﻿498 
  Mr. 
  W. 
  Sutherland 
  : 
  Another 
  Method 
  of 
  

  

  dielectric 
  capacity 
  of 
  the 
  solvent, 
  I 
  the 
  force 
  in 
  the 
  solvent 
  

   which 
  ionizes 
  the 
  solute 
  completely 
  at 
  all 
  concentrations, 
  

   and 
  \ 
  is 
  generally 
  identical 
  with 
  A 
  i-1-A 
  02 
  . 
  In 
  applying 
  

   equation 
  (1) 
  to 
  the 
  refined 
  measurements 
  of 
  Kohlrausch 
  and 
  

   his 
  pupils 
  on 
  very 
  dilute 
  aqueous 
  solutions 
  I 
  showed 
  that 
  

   Vi 
  v 
  2 
  did 
  not 
  suffice 
  to 
  express 
  the 
  whole 
  dependence 
  upon 
  

   valencies, 
  and 
  that 
  seemingly 
  a 
  factor 
  (y 
  x 
  + 
  v 
  2 
  ) 
  2 
  is 
  introduced 
  

   by 
  1/1. 
  Moreover, 
  Kohlrausch 
  has 
  recently 
  preferred 
  to 
  

   treat 
  X 
  as 
  linear 
  in 
  ??i 
  rather 
  than 
  in 
  m, 
  which 
  was 
  his 
  dis- 
  

   covery 
  of 
  years 
  ago. 
  I 
  believe 
  this 
  discrepancy 
  arises 
  in 
  the 
  

   assumption 
  made 
  in 
  calculating 
  \ 
  from 
  the 
  experimental 
  

   measurements 
  that 
  the 
  conductivity 
  of 
  the 
  water 
  is 
  not 
  

   altered 
  by 
  the 
  presence 
  of 
  the 
  solute. 
  Now 
  in 
  the 
  Mole- 
  

   cular 
  Constitution 
  of 
  Aqueous 
  Solutions 
  (Phil. 
  Mag. 
  [6] 
  xii. 
  

   p. 
  1) 
  I 
  showed 
  that 
  the 
  H 
  ions 
  of 
  acids 
  and 
  the 
  OH 
  ions 
  of 
  

   alkalies 
  ionize 
  H 
  2 
  powerfully. 
  It 
  is 
  possible 
  therefore 
  and 
  

   probable 
  that 
  other 
  ions 
  ionize 
  H 
  2 
  to 
  a 
  small 
  extent, 
  variable 
  

   with 
  the 
  concentration. 
  Probably 
  a 
  very 
  careful 
  discussion 
  

   of 
  Kohlrausch's 
  measurements 
  would 
  clear 
  up 
  the 
  discrepancy 
  

   between 
  his 
  experiments 
  and 
  (1) 
  and 
  would 
  give 
  the 
  law 
  of 
  

   the 
  ionization 
  of 
  H 
  2 
  by 
  all 
  ions. 
  Equation 
  (1) 
  is 
  well 
  

   verified 
  by 
  measurements 
  on 
  solutions 
  which 
  are 
  not 
  too 
  

   dilute, 
  though 
  even 
  with 
  them 
  v 
  1 
  v 
  2 
  (ni-f-n 
  2 
  )i 
  does 
  not 
  suffice 
  

   to 
  give 
  the 
  whole 
  of 
  the 
  dependence 
  upon 
  valency. 
  But 
  on 
  

   the 
  other 
  hand 
  equation 
  (1), 
  n 
  s 
  it 
  stands, 
  expresses 
  the 
  

   valency 
  rule 
  discovered 
  inductively 
  by 
  Ostwald 
  from 
  his 
  

   experiments 
  on 
  dilute 
  solutions 
  of 
  the 
  Na 
  salts 
  of 
  pobybasic 
  

   acids 
  (Ztschr. 
  f. 
  physik. 
  Chem. 
  i. 
  and 
  ii.). 
  The 
  form 
  in 
  

   which 
  Ostwakl/s 
  valency 
  rule 
  is 
  expressed 
  by 
  Bredig 
  (ibid. 
  

   xiii.) 
  is 
  equivalent 
  to 
  d\/dn 
  = 
  v 
  1 
  v 
  2 
  (f)(n) 
  , 
  whero 
  (f>(n) 
  is 
  a 
  

   function 
  of 
  the 
  concentration 
  the 
  same 
  for 
  all 
  solutes. 
  This 
  

   is 
  the 
  result 
  obtainable 
  from 
  (1) 
  by 
  differentiation. 
  Thus 
  

   (1) 
  is 
  in 
  agreement 
  with 
  a 
  large 
  body 
  of 
  experimental 
  

   evidence. 
  But 
  (1) 
  for 
  dilute 
  solutions 
  may 
  be 
  written 
  

   approximately 
  

  

  \ 
  /\ 
  = 
  1 
  + 
  2tt(A 
  01 
  + 
  A 
  Q2 
  )Cv 
  l 
  v 
  2 
  {n(n 
  1 
  + 
  n 
  2 
  )/A}i/3KI\ 
  . 
  (2) 
  

  

  But 
  a 
  better 
  value 
  of 
  the 
  coefficient 
  of 
  ni 
  can 
  be 
  obtained 
  

   by 
  improving 
  the 
  reasoning 
  by 
  which 
  X 
  comes 
  into 
  the 
  

   right-hand 
  side 
  of 
  (1). 
  In 
  (1) 
  X 
  measures 
  the 
  rate 
  at 
  

   which 
  a 
  positive 
  ion 
  and 
  a 
  neighbour 
  negative 
  one 
  tend 
  to 
  

   relax 
  the 
  strain 
  produced 
  in 
  them 
  by 
  electric 
  force. 
  But 
  it 
  

   will 
  be 
  better 
  to 
  regard 
  each 
  ion 
  relaxing 
  at 
  its 
  own 
  rate, 
  and 
  

   so 
  to 
  replace 
  1/X 
  by 
  1/A 
  01 
  + 
  1/A 
  02 
  . 
  If 
  in 
  the 
  usual 
  way 
  we 
  

   are 
  going 
  to 
  compare 
  solutions 
  of 
  equivalent 
  and 
  not 
  equi- 
  

  

  