﻿

  Osmosis 
  and 
  Osmotic 
  Pressure, 
  265 
  

  

  where 
  a 
  is 
  a 
  finite 
  quantity, 
  and 
  as 
  being 
  due 
  to 
  the 
  leaks 
  it 
  

   would 
  be 
  a 
  quantity 
  characteristic 
  of 
  the 
  membrane, 
  and 
  

   would 
  necessarily 
  change 
  with 
  the 
  properties 
  of 
  the 
  membrane, 
  

   and 
  we 
  might 
  expect 
  that 
  a 
  change 
  in 
  the 
  membrane 
  con- 
  

   stants 
  would 
  give 
  rise 
  to 
  a 
  change 
  in 
  the 
  reversion 
  pressure 
  

   of 
  the 
  same 
  order. 
  

  

  If, 
  then, 
  we 
  are 
  able 
  to 
  show 
  that 
  the 
  reversion 
  pressure 
  

   keeps 
  constant 
  while 
  the 
  qualities 
  of 
  the 
  membrane 
  or 
  the 
  

   mechanism 
  of 
  osmotic 
  flow 
  in 
  some 
  way 
  are 
  altered, 
  it 
  will 
  

   give 
  a 
  strong 
  evidence 
  for 
  the 
  correctness 
  of 
  the 
  assumption 
  

   as 
  to 
  the 
  continuity 
  of 
  7r 
  ' 
  to 
  the 
  point 
  of 
  ideal 
  semipermea- 
  

   bility, 
  so 
  the 
  pressure 
  measured 
  by 
  a 
  small 
  total 
  leak 
  must 
  

   be 
  near 
  to 
  the 
  ideal 
  pressure. 
  We 
  shall 
  later 
  have 
  an 
  

   occasion 
  to 
  come 
  back 
  to 
  this 
  question. 
  

  

  In 
  general 
  the 
  quantities 
  &,& 
  2 
  ...&c., 
  even 
  during 
  one 
  

   experiment, 
  will 
  vary 
  with 
  time. 
  In 
  the 
  following 
  we 
  shall 
  

   find 
  the 
  properties 
  of 
  the 
  membrane 
  at 
  a 
  certain 
  moment, 
  or, 
  

   in 
  other 
  words, 
  we 
  shall 
  find 
  the 
  properties 
  under 
  the 
  as- 
  

   sumption 
  that 
  kj,: 
  2 
  ... 
  can 
  be 
  kept 
  constant. 
  Further, 
  we 
  

   shall 
  consider 
  C 
  and 
  T 
  constant. 
  As 
  to 
  the 
  concentration 
  it 
  

   will 
  change 
  on 
  account 
  of 
  X 
  and 
  /, 
  but 
  we 
  shall 
  assume 
  that 
  

   this 
  variation 
  is 
  so 
  small 
  as 
  not 
  to 
  produce 
  any 
  appreciable 
  

   effect 
  upon 
  the 
  velocities. 
  Then 
  we 
  may 
  write 
  the 
  equations 
  

   2a 
  and 
  2b 
  

  

  \=yfr{7rl 
  1 
  l 
  2 
  ...l 
  n 
  ) 
  

  

  / 
  x 
  = 
  e, 
  (ttX) 
  

  

  / 
  2 
  = 
  6 
  2 
  (7r\) 
  

  

  / 
  = 
  e 
  (7r) 
  

  

  (2c) 
  

  

  If 
  we 
  put 
  into 
  the 
  functions 
  e 
  1 
  e 
  2 
  ... 
  e 
  n 
  the 
  value 
  of 
  X 
  from 
  

   the 
  first 
  equation, 
  we 
  get 
  n 
  equations 
  between 
  the 
  >i 
  + 
  l 
  

   quantities 
  l 
  x 
  l 
  2 
  . 
  . 
  . 
  i 
  a 
  and 
  it. 
  And 
  by 
  this 
  means 
  l 
  Y 
  l 
  2 
  ... 
  In, 
  

   and 
  thence 
  A, 
  can 
  be 
  found 
  in 
  terms 
  of 
  ir. 
  From 
  this 
  it 
  

   follows 
  that 
  we 
  always 
  can 
  put 
  

  

  V 
  = 
  ?(tt) 
  

  

  / 
  = 
  7?(7t). 
  

  

  These 
  two 
  functions 
  can 
  be 
  found 
  by 
  experiment. 
  X' 
  can 
  

   be 
  found 
  by 
  determining 
  the 
  apparent 
  velocity 
  corresponding 
  

   to 
  different 
  pressures, 
  and 
  to 
  find 
  rj(7r) 
  we 
  should 
  have 
  to 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  16. 
  No. 
  92. 
  Aug. 
  1908. 
  T 
  

  

  