﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds, 
  39 
  

  

  additional 
  forces 
  are 
  brought 
  into 
  play, 
  but 
  the 
  forces 
  that 
  

   act 
  when 
  they 
  were 
  at 
  rest 
  still 
  continue 
  to 
  act. 
  If 
  the 
  

   atoms 
  are 
  A 
  and 
  A' 
  and 
  the 
  electrons 
  within 
  A 
  are 
  e^ 
  e 
  2 
  , 
  and 
  

   within 
  A' 
  ei, 
  e 
  2 
  \ 
  the 
  electron 
  e 
  1 
  repels 
  <?/ 
  with 
  a 
  force 
  <? 
  2 
  /r 
  3 
  , 
  

  

  e 
  7* 
  

   and 
  e 
  x 
  repels 
  fc 
  , 
  diagonally 
  opposite, 
  with 
  a 
  force 
  * 
  

  

  when 
  resolved 
  along 
  00', 
  "a" 
  denoting 
  the 
  radius 
  of 
  the 
  

  

  orbit 
  of 
  each 
  electron. 
  e 
  2 
  repels 
  e 
  2 
  ' 
  and 
  e 
  2 
  repels 
  e\ 
  in 
  like 
  

  

  manner, 
  thus 
  doubling 
  the 
  sum 
  of 
  the 
  forces 
  found, 
  for 
  the 
  

  

  total 
  repulsion 
  between 
  the 
  electrons 
  themselves. 
  Electron 
  

  

  e 
  x 
  attracts 
  the 
  positive 
  sphere 
  2e 
  of 
  the 
  opposite 
  atom 
  with 
  a 
  

  

  force 
  which, 
  when 
  resolved 
  along 
  the 
  line 
  00' 
  joining 
  the 
  

  

  2e 
  2 
  r 
  

   centres, 
  is 
  equal 
  to 
  — 
  - 
  — 
  — 
  j« 
  Each 
  of 
  the 
  four 
  electrons 
  

   H 
  (r 
  2 
  + 
  a 
  2 
  )t 
  

  

  acts 
  upon 
  the 
  opposite 
  sphere 
  in 
  the 
  same 
  manner, 
  giving 
  a 
  

  

  total 
  attraction 
  four 
  times 
  the 
  preceding. 
  There 
  is, 
  in 
  

  

  addition, 
  the 
  repulsion 
  between 
  the 
  positive 
  spheres 
  them- 
  

  

  e 
  2 
  

   selves, 
  which 
  is 
  4 
  -5. 
  Hence 
  the 
  total 
  electrostatic 
  force 
  

  

  i 
  

   between 
  the 
  atoms, 
  assuming 
  that 
  they 
  are 
  at 
  rest, 
  is 
  

  

  Se 
  2 
  r 
  2e 
  2 
  r 
  _6f 
  

  

  If 
  the 
  distance 
  r 
  is 
  expressed 
  as 
  av, 
  where 
  v 
  denotes 
  the 
  

   distance 
  between 
  the 
  atoms 
  measured 
  in 
  radii, 
  the 
  force 
  

   becomes 
  

  

  f 
  = 
  - 
  r 
  Sv 
  2v 
  ii 
  

  

  « 
  2 
  L( 
  v 
  2 
  + 
  l)f 
  (t, 
  2 
  + 
  4)f 
  ~ 
  ^ 
  2 
  J 
  

   The 
  negative 
  terms 
  denoting 
  repulsion 
  may 
  be 
  shown 
  to 
  

   exceed 
  the 
  positive 
  term 
  at 
  all 
  distances. 
  If 
  each 
  term 
  is 
  

   expanded 
  into 
  a 
  series 
  of 
  terms 
  by 
  the 
  binomial 
  theorem, 
  

   we 
  find 
  

  

  (i« 
  2 
  +l)£ 
  2 
  16 
  

  

  _— 
  ?^— 
  =-2v- 
  2 
  + 
  l2v-*-60v- 
  6 
  + 
  2S0v- 
  8 
  -V260u- 
  10 
  +..., 
  

  

  c 
  

   Hence 
  

  

  F 
  = 
  ^(-45*- 
  6 
  + 
  262-5tr 
  8 
  -1240-31r- 
  10 
  + 
  ...), 
  

  

  which 
  gives 
  the 
  electrostatic 
  force 
  between 
  the 
  two 
  atoms 
  at 
  

  

  