﻿Osmosis 
  and 
  Osmotic 
  Pressur 
  

  

  e. 
  

  

  263 
  

  

  the 
  same 
  concentration 
  as 
  the 
  solution 
  in 
  the 
  osmometer. 
  

   This 
  assumption 
  will 
  only 
  cause 
  some 
  difference 
  as 
  to 
  what 
  

   we 
  understand 
  by 
  the 
  velocity 
  of 
  osmotic 
  flow. 
  The 
  leak 
  

   defined 
  in 
  this 
  manner 
  will 
  be 
  proportional 
  to 
  the 
  actual 
  

   leak, 
  and 
  they 
  will 
  both 
  of 
  them 
  disappear 
  simultaneously. 
  

   When 
  the 
  leaks 
  are 
  defined 
  in 
  this 
  manner 
  we 
  can 
  consider 
  

   the 
  total 
  leak 
  as 
  a 
  measurable 
  quantity, 
  when 
  we 
  are 
  able 
  to 
  

   determine 
  the 
  amount 
  o£ 
  solute 
  that 
  has 
  passed 
  through 
  by 
  a 
  

   certain 
  pressure 
  in 
  a 
  certain 
  time. 
  

  

  Let 
  us 
  in 
  general 
  assume 
  that 
  the 
  total 
  leak 
  is 
  I 
  and 
  the 
  

   total 
  amount 
  of 
  solution 
  leak 
  l 
  . 
  Further, 
  we 
  shall 
  assume 
  

   that 
  there 
  are 
  a 
  certain 
  number 
  of 
  leaks 
  l 
  x 
  l 
  2 
  ... 
  l 
  n 
  which 
  each 
  

   influence 
  the 
  osmotic 
  flow 
  in 
  its 
  own 
  manner. 
  According 
  to 
  

   their 
  nature 
  the 
  leaks 
  must 
  be 
  absolute 
  quantities 
  that 
  cannot 
  

   change 
  their 
  signs, 
  so 
  when 
  Z 
  = 
  all 
  the 
  other 
  leaks 
  must 
  be 
  

   equal 
  to 
  zero. 
  

  

  The 
  apparent 
  velocity 
  of 
  osmotic 
  flow 
  we 
  shall 
  call 
  X'. 
  

   This 
  is 
  the 
  velocity 
  directly 
  examined. 
  The 
  velocity 
  of 
  

   osmotic 
  flow 
  X 
  we 
  shall 
  define 
  by 
  the 
  equation 
  

  

  \ 
  = 
  \'— 
  I 
  . 
  . 
  . 
  

  

  In 
  general 
  we 
  must 
  be 
  able 
  to 
  put 
  

  

  \ 
  = 
  \]r(jr 
  ? 
  l5 
  l 
  2 
  , 
  ... 
  In 
  0, 
  T, 
  k 
  r 
  k 
  2 
  . 
  

   l 
  1 
  = 
  e 
  1 
  {ir\CTk 
  1 
  f 
  h 
  2 
  , 
  . 
  t 
  .) 
  

  

  / 
  2 
  = 
  6 
  2 
  (7T\CT^ 
  2 
  )/J 
  2 
  ( 
  2 
  )...) 
  

  

  l 
  n 
  =e 
  n 
  (ir\GTk 
  1 
  ^k^...) 
  

  

  (2a) 
  

  

  >. 
  . 
  . 
  (2b) 
  

  

  eoCTrCT*! 
  ^ 
  

  

  ) 
  

  

  7T 
  denotes 
  an 
  arbitrary 
  pressure 
  difference 
  between 
  the 
  

   solution 
  and 
  the 
  solvent; 
  k, 
  Jc 
  ± 
  ... 
  &/A' 
  ■•« 
  &c., 
  are 
  parameters 
  

   dependent 
  upon 
  the 
  qualities 
  of 
  the 
  membrane 
  and 
  the 
  

   mechanism 
  of 
  osmotic 
  flow. 
  

  

  In 
  order 
  to 
  find 
  a 
  mathematical 
  expression 
  for 
  the 
  relation 
  

   between 
  7r 
  and 
  ir 
  f 
  , 
  we 
  must 
  be 
  able 
  to 
  define 
  the 
  ideal 
  

   equilibrium 
  pressure 
  by 
  means 
  of 
  the 
  quantities 
  in 
  equations 
  

   2a 
  and 
  2b. 
  This 
  definition 
  we 
  get 
  by 
  fixing 
  the 
  conception 
  

   of 
  semipermeability. 
  We 
  shall 
  have 
  perfect 
  semipermeability 
  

   when 
  Z=0, 
  and 
  X 
  is 
  a 
  function 
  of 
  ir 
  defined 
  as 
  a 
  single- 
  

   valued 
  function 
  in 
  the 
  neighbourhood 
  of 
  the 
  reversion 
  point, 
  

  

  and 
  further 
  we 
  must 
  have 
  ( 
  j- 
  | 
  different 
  from 
  zero. 
  Then 
  

  

  the 
  manipulations 
  necessary 
  for 
  the 
  thermodynamic 
  treatment 
  

   can 
  be 
  carried 
  out. 
  

  

  