﻿Ionic 
  Velocities, 
  and 
  Atomic 
  Sizes* 
  167 
  

  

  dE/(lv=l; 
  and 
  if 
  at 
  infinite 
  dilution 
  i 
  is 
  assumed 
  to 
  become 
  

   1, 
  then 
  i 
  is 
  given 
  by 
  the 
  ratio 
  of 
  the 
  specific 
  molecular 
  

   conductivity 
  at 
  strength 
  m 
  to 
  that 
  at 
  strength 
  1/oc 
  . 
  But 
  for 
  

   solutions 
  in 
  general 
  we 
  take 
  rj 
  to 
  be 
  the 
  viscosity 
  of 
  the 
  

   solvent, 
  and 
  rj 
  to 
  be 
  that 
  of 
  a 
  solution 
  of 
  strength 
  m, 
  and 
  if 
  

   again 
  we 
  assume 
  that 
  i 
  becomes 
  1 
  at 
  infinite 
  dilution 
  when 
  X 
  

   becomes 
  A 
  , 
  then 
  

  

  ._ 
  \y 
  

  

  Thus 
  the 
  ionization 
  is 
  found 
  by 
  multiplying 
  the 
  usual 
  \/\ 
  

   by 
  v/vo- 
  

  

  Now 
  this 
  simple 
  theory 
  must 
  have 
  been 
  written 
  down 
  by 
  

   ninny 
  a 
  physicist 
  and 
  found 
  to 
  be 
  wanting, 
  for 
  it 
  makes 
  the 
  

   ionic 
  velocities 
  of 
  the 
  different 
  atoms 
  at 
  infinite 
  dilution 
  stand 
  

   to 
  one 
  another 
  inversely 
  as 
  their 
  radii, 
  a 
  result 
  which 
  a 
  brief 
  

   study 
  of 
  data 
  as 
  to 
  ionic 
  velocities 
  and 
  relative 
  atomic 
  sizes 
  

   shows 
  to 
  be 
  not 
  verified. 
  

  

  But 
  we 
  need 
  to 
  introduce 
  a 
  correction 
  into 
  the 
  too 
  simplified 
  

   equation 
  (6). 
  The 
  electron 
  of 
  the 
  ion 
  must 
  be 
  treated 
  as 
  if 
  it 
  

   were 
  embedded 
  in 
  the 
  atom, 
  which 
  has 
  a 
  different 
  dielectric 
  

   capacity 
  from 
  that 
  of 
  the 
  water 
  or 
  other 
  solvent. 
  

  

  Now 
  if 
  K 
  is 
  the 
  dielectric 
  capacity 
  of 
  water, 
  and 
  K 
  that 
  

   of 
  the 
  matter 
  of 
  the 
  atom 
  of 
  our 
  ion, 
  and 
  if 
  all 
  the 
  ions 
  

   gathered 
  into 
  a 
  single 
  slab 
  at 
  right 
  angles 
  to 
  the 
  current 
  

   would 
  give 
  it 
  a 
  thickness 
  t 
  in 
  a 
  distance 
  I) 
  between 
  the 
  elec- 
  

   trodes 
  whose 
  potentials 
  are 
  E 
  3 
  and 
  E 
  2 
  , 
  then 
  the 
  electric 
  force 
  

   in 
  the 
  slab 
  F 
  l 
  would 
  be 
  K 
  /K 
  times 
  that 
  in 
  the 
  water, 
  which 
  

   may 
  be 
  denoted 
  by 
  F, 
  and 
  

  

  E 
  1 
  -E 
  2 
  = 
  F(D-0 
  + 
  F 
  1 
  ^ 
  

  

  = 
  F(D^+*K 
  /K), 
  

  

  T7 
  K 
  1 
  E, 
  — 
  E 
  2 
  

  

  1 
  D\ 
  K/ 
  

  

  As 
  (Ej 
  — 
  E 
  2 
  )/D 
  is 
  the 
  same 
  as 
  dEijdoc 
  of 
  our 
  previous 
  reason- 
  

   ing, 
  we 
  find 
  the 
  electric 
  force 
  acting 
  on 
  the 
  electron 
  of 
  the 
  

   ion 
  to 
  be 
  K 
  /K{1 
  — 
  t/D(l— 
  K 
  /K)}times 
  what 
  we 
  assumed 
  it 
  

   to 
  be 
  according 
  to 
  the 
  ordinary 
  too 
  simplified 
  method 
  of 
  

   treating 
  ions 
  in 
  the 
  theory 
  of 
  electrolysis. 
  We 
  therefore 
  

   amend 
  equation 
  (8) 
  to 
  the 
  following 
  form 
  : 
  — 
  

  

  ' 
  67™ 
  \Kiai 
  Korto/1 
  — 
  — 
  

  

  K„ 
  

  

  birr, 
  \K 
  x 
  a, 
  K 
  2 
  « 
  2 
  /l-(] 
  -KyK^/D-tl-Ko/K^/D' 
  

  

  (9) 
  

  

  