﻿Molecules 
  of 
  tlie 
  Elements 
  and 
  their 
  Compounds. 
  77 
  

  

  resolving 
  all 
  the 
  forces 
  upon 
  one 
  electron 
  in 
  the 
  ring 
  along 
  the 
  

   direction 
  of 
  the 
  radius, 
  and 
  equating 
  this 
  to 
  the 
  centrifugal 
  

   force 
  developed 
  by 
  the 
  revolving 
  electron. 
  If 
  the 
  electron, 
  the 
  

   forces 
  upon 
  which 
  are 
  to 
  be 
  calculated, 
  is 
  situated 
  at 
  A, 
  and 
  

   the 
  next 
  adjacent 
  electron 
  at 
  B, 
  the 
  angle 
  AOB 
  = 
  2tt/?i. 
  

   The 
  four 
  forces 
  upon 
  A 
  due 
  to 
  B 
  become 
  from 
  equations 
  (1) 
  

   to 
  (4) 
  

  

  e 
  2 
  

   Fi= 
  -pTT 
  2 
  ' 
  a 
  repulsion 
  along 
  the 
  line 
  BA. 
  

  

  Fo= 
  ^S- 
  cos 
  — 
  , 
  an 
  attraction 
  along 
  AB. 
  

   1\- 
  n 
  

  

  F 
  a 
  = 
  

  

  l±e 
  2 
  <f 
  a 
  force 
  directed 
  from 
  A 
  parallel 
  to 
  the 
  

  

  }ia 
  1 
  ' 
  line 
  BO, 
  and 
  in 
  the 
  direction 
  OB. 
  

  

  r>o. 
  

  

  Since 
  the 
  angle 
  AOB 
  equals 
  27r/re, 
  ACB=w/« 
  5 
  and 
  R 
  = 
  

   2a! 
  sin 
  w/n, 
  we 
  have 
  

  

  2 
  

  

  ¥i= 
  , 
  a 
  repulsion 
  along 
  BA. 
  

  

  ■±L\ar 
  sin 
  z 
  - 
  

  

  n 
  

  

  2-2 
  O 
  

  

  F. 
  = 
  — 
  — 
  — 
  cos—-? 
  an 
  attraction 
  along 
  AB. 
  

  

  4ai 
  snr 
  — 
  

  

  F,= 
  

  

  L1 
  

  

  9 
  9 
  

  

  2a, 
  2 
  sin 
  - 
  

  

  The 
  force 
  F 
  3 
  , 
  being 
  parallel 
  to 
  OB 
  would 
  be 
  tangential 
  to 
  

   the 
  circle 
  when 
  the 
  electron 
  is 
  situated 
  at 
  a 
  point 
  ninety 
  

   decrees 
  from 
  A. 
  TVhen 
  B 
  is 
  nearer 
  to 
  A 
  than 
  a 
  right 
  angle 
  

   the 
  component 
  along 
  OA 
  is 
  a 
  repulsion, 
  but 
  when 
  farther 
  it 
  

   is 
  an 
  attraction 
  toward 
  the 
  centre. 
  Resolving 
  these 
  three 
  

   component 
  parts 
  of 
  the 
  force 
  upon 
  the 
  electron 
  A 
  due 
  to 
  B 
  

   along 
  the 
  radius 
  OA, 
  we 
  have 
  

  

  2 
  

  

  F, 
  cos 
  Or-BAO) 
  = 
  -F, 
  sin 
  Z 
  = 
  _ 
  -j*-, 
  cosec^, 
  

  

  9 
  9 
  -> 
  \ 
  

  

  F, 
  cos 
  BAO=F, 
  sin 
  - 
  = 
  ^-?(cosec- 
  -2 
  sin 
  -), 
  

  

  a 
  ±ai 
  \ 
  n 
  nj 
  

  

  2lT 
  PL"' 
  2 
  '/ 
  1 
  I 
  • 
  7T 
  7T\ 
  

  

  F 
  3 
  cos 
  OAF,= 
  - 
  F 
  3 
  cos 
  - 
  = 
  g 
  (2 
  sin 
  - 
  - 
  coscc 
  -). 
  

  

  