﻿500 
  Mr. 
  W. 
  Sulherland 
  : 
  Another 
  Method 
  of 
  

  

  the 
  values 
  o£ 
  A 
  01 
  + 
  A 
  02 
  and 
  b 
  which 
  1 
  have 
  calculated 
  from 
  

   Ostwald's 
  data, 
  as 
  given 
  by 
  Bredig 
  (loc. 
  cit.), 
  after 
  I 
  have 
  

   converted 
  them 
  to 
  the 
  ohm 
  as 
  unit. 
  The 
  substances 
  repre- 
  

   sented 
  by 
  their 
  formulas 
  are 
  the 
  sodium 
  salts 
  of 
  pyridine- 
  

   monocarboxylic 
  acid, 
  -tricarboxylic, 
  -tetracarboxylic, 
  and 
  

   -pentacarboxylic 
  acids, 
  the 
  place 
  of 
  the 
  -dicarboxylic 
  acid 
  

   being 
  taken 
  by 
  that 
  of 
  phenylpyridine-dicarboxylic 
  acid,, 
  

   and 
  the 
  6-basic 
  salt 
  beino- 
  hexasodium 
  mellitate 
  : 
  — 
  

  

  o 
  

  

  Table 
  I. 
  

  

  C 
  5 
  NH 
  4 
  C0 
  2 
  Na. 
  C 
  5 
  1N 
  H 
  2 
  C 
  6 
  H 
  5 
  (C0 
  2 
  Na) 
  2 
  . 
  C 
  5 
  NH 
  2 
  (C0 
  2 
  Na) 
  3 
  . 
  C 
  5 
  NH(C0 
  2 
  NaV 
  

   A 
  i+A 
  02 
  ... 
  89-8 
  106-1 
  144-8 
  166-5 
  

  

  b 
  0-0838 
  0-1257 
  0*1450 
  01796 
  

  

  C 
  5 
  N(C0 
  2 
  Na) 
  5 
  C 
  6 
  (C0 
  2 
  Na) 
  6 
  . 
  

   Aoi+Aoa... 
  192-1 
  204-2 
  

  

  b 
  0-2197 
  0-2830 
  

  

  From 
  the 
  data 
  of 
  Kohlrausch 
  A 
  01 
  for 
  Na 
  at 
  25° 
  0. 
  is 
  51*2,, 
  

   so 
  that 
  for 
  the 
  ions 
  of 
  these 
  six 
  acids 
  we 
  get 
  for 
  A 
  2 
  the 
  

   values 
  38-6, 
  54-9, 
  93*6, 
  115*3, 
  140'9, 
  and 
  153*0. 
  We 
  have 
  

   now 
  all 
  the 
  data 
  necessary 
  for 
  testing 
  the 
  implication 
  of 
  

   (7) 
  that 
  

  

  ?>(Ao2/v2){2wi/(wi 
  + 
  w 
  2 
  )}V(Aoi 
  + 
  A 
  2) 
  is 
  to 
  be 
  constant. 
  (8), 
  

  

  Here 
  are 
  the 
  products 
  x 
  10 
  4 
  for 
  the 
  six 
  Na 
  salts 
  : 
  — 
  

  

  361 
  358 
  358 
  363 
  382 
  423 
  

  

  We 
  shall 
  take 
  the 
  product 
  to 
  be 
  0*036 
  at 
  25°, 
  becoming 
  

   0*036 
  x 
  1*18 
  = 
  0-0425 
  at 
  18°. 
  The 
  factor 
  { 
  2n 
  1 
  /(n 
  1 
  + 
  n 
  2 
  ) 
  }i 
  enters 
  

   through 
  the 
  necessity 
  for 
  expressing 
  as 
  uniform 
  a 
  distribu- 
  

   tion 
  as 
  possible 
  throughout 
  the 
  solution 
  of 
  the 
  nn^ 
  positive 
  

   ions, 
  each 
  charged 
  with 
  v 
  x 
  electrons, 
  and 
  the 
  nn 
  2 
  negative 
  

   ions, 
  each 
  charged 
  with 
  v 
  2 
  electrons. 
  Mathematically 
  it 
  is 
  

   difficult 
  to 
  specify 
  such 
  a 
  distribution 
  ; 
  it 
  is 
  still 
  more 
  difficult 
  

   to 
  make 
  physical 
  allowance 
  for 
  the 
  effect 
  of 
  the 
  different 
  

   magnitudes 
  of 
  the 
  charges. 
  If 
  we 
  leave 
  out 
  \ 
  2n 
  1 
  /(n 
  1 
  + 
  n 
  2 
  ) 
  } 
  i 
  the 
  

   products 
  x 
  10 
  4 
  are 
  

  

  361 
  325 
  313 
  311 
  322 
  353 
  

  

  On 
  the 
  whole 
  then 
  the 
  theoretical 
  deduction 
  (7) 
  is 
  verified 
  

   by 
  experiment, 
  and 
  Ostwald's 
  valency 
  rule 
  in 
  its 
  amended 
  

   form 
  as 
  given 
  by 
  (7) 
  is 
  established 
  upon 
  a 
  theoretical 
  

   physical 
  basis. 
  By 
  its 
  means 
  the 
  ratio 
  A 
  2/v 
  2 
  can 
  be 
  found 
  

   for 
  an 
  ion 
  which 
  has 
  A 
  2 
  too 
  small 
  to 
  be 
  measured 
  with 
  

   sufficient 
  accuracy 
  in 
  the 
  ordinary 
  way. 
  From 
  this 
  ratio 
  

   the 
  volume 
  of 
  the 
  large 
  slow 
  ion 
  can 
  be 
  found 
  by 
  one 
  of 
  the 
  

  

  