﻿Osmosis 
  and 
  Osmotic 
  Pressure. 
  26*J 
  

  

  By 
  addition 
  of 
  equations 
  4 
  and 
  5 
  and 
  by 
  putting 
  

  

  (ta^(£).^ 
  ■■■(!»«:'-* 
  

  

  we 
  get 
  

  

  When 
  the 
  leaks 
  are 
  very 
  small 
  we 
  can 
  regard 
  ^-^ 
  as 
  

  

  . 
  dX' 
  ^ 
  

  

  small 
  quantities 
  in 
  comparison 
  to 
  ~^~ 
  , 
  then 
  we 
  can 
  put 
  

  

  f'd±\ 
  _(^\ 
  

  

  ~) 
  = 
  ^+ 
  , 
  d 
  J. 
  ftr' 
  + 
  S). 
  • 
  • 
  (66) 
  

  

  and 
  we 
  get 
  

  

  /aA/ 
  \ 
  

   W7T 
  /it' 
  

  

  This 
  equation 
  is 
  the 
  most 
  general, 
  it 
  contains 
  also 
  the 
  case 
  

   when 
  the 
  velocity 
  o£ 
  osmotic 
  flow 
  is 
  independent 
  of 
  the 
  leak; 
  

   e. 
  g., 
  if 
  the 
  leak 
  l 
  x 
  could 
  be 
  regarded 
  as 
  a 
  solution 
  leak 
  we 
  

  

  should 
  have 
  in 
  the 
  sum 
  2 
  to 
  put 
  ^y- 
  =0. 
  

  

  Oh 
  

  

  Even 
  in 
  the 
  case 
  of 
  a 
  small 
  leak 
  we 
  are, 
  at 
  least 
  with 
  the 
  

   present 
  knowledge 
  about 
  the 
  osmotic 
  process, 
  unable 
  to 
  find 
  

   the 
  correction 
  due 
  to 
  that 
  part 
  of 
  the 
  leak 
  which 
  is 
  able 
  

   to 
  influence 
  the 
  osmotic 
  activity. 
  We 
  can 
  only 
  find 
  the 
  

   pressure 
  T 
  \ 
  

  

  As 
  to 
  the 
  quantity 
  2 
  we 
  know 
  at 
  present 
  very 
  little 
  about 
  

   its 
  actual 
  size. 
  In 
  the 
  case 
  of 
  copper 
  ferrocyanide 
  and 
  sugar 
  

   solutions 
  we 
  have 
  reason 
  to 
  believe 
  that 
  it 
  will 
  be 
  positive. 
  

   It 
  is 
  stated 
  by 
  Berkeley 
  and 
  Hartley* 
  that 
  in 
  their 
  experi- 
  

   ments 
  the 
  corrected 
  pressure 
  (tT(/) 
  generally 
  comes 
  out 
  smaller 
  

   for 
  a 
  greater 
  leak. 
  It 
  appears 
  from 
  this 
  that 
  as 
  far 
  as 
  the 
  

   leaks 
  are 
  able 
  to 
  influence 
  the 
  pressure 
  w 
  ' 
  the 
  latter 
  will 
  be 
  

   diminished 
  by 
  the 
  leak. 
  This 
  is 
  also 
  confirmed 
  by 
  some 
  

   experiments 
  that 
  will 
  be 
  described 
  later. 
  

  

  As 
  there 
  probably 
  always 
  will 
  be 
  some 
  osmotic 
  leak 
  we 
  

   have 
  

  

  7r 
  >7r 
  / 
  >7r' 
  (7) 
  

  

  d\' 
  

   And, 
  as 
  shown 
  by 
  the 
  experiments, 
  ■=— 
  will 
  be 
  a 
  positive 
  

  

  quantity, 
  then 
  d7r 
  

  

  2>0. 
  

  

  * 
  Loc. 
  cit. 
  p. 
  503. 
  

  

  