﻿Aepinus 
  Atomized. 
  265 
  

  

  in 
  which 
  the 
  surface 
  of 
  A' 
  is 
  cut 
  by 
  the 
  line 
  of 
  centres 
  ; 
  but 
  

   the 
  equilibrium 
  would 
  be 
  obviously 
  unstable, 
  and 
  a 
  simple 
  

   calculation* 
  shows 
  that 
  the 
  stable 
  position 
  actually 
  taken 
  by 
  

   the 
  electrion 
  is 
  *38 
  ex! 
  from 
  C, 
  when 
  the 
  distance 
  between 
  the 
  

   centres 
  is 
  2a! 
  (fig, 
  4). 
  If 
  the 
  distance 
  between 
  the 
  centres 
  

   is 
  now 
  diminished 
  from 
  2a! 
  to 
  l*89a' 
  (a 
  being 
  now 
  supposed 
  

   to 
  be 
  anything 
  less 
  than 
  '89 
  a!) 
  the 
  electrion 
  comes 
  gradually 
  

   to 
  distance 
  *63a' 
  from 
  C 
  (fig. 
  5) 
  ; 
  its 
  equilibrium 
  there 
  becomes 
  

   unstable 
  ; 
  and 
  it 
  jumps 
  out 
  of 
  A' 
  towards 
  A 
  (like 
  a 
  cork 
  

   jumping 
  out 
  of 
  a 
  bottle). 
  It 
  will 
  shoot 
  through 
  A 
  (A 
  ; 
  and 
  

   A 
  being 
  held 
  fixed) 
  ; 
  and 
  after 
  several 
  oscillations 
  to 
  and 
  fro* 
  

   perhaps 
  f 
  ten 
  or 
  twenty, 
  if 
  it 
  has 
  only 
  quasi 
  inertia 
  due 
  to 
  

   condensation 
  or 
  rarefaction 
  J 
  produced 
  by 
  it 
  in 
  ether 
  ; 
  or 
  

   perhaps 
  many 
  times 
  more 
  if 
  it 
  has 
  intrinsic 
  inertia 
  of 
  its 
  

   own; 
  it 
  will 
  settle, 
  with 
  decreasing 
  range 
  of 
  excursions, 
  

   sensibly 
  to 
  rest 
  within 
  A, 
  attracted 
  somewhat 
  from 
  the 
  centre 
  

   by 
  A'. 
  If, 
  lastly, 
  A' 
  and 
  A 
  be 
  drawn 
  asunder 
  to 
  their 
  

   original 
  great 
  distance, 
  the 
  electrion 
  will 
  not 
  regain 
  its 
  

   original 
  position 
  in 
  A', 
  but 
  will 
  come 
  to 
  the 
  centre 
  of 
  A 
  and 
  

   rest 
  there. 
  Here 
  then 
  we 
  have 
  another 
  illustration 
  of 
  the 
  

   tendency 
  found 
  in 
  § 
  9, 
  of 
  the 
  smaller 
  atom 
  to 
  take 
  electrions 
  

   from 
  the 
  larger. 
  

  

  § 
  14. 
  In 
  preventing 
  the 
  two 
  atoms 
  from 
  rushing 
  together 
  

   by 
  holding 
  them 
  against 
  the 
  attractive 
  force 
  of 
  the 
  electrion^ 
  

   we 
  shall 
  have 
  gained 
  more 
  work 
  during 
  the 
  approach 
  than 
  

   we 
  afterwards 
  spent 
  on 
  the 
  separation 
  ; 
  and 
  we 
  have 
  now 
  

  

  * 
  Denoting 
  by 
  £ 
  the 
  distance 
  between 
  the 
  centres, 
  and 
  by 
  X 
  the 
  force 
  

   on 
  E 
  when 
  its 
  distance 
  from 
  C 
  is 
  x\ 
  we 
  have 
  

  

  x=e 
  *[{^>~^] 
  

  

  x 
  

  

  Hence 
  for 
  equilibrium 
  — 
  — 
  - 
  = 
  "-r- 
  . 
  This 
  is 
  a 
  cubic 
  for 
  x 
  of 
  which 
  

  

  the 
  proper 
  root 
  (the 
  smallest 
  root) 
  for 
  the 
  case 
  £=2 
  a 
  ' 
  is 
  '38 
  a'. 
  The 
  

   formula 
  for 
  X 
  has 
  a 
  minimum 
  value 
  when 
  ^—x' 
  — 
  a 
  \/2, 
  which 
  makes 
  

  

  Hence 
  the 
  value 
  of 
  x' 
  for 
  equilibrium 
  coincides 
  with 
  the 
  value 
  of 
  X, 
  a 
  

   minimum, 
  and 
  the 
  equilibrium 
  becomes 
  unstable, 
  when 
  £ 
  is 
  diminished 
  to 
  

  

  Eth 
  

  

  L-^a' 
  = 
  l-89(V. 
  For 
  this, 
  the 
  value 
  of 
  x' 
  is-V 
  «' 
  = 
  *63a'. 
  

  

  f 
  " 
  On 
  the 
  Production 
  of 
  Wave 
  Motion 
  in 
  an 
  Elastic 
  Solid," 
  Phil 
  

   ig\ 
  Oct. 
  1899, 
  § 
  44. 
  

  

  \ 
  " 
  On 
  the 
  Motion 
  of 
  Ponderable 
  Matter 
  through 
  Space 
  Occupied 
  bv 
  

   her," 
  Phil. 
  Mag. 
  Aug. 
  1900, 
  §§ 
  15, 
  17. 
  

  

  