﻿Aepinus 
  Atomized. 
  281 
  

  

  structural 
  octahedron 
  has 
  four 
  of 
  its 
  faces 
  pointed 
  towards, 
  

   and 
  four 
  pointed 
  from, 
  by 
  its 
  electronic 
  quartets. 
  This 
  is 
  

   essentially 
  a 
  dynamically 
  octo-polar 
  * 
  assemblage 
  ; 
  and 
  it 
  

   supplies 
  us 
  with 
  a 
  perfect 
  explanation 
  of 
  the 
  piezo-electric 
  

   quality 
  to 
  be 
  inferred 
  from 
  the 
  brothers 
  Curie's 
  experimental 
  

   discovery, 
  and 
  Voigt's 
  mathematical 
  theory. 
  

  

  § 
  42. 
  Look 
  at 
  the 
  diagram 
  in 
  § 
  39; 
  and 
  remember 
  that 
  it 
  

   indicates 
  a 
  vast 
  homogeneous 
  assemblage 
  consisting 
  of 
  a 
  vast 
  

   number 
  of 
  parallel 
  plane 
  layers 
  of 
  atoms 
  on 
  each 
  side 
  of 
  the 
  

   plane 
  of 
  the 
  paper, 
  in 
  which 
  seven 
  atoms 
  are 
  shown. 
  The 
  

   quartets 
  of 
  electrions 
  were 
  described 
  as 
  all 
  similarly 
  oriented, 
  

   and 
  each 
  of 
  them 
  equilateral, 
  and 
  having 
  its 
  geometrical 
  

   centre 
  at 
  the 
  centre 
  of 
  its 
  atom 
  ; 
  conditions 
  all 
  necessary 
  for 
  

   stable 
  equilibrium. 
  

  

  § 
  43. 
  Let 
  now 
  the 
  assemblage 
  of 
  atoms 
  be 
  homogeneously 
  

   stretched 
  from 
  the 
  plane 
  on 
  both 
  sides 
  to 
  any 
  extent, 
  small 
  or 
  

   great, 
  without 
  any 
  component 
  motions 
  of 
  the 
  centres 
  of 
  the 
  

   atoms 
  parallel 
  to 
  the 
  planes 
  of 
  the 
  layers. 
  First 
  let 
  the 
  stretch 
  

   be 
  very 
  great; 
  great 
  enough 
  to 
  leave 
  undisturbed 
  by 
  the 
  other 
  

   layers 
  the 
  layer 
  for 
  which 
  the 
  centres 
  of 
  atoms 
  are, 
  and 
  the 
  

   geometrical 
  centres 
  of 
  the 
  quartets 
  were, 
  in 
  the 
  plane 
  of 
  the 
  

   paper. 
  The 
  geometrical 
  centres 
  of 
  the 
  quartets 
  are 
  not 
  now 
  

   in 
  the 
  plane 
  of 
  the 
  paper. 
  The 
  single 
  electrions 
  on 
  the 
  near 
  

   side 
  seen 
  in 
  the 
  diagram 
  over 
  the 
  centres 
  of 
  the 
  circles 
  are 
  

   drawn 
  towards 
  the 
  plane 
  of 
  the 
  paper 
  ; 
  the 
  equilateral 
  tri- 
  

   angles 
  on 
  the 
  far 
  side 
  are 
  also 
  drawn 
  nearer 
  to 
  the 
  paper 
  ; 
  and 
  

   the 
  equilateral 
  triangles 
  are 
  enlarged 
  in 
  each 
  atom 
  by 
  the 
  

   attractions 
  of 
  the 
  surrounding 
  atoms. 
  The 
  contrary 
  inward 
  

   movements 
  of 
  the 
  single 
  atoms 
  on 
  one 
  side 
  of 
  the 
  plane, 
  and 
  

   of 
  the 
  triplets 
  on 
  the 
  other 
  side, 
  cannot 
  in 
  general 
  be 
  in 
  the 
  

   proportion 
  of 
  three 
  to 
  one. 
  Hence 
  the 
  geometrical 
  centres 
  of 
  

   gravity 
  of 
  the 
  quartets 
  are 
  now 
  displaced 
  perpendicularly 
  to 
  

   the 
  plane 
  of 
  the 
  paper 
  to 
  far 
  side 
  or 
  near 
  side 
  ; 
  I 
  cannot 
  tell 
  

   which 
  without 
  calculation. 
  The 
  calculation 
  is 
  easy 
  but 
  

   essentially 
  requires 
  much 
  labour 
  ; 
  involving 
  as 
  it 
  does 
  the 
  

   determination 
  of 
  three 
  unknowns, 
  the 
  length 
  of 
  each 
  side 
  of 
  

   the 
  equilateral 
  triangle 
  seen 
  in 
  the 
  diagram, 
  the 
  distance 
  of 
  

   each 
  of 
  its 
  corners 
  from 
  the 
  electrion 
  on 
  the 
  near 
  side 
  of 
  the 
  

   paper, 
  and 
  the 
  displacement 
  of 
  the 
  geometrical 
  centre 
  of 
  

  

  * 
  The 
  octo-polar 
  pyro-electricity 
  ', 
  which 
  is 
  supposed 
  to 
  have 
  been 
  

   proved 
  by 
  Haiiy's 
  experiment, 
  must 
  have 
  been 
  due 
  to 
  something 
  aeolo- 
  

   tropic 
  in 
  the 
  heating. 
  Uniform 
  heating 
  throughout 
  a 
  regular 
  cube 
  or 
  

   octahedron 
  could 
  not 
  give 
  opposite 
  electric 
  manifestations 
  in 
  the 
  four 
  

   pairs 
  of 
  alternate 
  corners 
  of 
  the 
  cube, 
  or 
  alternate 
  faces 
  of 
  the 
  octahedron. 
  

   Nevertheless 
  the 
  irregular 
  finding 
  of 
  electric 
  octo-polarity 
  by 
  Haiiy 
  is 
  a 
  

   splendid 
  discovery 
  ; 
  of 
  which 
  we 
  only 
  now 
  know 
  the 
  true 
  and 
  full 
  

   significance, 
  through 
  the 
  experimental 
  and 
  mathematical 
  labours 
  of 
  the 
  

   brothers 
  Curie, 
  of 
  Friedel, 
  and 
  of 
  Voigt. 
  

  

  