﻿282 
  Aepinus 
  Atomized. 
  

  

  gravity 
  of 
  the 
  four 
  to 
  one 
  side 
  or 
  other 
  of 
  the 
  plane. 
  Each 
  

   one 
  of 
  the 
  three 
  equations 
  involves 
  summations 
  of 
  infinite 
  

   convergent 
  series, 
  expressing 
  force-components 
  due 
  to 
  all 
  the 
  

   atoms 
  surrounding 
  any 
  chosen 
  one 
  in 
  the 
  plane. 
  A 
  method 
  

   of 
  approximation 
  on 
  the 
  same 
  general 
  plan 
  as 
  that 
  of 
  the 
  

   footnote 
  to 
  § 
  9 
  above 
  would 
  give 
  a 
  practicable 
  method 
  of 
  

   calculation 
  . 
  

  

  § 
  44. 
  Return 
  to 
  § 
  42, 
  and 
  consider 
  the 
  diagram 
  as 
  repre- 
  

   senting 
  a 
  crystal 
  in 
  its 
  natural 
  unstressed 
  condition, 
  consisting 
  

   of 
  a 
  vast 
  train 
  of 
  assemblages 
  of 
  atoms 
  with 
  centres 
  in 
  the 
  

   plane 
  of 
  the 
  paper, 
  and 
  in 
  parallel 
  planes 
  on 
  each 
  side 
  of 
  it. 
  

   We 
  now 
  see 
  that 
  the 
  forces 
  experienced 
  by 
  the 
  electrions 
  of 
  

   one 
  quartet 
  from 
  all 
  the 
  surrounding 
  atoms 
  in 
  the 
  plane 
  of 
  

   the 
  paper 
  would, 
  if 
  uncompensated, 
  displace 
  the 
  geometrical 
  

   centre 
  of 
  gravity 
  of 
  the 
  quartet 
  to 
  one 
  side 
  or 
  other 
  of 
  the 
  

   plane 
  of 
  the 
  paper, 
  and 
  we 
  infer 
  that 
  the 
  forces 
  experienced 
  

   from 
  all 
  the 
  atoms 
  on 
  the 
  two 
  sides 
  of 
  this 
  plane 
  give 
  this 
  

   compensation 
  to 
  keep 
  the 
  centre 
  of 
  gravity 
  of 
  the 
  quartet 
  in 
  

   the 
  plane. 
  Stretch 
  now 
  the 
  assemblage 
  to 
  any 
  degree 
  equally 
  

   in 
  all 
  directions. 
  The 
  quartets 
  remain 
  equilateral 
  with 
  their 
  

   centres 
  of 
  gravity 
  in 
  the 
  plane 
  of 
  the 
  paper 
  and 
  parallel 
  

   planes. 
  Lastly 
  stretch 
  it 
  farther 
  equally 
  in 
  all 
  directions 
  

   parallel 
  to 
  the 
  plane 
  of 
  the 
  paper, 
  with 
  no 
  component 
  motion 
  

   perpendicular 
  to 
  this 
  plane. 
  This 
  last 
  stretching 
  diminishes 
  

   the 
  influence 
  of 
  all 
  the 
  atoms 
  whose 
  centres 
  are 
  in 
  the 
  plane 
  

   of 
  the 
  paper 
  tending 
  to 
  displace 
  the 
  centres 
  of 
  gravity 
  of 
  

   their 
  electrions 
  in 
  one 
  direction 
  from 
  this 
  plane 
  ; 
  and 
  therefore 
  

   leaves 
  all 
  the 
  atoms 
  out 
  of 
  this 
  plane 
  to 
  predominate, 
  and 
  to 
  

   cause 
  a 
  definite 
  calculable 
  displacement 
  of 
  the 
  centres 
  of 
  

   gravity 
  of 
  all 
  the 
  quartets 
  in 
  the 
  contrary 
  direction 
  to 
  the 
  

   former. 
  

  

  § 
  45. 
  To 
  realize 
  the 
  operations 
  of 
  § 
  44, 
  cut 
  a 
  thin 
  hexa- 
  

   gonal 
  plate 
  from 
  the 
  middle 
  between 
  two 
  opposite 
  corners 
  of 
  

   a 
  cubic 
  crystal, 
  or 
  parallel 
  faces 
  of 
  an 
  octahedron. 
  Fix 
  

   clamps 
  to 
  the 
  six 
  edges 
  of 
  this 
  plate, 
  and 
  apply 
  forces 
  pulling 
  

   their 
  pairs 
  equally 
  in 
  contrary 
  directions. 
  The 
  whole 
  material 
  

   of 
  the 
  plate 
  becomes 
  electro-polar 
  with 
  electric 
  moment 
  per 
  

   unit 
  bulk 
  equal 
  to 
  4Ng# 
  ; 
  of 
  which 
  the 
  measurable 
  result 
  is 
  

   uniform 
  electrostatical 
  potentials 
  * 
  in 
  vacuous 
  ether 
  close 
  to 
  

   the 
  two 
  sides 
  of 
  the 
  plate, 
  differing 
  by 
  4-7T 
  . 
  4Naatf, 
  where 
  t 
  

   denotes 
  the 
  thickness 
  of 
  the 
  plate, 
  x 
  the 
  calculated 
  displace- 
  

   ment 
  of 
  the 
  centre 
  of 
  gravity 
  of 
  each 
  quartet 
  from 
  the 
  centres 
  

   of 
  the 
  atoms 
  parallel 
  to 
  the 
  two 
  faces 
  of 
  the 
  plate, 
  e 
  the 
  electric 
  

   mass 
  of 
  an 
  electrion, 
  and 
  N 
  the 
  number 
  of 
  atoms 
  per 
  cubic 
  

  

  * 
  See 
  my 
  ' 
  Electrostatics 
  and 
  Magnetism/ 
  § 
  512, 
  cor. 
  3. 
  

  

  