﻿266 
  Mr. 
  L. 
  Vegard 
  : 
  Researches 
  upon 
  

  

  analyse 
  the 
  solvent 
  when 
  the 
  solution 
  has 
  been 
  standing 
  for 
  

   a 
  given 
  time 
  under 
  a 
  certain 
  pressure. 
  

  

  The 
  two 
  functions 
  can 
  be 
  graphically 
  represented 
  by 
  two 
  

   curves, 
  and 
  the 
  intersection 
  of 
  these 
  two 
  curves 
  would 
  give 
  

   a 
  point 
  corresponding 
  to 
  a 
  pressure 
  7r 
  ' 
  and 
  a 
  total 
  leak 
  V, 
  

   This 
  point 
  will, 
  on 
  account 
  of 
  the 
  last 
  equation 
  in 
  2c, 
  satisfy 
  

   the 
  condition 
  

  

  X=0. 
  

  

  The 
  point 
  7r 
  ' 
  will 
  in 
  general 
  be 
  different 
  from 
  7r 
  . 
  There 
  

   is 
  only 
  one 
  case 
  in 
  which 
  the 
  point 
  determined 
  in 
  this 
  manner 
  

   will 
  give 
  the 
  ideal 
  equilibrium 
  pressure. 
  That 
  occurs 
  when 
  

   the 
  total 
  leak 
  is 
  a 
  solution 
  leak. 
  Then 
  we 
  have 
  

  

  I 
  — 
  l 
  and 
  

  

  Then 
  we 
  see 
  from 
  equation 
  3 
  that 
  the 
  point 
  that 
  satisfies 
  the 
  

   equation 
  X 
  — 
  will 
  give 
  the 
  ideal 
  equilibrium 
  pressure. 
  

  

  Thus 
  we 
  see 
  that 
  in 
  the 
  case 
  when 
  the 
  velocity 
  of 
  osmotic 
  

   flow 
  X 
  can 
  be 
  considered 
  independent 
  of 
  the 
  leak, 
  it 
  should 
  

   be 
  possible 
  to 
  determine 
  the 
  ideal 
  equilibrium 
  pressure 
  even 
  

   with 
  a 
  leak 
  of 
  the 
  same 
  order 
  of 
  size 
  as 
  X 
  itself. 
  If 
  the 
  leak 
  

   is 
  not 
  very 
  great, 
  we 
  do 
  not 
  need 
  to 
  determine 
  the 
  whole 
  

   leak 
  curve; 
  we 
  only 
  need 
  to 
  determine 
  a 
  point 
  corresponding 
  

   to 
  the 
  apparent 
  equilibrium 
  pressure. 
  

  

  On 
  account 
  of 
  the 
  nature 
  of 
  the 
  leak 
  we 
  must 
  have 
  that 
  

  

  l 
  as 
  well 
  as 
  ^—- 
  never 
  can 
  be 
  negative. 
  If, 
  then, 
  for 
  a 
  

   somewhat 
  large 
  value 
  of 
  it 
  I 
  is 
  maintained 
  fairly 
  low, 
  it 
  

   seems 
  allowable 
  to 
  conclude 
  that 
  -r— 
  is 
  a 
  very 
  small 
  quantity, 
  

   and 
  for 
  the 
  surroundings 
  of 
  the 
  equilibrium 
  point 
  we 
  can 
  put 
  

   1 
  = 
  1^' 
  = 
  constant. 
  

  

  We 
  shall 
  now 
  treat 
  the 
  general 
  case 
  when 
  we 
  have 
  only 
  

   osmotic 
  leaks. 
  

  

  In 
  this 
  case 
  the 
  intersection 
  point 
  will 
  not 
  give 
  the 
  ideal 
  

   equilibrium 
  pressure. 
  If 
  we 
  knew 
  the 
  functions 
  e 
  l5 
  e 
  2 
  . 
  . 
  . 
  e 
  n 
  

   we 
  should 
  by 
  putting 
  7r 
  = 
  7r 
  ' 
  and 
  X 
  = 
  get 
  a 
  series 
  of 
  values 
  

   li, 
  / 
  2 
  ' 
  ... 
  In- 
  The 
  pressure 
  ir^ 
  must 
  satisfy 
  the 
  equation 
  

  

  +(*Jl 
  l 
  'lJ...l 
  m 
  ')=Q 
  (36) 
  

  

  The 
  ideal 
  equilibrium 
  pressure, 
  however, 
  must 
  satisfy 
  the 
  

   equation 
  3: 
  

  

  f(7T 
  0, 
  0...0) 
  = 
  (3a) 
  

  

  