
  q' 
  respectively. 
  

   Let 
  the 
  distance 
  between 
  them 
  be 
  R 
  at 
  the 
  time 
  t, 
  and 
  the 
  

   angle 
  between 
  their 
  directions 
  of 
  motion 
  be 
  7, 
  then 
  the 
  

   mechanical 
  force 
  which 
  the 
  second 
  charge, 
  e\ 
  exerts 
  upon 
  

   the 
  first 
  charge, 
  e, 
  at 
  the 
  instant 
  t, 
  is 
  expressed 
  as 
  a 
  vector 
  

   sum 
  of 
  four 
  component 
  vectors 
  : 
  

  

  -p 
  _ 
  <? 
  e 
  a 
  repulsion 
  along 
  the 
  line 
  joining 
  

  

  1 
  ~KR 
  2 
  ' 
  the 
  centres 
  of 
  the 
  charges 
  . 
  . 
  . 
  (1) 
  

  

  -^ 
  _ 
  fxee' 
  , 
  an 
  attraction 
  along 
  the 
  line 
  joining 
  

  

  2 
  ~ 
  R 
  2 
  ^ 
  the 
  centres 
  of 
  the 
  charges 
  . 
  . 
  (2) 
  

  

  -p 
  _/^'a/ 
  a 
  force 
  in 
  a 
  direction 
  opposite 
  to 
  

  

  3 
  ~ 
  R 
  ' 
  the 
  acceleration 
  of 
  the 
  second 
  

  

  charge 
  (3) 
  

  

  t? 
  t 
  f^/jL\ 
  a 
  force 
  in 
  a 
  direction 
  opposite 
  to 
  

  

  ^"^^ 
  dt\RJ, 
  the 
  direction 
  of 
  motion 
  of 
  the 
  

  

  second 
  charge 
  (4) 
  

  

  These 
  equations 
  will 
  now 
  be 
  applied 
  to 
  the 
  case 
  where 
  each 
  

   of 
  the 
  charges 
  e 
  and 
  e 
  1 
  is 
  revolving 
  at 
  uniform 
  angular 
  

   velocities 
  co 
  and 
  oJ 
  in 
  circular 
  orbits 
  of 
  radii 
  a 
  and 
  a 
  1 
  respec- 
  

   tively. 
  The 
  orbits 
  are 
  situated 
  in 
  the 
  most 
  general 
  position, 
  

   the 
  two 
  axes 
  of 
  rotation 
  having 
  an 
  angle 
  « 
  between 
  their 
  

   directions, 
  and 
  the 
  distance, 
  r, 
  between 
  the 
  centres 
  of 
  the 
  

   two 
  orbits 
  being 
  any 
  value 
  large 
  or 
  small. 
  Select 
  two 
  

   systems 
  of 
  rectangular 
  axes, 
  i, 
  j, 
  and 
  k, 
  and 
  i 
  ; 
  , 
  /, 
  and 
  k\ 
  

   these 
  letters 
  representing 
  unit 
  vectors 
  along 
  their 
  respective 
  

   directions, 
  the 
  first 
  set 
  of 
  axes 
  referring 
  to 
  the 
  charge 
  e 
  and 
  

  

  