﻿280 
  Lord 
  Kelvin 
  : 
  

  

  according 
  to 
  the 
  value 
  *612a 
  given 
  for 
  r 
  in 
  the 
  table 
  of 
  § 
  20 
  r 
  

   on 
  the 
  supposition 
  that 
  the 
  circles 
  shown 
  in 
  the 
  diagram 
  

   represent 
  the 
  electric 
  spheres 
  of 
  the 
  atoms 
  in 
  contact. 
  

  

  § 
  40. 
  Imagine 
  now 
  the 
  electrions 
  of 
  each 
  quartet 
  to 
  be 
  

   rigidly 
  connected 
  with 
  one 
  another 
  and 
  given 
  freedom 
  only 
  

   to 
  rotate 
  about 
  an 
  axis 
  perpendicular 
  to 
  the 
  plane 
  of 
  the 
  

   paper. 
  To 
  all 
  of 
  them 
  apply 
  torques 
  ; 
  turning 
  the 
  central 
  

   quartet 
  of 
  the 
  diagram 
  slowly 
  and 
  keeping 
  all 
  the 
  others 
  at 
  

   rest. 
  It 
  is 
  clear 
  that 
  the 
  first 
  60° 
  of 
  turning 
  brings 
  the 
  

   central 
  quartet 
  to 
  a 
  position 
  of 
  unstable 
  equilibrium, 
  and 
  60° 
  

   more 
  to 
  a 
  position 
  of 
  stable 
  equilibrium 
  corresponding 
  to 
  the 
  

   first 
  position, 
  which 
  we 
  now 
  see 
  was 
  stable 
  when 
  the 
  others 
  are 
  

   all 
  held 
  fixed. 
  We 
  are 
  now 
  judging 
  simply 
  from 
  the 
  mutual 
  

   actions 
  between 
  our 
  central 
  quartet 
  and 
  the 
  six 
  shown 
  around 
  

   it 
  in 
  the 
  diagram 
  ; 
  but 
  it 
  may 
  be 
  easily 
  proved 
  that 
  our 
  

   judgment 
  is 
  not 
  vitiated 
  by 
  the 
  mutual 
  action 
  between 
  the 
  

   central 
  quartet 
  and 
  all 
  around 
  it 
  in 
  space, 
  including 
  the 
  six 
  in 
  

   the 
  diagram. 
  Similarly 
  we 
  see 
  that 
  any 
  one 
  quartet 
  of 
  the 
  

   assemblage, 
  free 
  to 
  turn 
  round 
  an 
  axis 
  perpendicular 
  to 
  the 
  

   plane 
  of 
  the 
  paper 
  wdiile 
  all 
  the 
  others 
  are 
  fixed, 
  is 
  in 
  stable 
  

   equilibrium 
  when 
  oriented 
  as 
  are 
  those 
  shown 
  in 
  the 
  diagram.. 
  

   And 
  similarly 
  again 
  we 
  see 
  the 
  same 
  conclusion 
  in 
  respect 
  to 
  

   three 
  other 
  diagrams 
  in 
  the 
  three 
  other 
  planes 
  parallel 
  to 
  the 
  

   faces 
  of 
  the 
  tetrahedrons 
  or 
  corresponding 
  octahedrons 
  of 
  the 
  

   assemblage. 
  Hence 
  we 
  conclude 
  that 
  if 
  the 
  axial 
  constraints 
  

   are 
  all 
  removed, 
  and 
  the 
  quartets 
  left 
  perfectly 
  free, 
  every 
  

   one 
  of 
  them 
  rests 
  in 
  stable 
  equilibrium 
  when 
  oriented 
  either 
  

   as 
  one 
  set 
  or 
  as 
  the 
  other 
  set 
  of 
  equilateral 
  tetrahedronal 
  

   quartets 
  of 
  the 
  assemblage. 
  It 
  is 
  interesting 
  to 
  remark 
  that 
  

   if, 
  alter 
  we 
  turned 
  the 
  central 
  quartet 
  through 
  60°, 
  we 
  had 
  

   held 
  it 
  in 
  that 
  position 
  and 
  left 
  all 
  the 
  others 
  free 
  to 
  rotate* 
  

   rotational 
  vibrations 
  would 
  have 
  spread 
  out 
  among 
  them 
  from 
  

   the 
  centre; 
  and,, 
  after 
  losing 
  in 
  waves 
  spreading 
  through 
  

   ether 
  outside 
  the 
  assemblage 
  the 
  energy 
  which 
  we 
  gave 
  by 
  

   our 
  torque 
  acting 
  on 
  the 
  central 
  quartet, 
  they 
  would 
  come 
  to 
  

   stable 
  equilibrium 
  with 
  every 
  one 
  of 
  them 
  turned 
  60° 
  in 
  one 
  

   direction 
  or 
  the 
  other 
  from 
  its 
  primitive 
  position, 
  and 
  oriented 
  

   as 
  the 
  central 
  quartet 
  in 
  the 
  position 
  in 
  which 
  we 
  held 
  it. 
  

  

  § 
  41. 
  We 
  have 
  thus 
  found 
  that 
  an 
  equilateral 
  homogeneous- 
  

   assemblage 
  of 
  atoms 
  each 
  having 
  four 
  electrions 
  within 
  it,, 
  

   arranges 
  these 
  electrions 
  in 
  equilateral 
  quartets 
  all 
  oriented 
  

   in 
  one 
  or 
  other 
  of 
  two 
  ways. 
  The 
  assemblage 
  of 
  atoms 
  and 
  

   electrions 
  thus 
  produced 
  is 
  essentially 
  octo-polar. 
  Of 
  the 
  

   two 
  elementary 
  structural 
  tetrahedrons, 
  of 
  the 
  two 
  orien- 
  

   tations, 
  one 
  will 
  have 
  every 
  one 
  of 
  its 
  electrionic 
  quartets 
  

   pointing 
  towards, 
  the 
  other 
  from, 
  its 
  faces. 
  The 
  elementary 
  

  

  