﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  35 
  

  

  from 
  symmetry 
  that 
  the 
  charges 
  are 
  equal, 
  but 
  when 
  there 
  

   are 
  two 
  or 
  more 
  rings 
  the 
  relative 
  charges 
  should 
  be 
  

   measured. 
  By 
  giving 
  a 
  proper 
  curvature 
  to 
  the 
  surface 
  

   under 
  the 
  spheres, 
  and 
  adjusting 
  the 
  lengths 
  of 
  the 
  pendulums 
  

   to 
  suit, 
  it 
  seems 
  not 
  unlikely 
  that 
  all 
  the 
  conditions 
  may 
  be 
  

   met 
  to 
  obtain 
  ideal 
  experimental 
  atoms, 
  but 
  this 
  has 
  not 
  yet 
  

   been 
  attempted. 
  

  

  No 
  careful 
  measurements 
  of 
  the 
  negatives 
  were 
  made 
  

   until 
  those 
  were 
  obtained 
  which 
  gave 
  a 
  series 
  similar 
  to 
  the 
  

   calculated 
  table. 
  Such 
  a 
  series 
  is 
  given 
  in 
  fig. 
  5 
  (PL 
  II.) 
  It 
  

   is 
  seen 
  that 
  the 
  alternative 
  figures 
  for 
  the 
  same 
  number 
  of 
  

   spheres 
  persist 
  throughout 
  the 
  set, 
  it 
  being 
  possible 
  to 
  form 
  

   sometimes 
  two, 
  three, 
  or 
  four 
  different 
  equilibrium 
  figures 
  

   with 
  the 
  same 
  number 
  of 
  spheres. 
  

  

  Experimental 
  Results. 
  

  

  The 
  chief 
  results 
  of 
  the 
  experiment 
  are 
  summarized 
  in 
  the 
  

   Table 
  II. 
  (pp. 
  36-7) 
  and 
  the 
  charts, 
  figs. 
  6 
  & 
  7 
  (PL 
  I.). 
  The 
  

   radius, 
  b, 
  of 
  the 
  positive 
  sphere 
  of 
  the 
  atom 
  is 
  calculated 
  by 
  the 
  

   formula 
  (72) 
  on 
  the 
  assumption 
  that 
  the 
  density 
  of 
  the 
  posi- 
  

   tive 
  electricity 
  is 
  uniform, 
  so 
  that 
  the 
  volume 
  of 
  the 
  sphere 
  

   increases 
  in 
  proportion 
  to 
  the 
  number 
  of 
  electrons 
  within 
  it, 
  

   and 
  the 
  radius 
  as 
  the 
  cube 
  root 
  of 
  the 
  number 
  of 
  electrons. 
  

   This 
  gives 
  the 
  smooth 
  curve 
  in 
  fig. 
  6. 
  The 
  radius, 
  a^ 
  of 
  the 
  

   outside 
  ring 
  is 
  then 
  calculated 
  on 
  the 
  assumption 
  that 
  all 
  

   the 
  electrons 
  in 
  the 
  inside 
  rings 
  are 
  at 
  the 
  centre 
  of 
  the 
  

   sphere, 
  since 
  it 
  may 
  be 
  obtained 
  from 
  formula 
  (74). 
  A 
  

   correction 
  term, 
  c, 
  is 
  then 
  obtained, 
  as 
  explained 
  on 
  page 
  80, 
  

   for 
  the 
  purpose 
  of 
  correcting 
  the 
  radius 
  of 
  the 
  outside 
  ring, 
  

   so 
  that 
  the 
  true 
  radius 
  is 
  obtained 
  as 
  if 
  the 
  inside 
  electrons 
  

   are 
  distributed 
  in 
  rings 
  and 
  not 
  assumed 
  to 
  be 
  at 
  the 
  centre 
  

   of 
  the 
  sphere. 
  This 
  gives 
  a 
  slightly 
  larger 
  radius, 
  a 
  lcy 
  in 
  

   each 
  instance 
  than 
  is 
  given 
  by 
  the 
  formula. 
  

  

  Having 
  obtained 
  the 
  radius 
  of 
  the 
  outside 
  ring 
  of 
  electrons, 
  

   the 
  radii 
  of 
  the 
  other 
  rings 
  are 
  found 
  from 
  the 
  experimental 
  

   atoms, 
  since 
  the 
  ratios, 
  r 
  2 
  , 
  of 
  the 
  average 
  radii 
  of 
  the 
  outside 
  

   ring 
  to 
  the 
  second 
  ring 
  have 
  been 
  carefully 
  measured 
  in 
  each 
  

   instance. 
  a 
  2 
  gives 
  the 
  radius 
  of 
  the 
  second 
  ring, 
  and 
  a-2 
  C 
  its 
  

   corrected 
  value. 
  The 
  column 
  ^a 
  gives 
  the 
  sum 
  of 
  the 
  radii 
  

   of 
  the 
  orbit 
  of 
  each 
  electron 
  in 
  the 
  atom. 
  The 
  broken 
  lines 
  

   in 
  fig. 
  6 
  show 
  the 
  radii 
  of 
  the 
  outside 
  ring 
  in 
  the 
  various 
  

   experimental 
  atoms, 
  and 
  those 
  in 
  fig. 
  7 
  show 
  the 
  sums 
  of 
  the 
  

   radii 
  as 
  given 
  in 
  the 
  table. 
  The 
  experimental 
  work 
  can 
  be 
  

   judged 
  in 
  a 
  measure 
  from 
  this 
  chart 
  by 
  the 
  smoothness 
  of 
  

   the 
  curves, 
  each 
  point 
  of 
  which 
  is 
  determined 
  from 
  the 
  

  

  