﻿Osmosis 
  and 
  Osmotic 
  Pressure. 
  415 
  

  

  generally 
  be 
  true. 
  At 
  all 
  events, 
  we 
  shall 
  never 
  be 
  able 
  to 
  

   prove 
  that 
  such 
  a 
  statement 
  is 
  false. 
  

  

  The 
  second 
  statement 
  is 
  identical 
  with 
  the 
  denial 
  of 
  con- 
  

   tinuity 
  of 
  7T 
  ' 
  up 
  to 
  the 
  point 
  of 
  no 
  leak, 
  or 
  when 
  the 
  leak 
  

   approaches 
  zero 
  the 
  reversion 
  pressure 
  should 
  approach 
  the 
  

   value 
  

  

  where 
  a 
  is 
  a 
  finite 
  quantity 
  so 
  large 
  as 
  to 
  make 
  ir 
  ' 
  essentially 
  

   different 
  from 
  7r 
  , 
  and 
  the 
  cause 
  of 
  the 
  quantity 
  a 
  he 
  finds 
  

   in 
  the 
  so-called 
  selective 
  action 
  of 
  the 
  membrane. 
  

  

  It 
  seems 
  that 
  such 
  a 
  point 
  of 
  discontinuity 
  is 
  such 
  an 
  

   unfrequent 
  occurrence 
  in 
  nature, 
  that 
  it 
  cannot 
  be 
  accepted 
  

   without 
  a 
  positive 
  proof. 
  And 
  as 
  a 
  matter 
  of 
  fact, 
  we 
  shall 
  

   in 
  most 
  theoretical 
  reasoning 
  on 
  physics 
  be 
  compelled 
  to 
  

   assume 
  continuity 
  up 
  to 
  the 
  point 
  of 
  ideality. 
  So, 
  for 
  instance, 
  

   the 
  proof 
  of 
  the 
  second 
  law 
  of 
  thermodynamics 
  rests 
  upon 
  the 
  

   assumption 
  that 
  the 
  properties 
  of 
  cycles 
  that 
  can 
  be 
  actually 
  

   carried 
  out 
  converge 
  toward 
  the 
  properties 
  derived 
  from 
  an 
  

   ideal 
  reversible 
  cycle. 
  

  

  The 
  same 
  statement, 
  however, 
  is 
  only 
  built 
  upon 
  the 
  fact 
  

   that 
  the 
  pressures 
  measured 
  by 
  imperfect 
  membranes 
  gene- 
  

   rally 
  depend 
  to 
  a 
  great 
  extent 
  upon 
  the 
  membrane 
  used. 
  But 
  

   this 
  fact 
  gives 
  no 
  support 
  for 
  the 
  view 
  put 
  forth 
  by 
  Professor 
  

   Kahlenberg 
  ; 
  for, 
  as 
  we 
  have 
  seen 
  in 
  § 
  3, 
  even 
  if 
  we 
  assume 
  

   continuity 
  up 
  to 
  the 
  point 
  of 
  no 
  osmotic 
  leak, 
  we 
  came 
  to 
  the 
  

   conclusion 
  that 
  the 
  existence 
  of 
  a 
  leak 
  that 
  is 
  able 
  to 
  influence 
  

   the 
  osmotic 
  activity 
  would 
  make 
  the 
  pressure 
  7r 
  / 
  a 
  function 
  of 
  

   the 
  properties 
  of 
  the 
  membrane. 
  

  

  AVe 
  should 
  have 
  a 
  positive 
  support 
  for 
  the 
  view 
  of 
  

   Kahlenberg 
  if 
  we 
  were 
  able 
  to 
  show 
  that 
  the 
  measured 
  

   equilibrium 
  pressure 
  would 
  come 
  out 
  greater 
  than 
  the 
  thermo- 
  

   dynamic 
  osmotic 
  pressure. 
  

  

  In 
  the 
  case 
  of 
  ferrocyanide 
  and 
  cane-sugar, 
  on 
  the 
  contrary, 
  

   we 
  have, 
  as 
  we 
  have 
  seen, 
  a 
  positive 
  support 
  for 
  the 
  assumption 
  

   of 
  continuity. 
  

  

  As 
  seen 
  from 
  § 
  3, 
  the 
  correction 
  for 
  osmotic 
  leaks 
  would 
  

   require 
  an 
  acquaintance 
  with 
  the 
  mechanism 
  of 
  osmotic 
  flow 
  

   that 
  we 
  do 
  not 
  possess. 
  But 
  for 
  the 
  system 
  considered 
  we 
  

   have 
  

  

  r 
  7T 
  >7r 
  / 
  >7r'. 
  

  

  By 
  experiment 
  we 
  only 
  get 
  a 
  lower 
  limit 
  for 
  the 
  pressure 
  7r 
  '. 
  

   The 
  best 
  way 
  of 
  coming 
  to 
  a 
  value 
  near 
  to 
  it 
  q 
  would 
  be 
  to 
  

   determine 
  tt 
  ' 
  in 
  each 
  case 
  as 
  accurately 
  as 
  possible, 
  and 
  then 
  

   the 
  highest 
  pressure 
  would 
  give 
  the 
  value 
  nearest 
  to 
  the 
  ideal 
  

   pressure. 
  And 
  by 
  the 
  method 
  described 
  the 
  pressure 
  ttq 
  can 
  

  

  