﻿Aepinus 
  Atomized. 
  261 
  

  

  attracted 
  by 
  the 
  atom 
  A'. 
  Hence 
  both 
  electrions 
  being- 
  

   supposed 
  free, 
  E 
  will 
  move 
  to 
  the 
  right 
  ; 
  and 
  because 
  of 
  its 
  

   diminished 
  repulsion 
  on 
  E', 
  E' 
  will 
  follow 
  it 
  in 
  the 
  same 
  

   direction. 
  The 
  equations 
  of 
  equilibrium 
  of 
  the 
  two 
  are 
  

   easily 
  written 
  down, 
  not 
  so 
  easily 
  solved 
  without 
  some 
  slight 
  

   arithmetical 
  artifice. 
  The 
  solution 
  is 
  correctly 
  shown 
  in 
  

   fig. 
  2, 
  for 
  the 
  case 
  in 
  which 
  one 
  radius 
  is 
  three 
  times 
  the 
  

  

  Fig-. 
  1. 
  

  

  Fig-. 
  2. 
  

  

  Kadii 
  3 
  and 
  1. 
  

   C'C 
  = 
  2-7. 
  C'E' 
  = 
  -1458. 
  

  

  CE=-0462. 
  

  

  other, 
  and 
  the 
  distance 
  between 
  the 
  centres 
  is 
  2*7 
  times 
  the 
  

   smaller 
  radius 
  *. 
  The 
  investigation 
  in 
  the 
  footnote 
  shows 
  

   that 
  if 
  the 
  atoms 
  are 
  brought 
  a 
  little 
  nearer, 
  the 
  equilibrium 
  

   becomes 
  unstable 
  ; 
  and 
  we 
  may 
  infer 
  that 
  both 
  electrions 
  

   jump 
  to 
  the 
  right, 
  E' 
  to 
  settle 
  at 
  a 
  point 
  within 
  the 
  atom 
  A 
  

   on 
  the 
  left-hand 
  side 
  of 
  its 
  centre 
  ; 
  and 
  E 
  outside 
  A! 
  , 
  to 
  

   settle 
  at 
  a 
  point 
  still 
  within 
  A. 
  If, 
  lastly, 
  we 
  bring 
  the 
  centres 
  

   closer 
  and 
  closer 
  together 
  till 
  they 
  coincide, 
  E 
  comes 
  again 
  

   within 
  A', 
  and 
  the 
  two 
  electrions 
  settle, 
  as 
  shown 
  in 
  fig. 
  3, 
  at 
  

   distances 
  on 
  the 
  two 
  sides 
  of 
  the 
  common 
  centre, 
  each 
  equal 
  to 
  

  

  \v 
  \ 
  

  

  * 
  Calling 
  e 
  the 
  quantity 
  of 
  electricity, 
  vitreous 
  or 
  resinous, 
  in 
  each 
  

   atom 
  or 
  electrion 
  ; 
  £ 
  the 
  distance 
  between 
  the 
  centres 
  of 
  the 
  atoms 
  ; 
  a, 
  a' 
  

   the 
  radii 
  of 
  the 
  two 
  atoms 
  : 
  x, 
  x 
  the 
  displacements 
  of 
  the 
  electrions 
  from 
  

   the 
  centres 
  ; 
  X, 
  X' 
  the 
  forces 
  experienced 
  by 
  the 
  electrions 
  ; 
  we 
  have 
  

  

  x= 
  e 
  L-?+-(c+j-*r 
  ^ 
  3 
  _r 
  

   xw 
  [- 
  ^ 
  + 
  (7=iT 
  _ 
  (C+^-^)-']* 
  

  

  Each 
  of 
  these 
  being- 
  equated 
  to 
  zero 
  for 
  equilibrium 
  gives 
  us 
  two 
  equations 
  

  

  