﻿Aepinus 
  Atomized. 
  275 
  

  

  crystals 
  composed 
  of 
  our 
  hypothetical 
  atoms 
  with 
  electrions, 
  

   consider 
  first 
  merely 
  a 
  row 
  of 
  equal 
  tetraelectrionic 
  atoms 
  in 
  

   a 
  straight 
  line, 
  each 
  having 
  its 
  quantum 
  of 
  four 
  electrions 
  

   within 
  it. 
  Fig. 
  6 
  shows 
  a 
  configuration 
  of 
  stable 
  equilibrium 
  

   of 
  the 
  electrions 
  not, 
  however, 
  truly 
  to 
  scale. 
  The 
  sets 
  of 
  

  

  three 
  dots 
  indicate 
  trios 
  of 
  electrions 
  at 
  the 
  corners 
  of 
  equi- 
  

   lateral 
  triangles, 
  the 
  middle 
  dot 
  in 
  each 
  row 
  being 
  alternately 
  

   on 
  the 
  far 
  side 
  and 
  the 
  near 
  side 
  of 
  the 
  plane 
  of 
  the 
  paper, 
  

   which 
  contains 
  the 
  centres 
  of 
  the 
  atoms 
  and 
  the 
  remaining 
  

   electrion 
  of 
  each 
  four. 
  Let 
  C 
  l5 
  C, 
  C/ 
  9 
  be 
  the 
  centres 
  of 
  the 
  

   atom 
  A 
  ls 
  A, 
  A'. 
  An 
  easy 
  calculation 
  shows 
  that 
  the 
  quartet 
  

   of 
  electrions 
  within 
  A, 
  regarded 
  for 
  the 
  moment 
  as 
  a 
  group 
  

   of 
  four 
  material 
  points 
  rigidly 
  connected, 
  is 
  attracted 
  to 
  the 
  

   left 
  with 
  a 
  less 
  force 
  by 
  A 
  x 
  than 
  to 
  the 
  right 
  by 
  A' 
  (in 
  making 
  

   the 
  calculation 
  remember 
  that 
  A 
  ± 
  attracts 
  all 
  the 
  electrions 
  

   within 
  A 
  as 
  if 
  it 
  were 
  a 
  quantity 
  e 
  of 
  vitreous 
  electricity 
  

   collected 
  at 
  C 
  1? 
  and 
  similarly 
  in 
  respect 
  to 
  A'). 
  There 
  are 
  

   corresponding 
  smaller 
  differences 
  between 
  the 
  opposite 
  

   attractions 
  of 
  the 
  more 
  and 
  more 
  remote 
  atoms 
  on 
  the 
  two 
  

   sides 
  of 
  A. 
  Let 
  8 
  denote 
  the 
  excess 
  of 
  the 
  sum 
  of 
  the 
  right- 
  

   wards 
  of 
  these 
  attractions 
  above 
  the 
  leftwards. 
  The 
  geometrical 
  

   centre 
  of 
  the 
  electrions 
  within 
  A 
  is 
  displaced 
  rightwards 
  to 
  a 
  

  

  distance, 
  Z, 
  from 
  C 
  equal 
  to 
  y^ 
  2 
  . 
  

  

  § 
  33. 
  Imagine 
  now 
  a 
  crystal 
  or 
  a 
  solid 
  of 
  any 
  shape 
  built 
  

   up 
  of 
  parallel 
  rows 
  of 
  atoms 
  such 
  as 
  those 
  of 
  § 
  32. 
  The 
  

   amount 
  of 
  the 
  displacing 
  force 
  on 
  each 
  quartet 
  of 
  electrions 
  

   will 
  be 
  somewhat 
  altered 
  by 
  mutual 
  action 
  between 
  the 
  rows, 
  

   but 
  the 
  general 
  character 
  of 
  the 
  result 
  will 
  be 
  the 
  same 
  ; 
  and 
  

   we 
  see 
  that 
  throughout 
  the 
  solid, 
  except 
  in 
  a 
  thin 
  superficial 
  

   layer 
  of 
  perhaps 
  five 
  or 
  ten 
  atoms 
  deep, 
  the 
  whole 
  interior 
  

   is 
  in 
  a 
  state 
  of 
  homogeneous 
  electric 
  polarization, 
  of 
  which 
  

   the 
  electric 
  moment 
  per 
  unit 
  of 
  volume 
  is 
  4eN7 
  ; 
  where 
  N 
  is 
  

   the 
  number 
  of 
  atoms 
  per 
  unit 
  volume, 
  and 
  I 
  is 
  the 
  displace- 
  

   ment 
  of 
  the 
  geometrical 
  centre 
  of 
  each 
  quartet 
  from 
  the 
  

   centre 
  of 
  its 
  atom. 
  This 
  is 
  the 
  interior 
  molecular 
  condition 
  

   of 
  a 
  di-polar 
  pyro-electric 
  crystal, 
  which 
  I 
  described 
  in 
  I860* 
  

   as 
  probably 
  accounting 
  for 
  their 
  known 
  pyro-electric 
  quality, 
  

   * 
  ' 
  Collected 
  Mathematical 
  and 
  Physical 
  Papers/ 
  vol. 
  i. 
  p. 
  315. 
  

  

  T2 
  

  

  