﻿268 
  . 
  Lord 
  Kelvin: 
  

  

  o£ 
  the 
  number 
  in 
  two 
  planes 
  at 
  equal 
  distances 
  on 
  the 
  two 
  

  

  sides 
  o£ 
  the 
  centre. 
  For 
  twelve 
  we 
  have 
  a 
  configuration 
  of 
  

  

  stable 
  equilibrium 
  with 
  the 
  electrions 
  at 
  positions 
  of 
  the 
  

  

  twelve 
  nearest 
  neighbours 
  to 
  C 
  in 
  an 
  equilateral 
  homogeneous 
  

  

  assemblage 
  of 
  points*; 
  for 
  twenty 
  at 
  , 
  the 
  twenty 
  corners 
  of 
  

  

  a 
  pentagonal 
  dodecahedron. 
  All 
  these 
  configurations 
  of 
  § 
  19. 
  

  

  except 
  those 
  described 
  for 
  ten 
  electrions, 
  are 
  stable 
  if, 
  as 
  we 
  

  

  are 
  now 
  supposing, 
  the 
  electrions 
  are 
  constrained 
  to 
  a 
  spherical 
  

  

  surface 
  on 
  which 
  they 
  are 
  free 
  to 
  move. 
  

  

  § 
  20. 
  Except 
  the 
  cases 
  of 
  § 
  18, 
  the 
  forces 
  with 
  which 
  the 
  

  

  strings 
  are 
  stretched 
  are 
  the 
  same 
  for 
  all 
  the 
  electrions 
  of 
  

  

  each 
  case. 
  Hence 
  if 
  we 
  now 
  discard 
  the 
  strings 
  and 
  place 
  

  

  the 
  electrions 
  in 
  an 
  atom 
  on 
  a 
  spherical 
  surface 
  concentric 
  

  

  with 
  it, 
  its 
  attraction 
  on 
  the 
  electrions 
  towards 
  the 
  centre 
  

  

  takes 
  the 
  place 
  o£ 
  the 
  tension 
  of 
  the 
  string, 
  provided 
  it 
  is 
  

  

  of 
  the 
  proper 
  amount. 
  But 
  it 
  does 
  not 
  secure, 
  as 
  did 
  the 
  

  

  strings, 
  against 
  instability 
  relatively 
  to 
  radial 
  displacements, 
  

  

  different 
  for 
  the 
  different 
  electrions. 
  To 
  secure 
  the 
  proper 
  

  

  la 
  v 
  

   amount 
  of 
  the 
  radial 
  force 
  the 
  condition 
  is 
  — 
  o- 
  =T 
  ; 
  where 
  

  

  a 
  

  

  i 
  denotes 
  the 
  number 
  of 
  electrions 
  ; 
  e 
  the 
  electric 
  quantity 
  

   on 
  each 
  (and 
  therefore, 
  § 
  S,ie 
  the 
  electric 
  quantity 
  of 
  vitreous 
  

   electricity 
  in 
  the 
  atom) 
  ; 
  r 
  denotes 
  the 
  radius 
  of 
  the 
  spherical 
  

   surface 
  on 
  which 
  the 
  electrions 
  lie 
  ; 
  a 
  the 
  radius 
  of 
  the 
  atom 
  ; 
  

   and 
  T 
  the 
  tension 
  of 
  the 
  string 
  in 
  the 
  arrangement 
  of 
  § 
  17 
  „ 
  

  

  e 
  2 
  . 
  

  

  We 
  have 
  generally 
  T 
  = 
  g-^ 
  where 
  q 
  is 
  a 
  numeric 
  depending 
  

  

  on 
  the 
  number 
  and 
  configuration 
  of 
  the 
  electrions 
  found 
  in 
  

  

  each 
  case 
  by 
  geometry. 
  Hence 
  we 
  have 
  - 
  = 
  \ 
  /% 
  for 
  the 
  

  

  <x 
  V 
  I 
  

  

  ratio 
  of 
  the 
  radius 
  of 
  the 
  smaller 
  sphere 
  on 
  which 
  the 
  elec- 
  

   trions 
  lie 
  to 
  the 
  radius 
  of 
  the 
  atom. 
  For 
  example, 
  take 
  the 
  

   case 
  o£ 
  eight 
  electrions 
  at 
  the 
  eight 
  corners 
  of 
  a 
  cube. 
  T 
  is 
  

   the 
  resultant 
  of 
  seven 
  repulsions, 
  and 
  we 
  easily 
  find 
  

  

  q= 
  l( 
  ^ 
  3+ 
  \J\ 
  + 
  I) 
  and 
  finallj 
  a 
  =' 
  6756 
  - 
  

   Dealing 
  similarly 
  with 
  the 
  cases 
  of 
  two, 
  three, 
  four, 
  and 
  six 
  

   electrions, 
  we 
  have 
  the 
  following 
  table 
  of 
  values 
  of 
  ( 
  °~\ 
  and 
  

   - 
  ; 
  to 
  which 
  is 
  added 
  a 
  last 
  column 
  showing 
  values 
  o£ 
  

  

  * 
  " 
  Molecular 
  Tactics 
  of 
  a 
  Crystal," 
  § 
  4. 
  

  

  