﻿On 
  the 
  Conductivity 
  of 
  Aqueous 
  Solutions, 
  151 
  

  

  merits 
  on 
  conductivity 
  alluded 
  to 
  in 
  Section 
  13, 
  will 
  be 
  ready 
  

   for 
  publication 
  in 
  the 
  near 
  future. 
  

  

  In 
  conclusion, 
  I 
  desire 
  to 
  express 
  my 
  tbanks 
  to 
  Professor 
  

   Thomson 
  for 
  the 
  valuable 
  assistance 
  his 
  suggestions 
  have 
  

   afforded. 
  

  

  XIV. 
  On 
  the 
  Calculation 
  of 
  the 
  Conductivity 
  of 
  Aqueous 
  

   Solutions 
  containing 
  Two 
  Electrolytes 
  ivith 
  no 
  Common 
  Ion. 
  

   By 
  Prof. 
  J. 
  G. 
  MacGregor 
  and 
  Mr. 
  E. 
  H. 
  Archibald, 
  

  

  Dalhousie 
  College, 
  Halifax, 
  iV./S.* 
  

  

  ACCORDING 
  to 
  the 
  dissociation 
  theory 
  of 
  electrolysis 
  the 
  

   specific 
  conductivity 
  of 
  a 
  complex 
  solution, 
  volume 
  v 
  of 
  

   which 
  contains 
  Nj, 
  N 
  2 
  , 
  N 
  3 
  , 
  &c, 
  gramme-equivalents 
  of 
  the 
  

   electrolytes 
  1, 
  2, 
  3, 
  &c, 
  respectively, 
  is 
  given 
  by 
  the 
  expression 
  

  

  - 
  (aiN^i 
  +a 
  2 
  N 
  2 
  yLtoo 
  2 
  +«3^3A 
  t 
  »3 
  + 
  &C.), 
  

  

  where 
  the 
  a's 
  are 
  the 
  coefficients 
  of 
  ionization 
  of 
  the 
  electro- 
  

   lytes 
  and 
  the 
  fi^'s 
  their 
  specific 
  conductivities 
  per 
  gramme- 
  

   equivalent 
  at 
  infinite 
  dilution. 
  If 
  the 
  quantities 
  involved 
  in 
  

   this 
  expression 
  can 
  be 
  determined 
  in 
  the 
  case 
  of 
  any 
  solution, 
  

   its 
  conductivity 
  can 
  be 
  calculated. 
  

  

  Since 
  but 
  little 
  change 
  in 
  the 
  ionic 
  velocities 
  of 
  one 
  electro- 
  

   lyte 
  in 
  a 
  solution 
  can 
  be 
  produced 
  by 
  small 
  quantities 
  of 
  

   others, 
  the 
  value 
  of 
  fi 
  n 
  for 
  an 
  electrolyte 
  in 
  a 
  complex 
  solution 
  

   may 
  be 
  taken 
  to 
  be 
  the 
  same 
  as 
  in 
  a 
  simple 
  solution, 
  provided 
  

   the 
  complex 
  solution 
  be 
  sufficiently 
  dilute. 
  Hence 
  for 
  such 
  

   solutions, 
  the 
  //,^'s 
  of 
  the 
  above 
  expression 
  may 
  be 
  determined 
  

   by 
  observations 
  of 
  conductivity 
  made 
  on 
  sufficiently 
  extended 
  

   series 
  of 
  simple 
  solutions 
  of 
  1, 
  2. 
  3, 
  &c. 
  

  

  In 
  a 
  former 
  paper 
  by 
  one 
  of 
  usf 
  it 
  has 
  been 
  shown 
  that 
  

   equations 
  sufficient 
  for 
  the 
  determination 
  of 
  the 
  a 
  a 
  and 
  the 
  

   N's 
  may 
  be 
  obtained, 
  provided 
  the 
  following 
  assumptions 
  be 
  

   admissible, 
  viz., 
  (1) 
  that 
  any 
  dissolved 
  electrolyte, 
  which 
  is 
  in 
  

   dissociational 
  equilibrium, 
  may 
  be 
  regarded 
  as 
  being 
  in 
  this 
  

   state 
  not 
  only 
  throughout 
  the 
  whole 
  volume 
  of 
  the 
  solution, 
  

   but 
  also 
  throughout 
  any 
  finite 
  part 
  of 
  it, 
  and 
  (2) 
  that 
  each 
  

   electrolyte 
  in 
  a 
  complex 
  solution, 
  with 
  its 
  undissociated 
  and 
  

   its 
  dissociated 
  parts, 
  though 
  disseminated 
  throughout 
  the 
  

   whole 
  volume, 
  may 
  be 
  regarded 
  as 
  occupying 
  a 
  definite 
  

   portion 
  of 
  the 
  volume, 
  which 
  may 
  be 
  spoken 
  of 
  as 
  its 
  region. 
  

   It 
  would 
  follow 
  from 
  these 
  assumptions 
  that 
  the 
  law 
  of 
  

   equilibrium 
  may 
  be 
  applied 
  either 
  to 
  one 
  such 
  region 
  or 
  to 
  

  

  * 
  Communicated 
  by 
  the 
  Authors. 
  

  

  t 
  MacGregor, 
  Trans. 
  Koy. 
  Soc. 
  Canada 
  [2], 
  ii. 
  sec. 
  iii. 
  (1896), 
  p. 
  65. 
  

  

  