﻿262 
  Mr. 
  L. 
  Vegard 
  : 
  Researches 
  upon 
  

  

  way 
  or 
  other, 
  T 
  the 
  temperature, 
  and 
  p 
  and 
  p> 
  the 
  pressure 
  

   upon 
  the 
  solution 
  and 
  the 
  solvent 
  respectively. 
  In 
  the 
  

   measurements 
  here 
  given 
  p 
  ni 
  ^ 
  ne 
  function 
  <£ 
  can 
  be 
  regarded 
  

   as 
  a 
  constant, 
  and 
  we 
  have 
  

  

  7r 
  =4> 
  (C,T) 
  (16) 
  

  

  There 
  are 
  three 
  quantities 
  to 
  be 
  measured 
  : 
  

  

  (1) 
  The 
  osmotic 
  pressure 
  7r 
  . 
  

  

  (2) 
  The 
  concentration 
  actually 
  present 
  under 
  the 
  experiment. 
  

  

  (3) 
  The 
  temperature. 
  

  

  On 
  the 
  Calculation 
  of 
  the 
  Osmotic 
  Pressure. 
  

  

  9. 
  As 
  the 
  membranes 
  actually 
  used 
  probably 
  always 
  will 
  

   admit 
  some 
  solution 
  passing 
  through, 
  the 
  measured 
  apparent 
  

   equilibrium 
  pressure, 
  7T 
  7 
  , 
  will 
  be 
  different 
  from7r 
  . 
  It 
  may 
  be 
  

   of 
  importance 
  to 
  put 
  the 
  question 
  into 
  a 
  mathematical 
  

   form, 
  to 
  examine 
  more 
  closely 
  the 
  problem 
  with 
  which 
  we 
  

   have 
  to 
  deal 
  and 
  to 
  see 
  what 
  would 
  be 
  required 
  for 
  an 
  exact 
  

   determination 
  of 
  osmotic 
  pressure. 
  To 
  that 
  end 
  we 
  shall 
  

   consider 
  the 
  velocity 
  of 
  the 
  leak 
  and 
  the 
  velocity 
  of 
  osmotic 
  

   flow. 
  We 
  shall 
  assume 
  that 
  the 
  velocity 
  of 
  flow 
  as 
  well 
  as 
  

   the 
  leak 
  is 
  measured 
  by 
  the 
  increase 
  in 
  height 
  of 
  water-level 
  

   in 
  unit 
  time. 
  

  

  At 
  first 
  we 
  shall 
  make 
  some 
  remarks 
  as 
  regards 
  the 
  leak. 
  

   The 
  leak 
  may 
  be 
  due 
  to 
  a 
  mere 
  mechanical 
  defect 
  in 
  the 
  

   membrane. 
  In 
  this 
  case 
  the 
  leak, 
  if 
  it 
  is 
  too 
  small 
  to 
  call 
  

   forth 
  any 
  motion 
  in 
  the 
  fluids, 
  can 
  be 
  considered 
  as 
  taking- 
  

   place 
  independently 
  of 
  the 
  osmosis. 
  By 
  putting 
  the 
  appa- 
  

   ratus 
  up 
  under 
  a 
  certain 
  pressure 
  and 
  measuring 
  the 
  amount 
  

   of 
  solute 
  that 
  has 
  passed 
  through 
  in 
  a 
  certain 
  time, 
  we 
  should 
  

   be 
  able 
  to 
  find 
  the 
  velocity 
  of 
  leak 
  by 
  assuming 
  that 
  it 
  has 
  

   passed 
  through 
  the 
  membrane 
  with 
  the 
  concentration 
  of 
  the 
  

   solution. 
  

  

  For 
  this 
  kind 
  of 
  leak 
  that 
  will 
  not 
  effect 
  the 
  osmotic 
  

   activity 
  we 
  shall 
  adopt 
  the 
  name 
  used 
  by 
  Berkeley 
  and 
  

   Hartley 
  and 
  call 
  it 
  the 
  Solution 
  Leak. 
  

  

  There 
  may, 
  however, 
  be 
  another 
  kind 
  of 
  leak 
  due 
  to 
  the 
  

   fact 
  that 
  the 
  membrane 
  substance 
  itself, 
  even 
  in 
  the 
  good 
  

   parts 
  of 
  it, 
  does 
  not 
  give 
  conditions 
  for 
  perfect 
  semi- 
  

   permeability. 
  This 
  leak 
  will 
  be 
  a 
  function 
  of 
  the 
  osmotic 
  

   process, 
  and 
  the 
  latter 
  will 
  most 
  likely 
  be 
  influenced 
  by 
  the 
  

   leak. 
  This 
  leak 
  cannot 
  be 
  regarded 
  as 
  a 
  leak 
  of 
  solution, 
  

   but 
  rather 
  as 
  a 
  leak 
  of 
  solute. 
  This 
  kind 
  of 
  leak 
  we 
  shall 
  

   •call 
  the 
  Osmotic 
  Leak. 
  To 
  get 
  a 
  strict 
  definition 
  of 
  this 
  

   leak, 
  we 
  shall 
  assume 
  that 
  the 
  solute 
  also 
  in 
  this 
  case 
  is 
  con- 
  

   nected 
  with 
  so 
  much 
  of 
  the 
  solvent 
  as 
  to 
  give 
  a 
  solution 
  of 
  

  

  