﻿Aepinus 
  Atomized. 
  277 
  

  

  axes 
  : 
  it 
  may 
  be 
  null 
  for 
  each 
  of 
  them 
  : 
  it 
  may 
  be 
  null 
  or 
  of 
  any 
  

   value 
  for 
  the 
  so-called 
  optic 
  axis. 
  Haiiy 
  found 
  geometrical 
  

   differences 
  in 
  respect 
  to 
  crystalline 
  facets 
  at 
  the 
  two 
  ends 
  of 
  

   a 
  tourmaline 
  ; 
  and 
  between 
  the 
  opposite 
  corners 
  of 
  cubes, 
  as 
  

   leucite, 
  which 
  possess 
  electropolarity. 
  There 
  are 
  no 
  such 
  

   differences, 
  there 
  are 
  only 
  the 
  chiral 
  differences, 
  between 
  the 
  

   two 
  ends 
  of 
  a 
  quartz 
  crystal 
  (hexagonal 
  prism 
  with 
  hexagonal 
  

   pyramids 
  at 
  the 
  two 
  ends) 
  but 
  there 
  are 
  differences 
  (visible 
  or 
  

   invisible) 
  between 
  the 
  opposite 
  edges 
  of 
  the 
  hexagonal 
  prism. 
  

   The 
  electropolar 
  virtue 
  is 
  null 
  for 
  the 
  axis 
  of 
  the 
  prism, 
  and 
  

   is 
  proved 
  to 
  exist 
  between 
  the 
  opposite 
  edges 
  by 
  the 
  beautiful 
  

   piezo-electric 
  discovery 
  of 
  the 
  brothers 
  Curie, 
  according 
  to 
  

   which 
  a 
  thin 
  flat 
  bar, 
  cut 
  with 
  its 
  faces 
  and 
  its 
  length 
  perpen- 
  

   dicular 
  to 
  two 
  parallel 
  faces 
  of 
  the 
  hexagonal 
  prism 
  and 
  its 
  

   breadth 
  parallel 
  to 
  the 
  edges 
  of 
  the 
  prism, 
  shows 
  opposite 
  elec- 
  

   tricities 
  on 
  its 
  two 
  faces, 
  when 
  stretched 
  by 
  forces 
  pulling 
  its 
  

   ends. 
  This 
  proves 
  the 
  three 
  electropolar 
  axes 
  to 
  bisect 
  the 
  

   120° 
  angles 
  between 
  the 
  consecutive 
  plane 
  faces 
  of 
  the 
  prism. 
  

  

  § 
  35. 
  For 
  the 
  present 
  let 
  us 
  think 
  only 
  of 
  the 
  octopolar 
  

   electric 
  a?olotropy 
  discovered 
  by 
  Haiiy 
  in 
  the 
  cubic 
  class 
  of 
  

   crystals. 
  The 
  quartet 
  of 
  electrions 
  at 
  the 
  four 
  corners 
  of 
  a 
  

   tetrahedron 
  presents 
  itself 
  readily 
  as 
  possessing 
  intrinsically 
  

   the 
  symmetrical 
  octo-polar 
  quality 
  which 
  is 
  realized 
  in 
  the 
  

   natural 
  crystal. 
  If 
  we 
  imagine 
  an 
  assemblage 
  of 
  atoms 
  in 
  

   simple 
  cubic 
  order, 
  each 
  containing 
  an 
  equilateral 
  quartet 
  of 
  

   electrions, 
  all 
  similarly 
  oriented 
  with 
  their 
  four 
  faces 
  per- 
  

   pendicular 
  to 
  the 
  four 
  diagonals 
  of 
  each 
  structural 
  cube, 
  we 
  

   have 
  exactly 
  the 
  required 
  aeolotropy 
  ; 
  but 
  the 
  equilibrium 
  of 
  

   the 
  electrions 
  all 
  similarly 
  oriented 
  would 
  probably 
  be 
  un- 
  

   stable 
  ; 
  and 
  we 
  must 
  look 
  to 
  a 
  less 
  simple 
  assemblage 
  in 
  

   order 
  to 
  have 
  stability 
  with 
  similar 
  orientation 
  of 
  all 
  the 
  

   electrionic 
  quartets. 
  

  

  § 
  36. 
  This, 
  I 
  believe, 
  we 
  have 
  in 
  the 
  doubled 
  equilateral 
  

   homogeneous 
  assemblage 
  of 
  points 
  described 
  in 
  § 
  69 
  of 
  my 
  

   paper 
  on 
  " 
  Molecular 
  Constitution 
  of 
  Matter," 
  republished 
  

   from 
  the 
  Transactions 
  of 
  the 
  Royal 
  Society 
  of 
  Edinburgh 
  for 
  

   1889 
  in 
  volume 
  iii. 
  of 
  my 
  ' 
  Collected 
  Mathematical 
  and 
  

   Physical 
  Papers'' 
  (p. 
  426) 
  ; 
  which 
  may 
  be 
  described 
  as 
  

   follows 
  for 
  an 
  assemblage 
  of 
  equal 
  and 
  similar 
  globes 
  : 
  — 
  

   Beginning 
  with 
  an 
  equilateral 
  homogeneous 
  assemblage 
  of 
  

   points,, 
  A, 
  make 
  another 
  similar 
  assemblage 
  of 
  points, 
  B, 
  by 
  

   placing 
  a 
  B 
  in 
  the 
  centre 
  of 
  each 
  of 
  the 
  similarly 
  oriented 
  

   quartets 
  of 
  the 
  assemblage 
  of 
  A's. 
  It 
  will 
  be 
  found 
  that 
  

   every 
  A 
  is 
  at 
  the 
  centre 
  of 
  an 
  o^jositeli/ 
  oriented 
  quartet 
  of 
  the 
  

   W>. 
  To 
  understand 
  this, 
  let 
  A], 
  A 
  £ 
  , 
  A 
  3 
  , 
  A 
  4 
  be 
  an 
  equilateral 
  

   quartet 
  of 
  the 
  A's 
  ; 
  and 
  imagine 
  A 
  2 
  , 
  A 
  3 
  , 
  A 
  4 
  placed 
  on 
  a 
  

  

  