﻿Measuring 
  large 
  Molecular 
  Masses. 
  499 
  

  

  molecular 
  concentrations, 
  we 
  have 
  m 
  the 
  number 
  o£ 
  gram 
  

   -equivalents 
  per 
  cm. 
  3 
  equal 
  to 
  

  

  »(niv 
  1 
  + 
  n 
  1 
  v 
  8 
  ) 
  (3) 
  

  

  So 
  the 
  relation 
  between 
  A, 
  and 
  m 
  is 
  

  

  l/\ 
  = 
  { 
  1 
  + 
  27rC(A 
  01 
  + 
  A 
  02 
  ) 
  2 
  v 
  l 
  v 
  2 
  (n 
  1 
  + 
  n 
  2 
  )hni/3M(n 
  1 
  v 
  l 
  -f 
  n 
  2 
  v 
  2 
  )i 
  

  

  EIA 
  01 
  Ao 
  2 
  }/(A 
  01 
  + 
  A 
  02 
  ). 
  • 
  (4) 
  

   For 
  brevity 
  we 
  write 
  this 
  : 
  — 
  

  

  l/\=l/(A 
  01 
  +A 
  02 
  ) 
  + 
  &mi, 
  .... 
  (5) 
  

   where 
  

  

  £=27r0 
  1 
  v 
  2 
  (w 
  1 
  + 
  n 
  2 
  )i{A 
  01 
  + 
  A 
  02 
  )/37i3(n 
  1 
  v 
  1 
  + 
  7i 
  2 
  v 
  2 
  )iKIA 
  01 
  A 
  02 
  (G) 
  

  

  and 
  is 
  the 
  immediate 
  subject 
  of 
  study. 
  

  

  In 
  the 
  important 
  case 
  o£ 
  the 
  Na 
  salt 
  of 
  a 
  v 
  2 
  -basic 
  acid 
  we 
  

   have 
  712=1/!= 
  1, 
  u 
  1 
  = 
  v 
  2 
  , 
  and 
  

  

  /Wl 
  + 
  W 
  2 
  \3 
  V 
  l 
  V 
  2 
  A 
  01 
  +A 
  2 
  

  

  -^\ 
  2fll 
  J 
  a 
  01 
  A 
  02 
  3/**KI 
  * 
  * 
  * 
  ' 
  l 
  ; 
  

  

  The 
  experimental 
  material 
  from 
  which 
  Ostvvald 
  discovered 
  

   his 
  valency 
  rule 
  affords 
  a 
  suitable 
  test 
  for 
  this 
  theoretical 
  

   deduction. 
  It 
  will 
  be 
  noticed 
  that 
  b, 
  the 
  coefficient 
  of 
  rm, 
  

   depends 
  not 
  only 
  on 
  v 
  1 
  v 
  2 
  but 
  also 
  upon 
  both 
  A 
  01 
  and 
  A 
  02 
  , 
  

   whereas 
  in 
  Ostwald's 
  rule 
  there 
  is 
  no 
  mention 
  of 
  this 
  latter 
  

   dependence. 
  The 
  reason 
  for 
  A 
  01 
  and 
  A 
  02 
  not 
  entering 
  into 
  

   Ostwald's 
  statement 
  of 
  his 
  rule 
  is 
  that 
  he 
  worked 
  only 
  with 
  

   Na 
  salts, 
  so 
  that 
  A 
  i 
  was 
  constant, 
  and 
  that 
  although 
  he 
  

   worked 
  with 
  acids 
  with 
  basicity 
  ranging 
  from 
  1 
  to 
  6, 
  there 
  

   was 
  a 
  rough 
  tendency 
  for 
  {(n 
  l 
  -\-n 
  2 
  )/2n 
  1 
  }i(A 
  01 
  + 
  A 
  02 
  )/A 
  o2 
  to 
  

   be 
  constant 
  and 
  so 
  to 
  disguise 
  the 
  dependence 
  on 
  A 
  02 
  . 
  In 
  

   testing 
  our 
  equations 
  we 
  shall 
  first 
  apply 
  (5) 
  to 
  Ostwald's 
  

   data 
  for 
  the 
  sodium 
  salt 
  of 
  nicotinic 
  or 
  ^-pyridine 
  carboxylic 
  

   acid 
  C 
  <5 
  H 
  4 
  NCOOH 
  converting 
  them 
  from 
  the 
  Siemens 
  unit 
  of 
  

   resistance, 
  which 
  he 
  used, 
  to 
  the 
  ohm. 
  I 
  find 
  A 
  i 
  + 
  A 
  02 
  = 
  89"8, 
  

   and 
  6 
  = 
  0*0838, 
  which 
  give 
  the 
  following 
  comparison 
  : 
  — 
  

  

  1/103/w 
  32 
  64 
  128 
  256 
  512 
  1024 
  

  

  Xexp 
  72-9 
  75-4 
  78-0 
  80-3 
  82'4 
  84-0 
  

  

  A 
  calc 
  72-6 
  75-6 
  78-1 
  80-3 
  82*0 
  83'6 
  

  

  By 
  availing 
  himself 
  of 
  the 
  carboxyl 
  substitution 
  compounds 
  

   of 
  pyridine 
  up 
  to 
  pyridine 
  pentacarboxylic 
  acid, 
  Ostwald 
  

   obtained 
  a 
  series 
  of 
  similar 
  ions 
  with 
  v 
  2 
  ranging 
  from 
  1 
  to 
  5, 
  

   and 
  by 
  means 
  of 
  the 
  sodium 
  mellitate 
  6 
  (COONa) 
  6 
  he 
  carried 
  

   his 
  investigation 
  up 
  to 
  v 
  2 
  =6. 
  The 
  following 
  table 
  contains 
  

  

  2L2 
  

  

  