﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  81 
  

  

  correction 
  term 
  when 
  they 
  are 
  supposed 
  to 
  be 
  transferred 
  to 
  

   the 
  centre. 
  The 
  correction 
  term 
  denoted 
  by 
  c, 
  to 
  be 
  added 
  

   to 
  w, 
  may 
  be 
  found 
  from 
  measurements 
  upon 
  the 
  photographs 
  

   of 
  the 
  experimental 
  atoms, 
  and 
  the 
  method 
  is 
  as 
  follows. 
  

  

  Let 
  be 
  the 
  centre 
  of 
  the 
  atom, 
  A 
  an 
  electron 
  in 
  the 
  

   outside 
  ring, 
  and 
  B 
  one 
  in 
  an 
  inside 
  ring. 
  The 
  repulsion 
  

   of 
  B 
  upon 
  A 
  is 
  <? 
  2 
  /KR 
  2 
  , 
  and 
  this 
  force 
  resolved 
  along 
  the 
  

  

  radius 
  OA 
  is 
  VTiS 
  , 
  where 
  AC 
  is 
  the 
  geometrical 
  projection 
  

  

  of 
  the 
  distance 
  R 
  between 
  the 
  electrons 
  upon 
  the 
  diameter 
  

   through 
  A. 
  The 
  force 
  of 
  repulsion 
  of 
  all 
  the 
  u 
  electrons 
  

   within 
  the 
  outside 
  ring 
  upon 
  the 
  one 
  electron 
  A 
  in 
  the 
  

  

  outside 
  ring 
  is 
  ^2-™-, 
  the 
  summation 
  being 
  extended 
  to 
  

  

  all 
  of 
  the 
  outside 
  electrons. 
  If 
  it 
  is 
  supposed 
  that 
  all 
  these 
  

   inside 
  electrons 
  are 
  transferred 
  to 
  the 
  centre 
  of 
  the 
  sphere 
  

  

  ite 
  

   the 
  force 
  of 
  repulsion 
  upon 
  A 
  would 
  be 
  ^ 
  — 
  r 
  2 
  . 
  In 
  order 
  

  

  that 
  the 
  outside 
  ring 
  shall 
  not 
  be 
  disturbed 
  these 
  forces 
  

   should 
  equal 
  each 
  other, 
  but 
  it 
  is 
  found 
  by 
  the 
  measurements 
  

   on 
  the 
  negatives 
  that 
  the 
  former 
  is 
  always 
  larger 
  than 
  the 
  

   latter. 
  Let 
  h 
  be 
  the 
  measured 
  difference, 
  then 
  

  

  AC 
  

  

  h. 
  

  

  K^R 
  3 
  a{ 
  2 
  )~ 
  

  

  This 
  difference 
  may 
  be 
  considered 
  as 
  the 
  force 
  due 
  to 
  e 
  

   additional 
  electrons 
  at 
  the 
  centre 
  of 
  the 
  sphere, 
  and 
  c 
  is 
  the 
  

   correction 
  term 
  required. 
  Since 
  the 
  force 
  upon 
  A 
  due 
  to 
  

  

  one 
  

  

  electron 
  

  

  at 
  the 
  

  

  centre 
  is 
  

  

  e 
  2 
  

  

  we 
  have 
  

  

  

  

  KKaf 
  

  

  C= 
  2 
  

  

  e 
  2 
  

  

  = 
  a 
  2 
  t 
  

  

  AC 
  

  

  R 
  3 
  w 
  ' 
  

  

  . 
  . 
  . 
  (78) 
  

  

  by 
  which 
  it 
  is 
  evident 
  that 
  c 
  is 
  a 
  term 
  which 
  should 
  be 
  

   added 
  to 
  u 
  in 
  equation 
  (74), 
  and 
  it 
  may 
  be 
  found 
  from 
  the 
  

  

  AC 
  

   negatives 
  by 
  measuring 
  both 
  S-ftt 
  and 
  a 
  l9 
  the 
  average 
  

  

  radius 
  of 
  the 
  outside 
  ring. 
  

  

  Since 
  the 
  outside 
  ring 
  is 
  not 
  a 
  true 
  circle 
  in 
  the 
  experi- 
  

   mental 
  atoms, 
  it 
  is 
  found 
  that 
  the 
  value 
  of 
  c 
  cannot 
  be 
  

   obtained 
  with 
  sufficient 
  accuracy 
  by 
  selecting, 
  a 
  single 
  elec- 
  

   tron 
  in 
  the 
  outside 
  ring 
  and 
  calculating 
  the 
  forces 
  upon 
  it. 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  151. 
  July 
  1913. 
  G 
  

  

  