﻿264 
  Mr. 
  L. 
  Vegard 
  : 
  Researches 
  upon 
  

  

  For 
  perfect- 
  permeability 
  we 
  shall 
  have 
  that 
  the 
  ideal 
  

   equilibrium 
  pressure 
  is 
  defined 
  by 
  the 
  equation 
  X 
  = 
  0. 
  

  

  For 
  all 
  the 
  intervals 
  in 
  which 
  the 
  function 
  yfr 
  has 
  a 
  physical 
  

   interpretation 
  yfr 
  must, 
  on 
  account 
  of 
  the 
  continuity 
  of 
  nature, 
  

   be 
  a 
  continuous 
  function 
  with 
  regard 
  to 
  the 
  variables. 
  We 
  

   shall 
  in 
  general 
  consider 
  the 
  equation 
  

  

  f(7rl 
  1 
  l 
  2 
  ...l 
  n 
  C.Tk 
  1 
  lc 
  2 
  .. 
  ) 
  = 
  0. 
  . 
  

  

  By 
  this 
  equation 
  the 
  pressure 
  is 
  implicitly 
  given 
  as 
  a 
  

   function 
  of 
  C.Tli... 
  Z„and 
  h\k 
  2 
  ... 
  . 
  This 
  pressure 
  we 
  shall 
  

   call 
  7r 
  '. 
  In 
  the 
  interval 
  of 
  physical 
  interpretation 
  7r 
  ' 
  is 
  a 
  

   continuous 
  and 
  single-valued 
  function 
  of 
  the 
  named 
  variables. 
  

   But 
  as 
  we 
  cannot 
  produce 
  perfect 
  semipermeability 
  we 
  cannot 
  

   be 
  sure 
  that 
  the 
  continuity 
  with 
  regard 
  to 
  the 
  leaks 
  will 
  

   hold 
  quite 
  up 
  to 
  the 
  point 
  l 
  x 
  = 
  l 
  2 
  = 
  . 
  . 
  . 
  = 
  l 
  n 
  = 
  . 
  If 
  it 
  was 
  not 
  

   allowed 
  to 
  assume 
  continuity 
  up 
  to 
  this 
  point 
  it 
  would 
  mean 
  

   that 
  the 
  conception 
  perfect 
  semipermeability, 
  as 
  applied 
  to 
  

   nature 
  in 
  the 
  case 
  considered, 
  would 
  be 
  an 
  absurdity. 
  It 
  

   might 
  also 
  be 
  that 
  for 
  certain 
  membranes 
  and 
  solutions 
  the 
  

   assumption 
  is 
  not 
  allowed, 
  while 
  it 
  is 
  allowed 
  for 
  others. 
  

   At 
  all 
  events, 
  if 
  we 
  cannot 
  assume 
  continuity 
  up 
  to 
  the 
  point 
  

   / 
  = 
  0, 
  we 
  have 
  no 
  means 
  of 
  combining 
  the 
  ideal 
  equilibrium 
  

   pressure 
  with 
  the 
  reversion 
  pressure 
  actually 
  measured. 
  

  

  The 
  following 
  development 
  is 
  restricted 
  to 
  those 
  cases 
  for 
  

   which 
  7r 
  ' 
  can 
  be 
  considered 
  a 
  continuous 
  function 
  of 
  the 
  

   leaks 
  quite 
  up 
  to 
  the 
  point 
  l 
  x 
  =l 
  2 
  = 
  ...= 
  l 
  n 
  =0. 
  This 
  condition 
  

   we 
  can 
  write 
  

  

  l-l 
  = 
  0. 
  

  

  Under 
  these 
  conditions 
  the 
  ideal 
  equilibrium 
  pressure 
  is 
  

   defined 
  by 
  the 
  equation 
  

  

  f(7ry 
  2 
  ...ZXW 
  2 
  ...)=0 
  .... 
  (3) 
  

   l-l 
  =0 
  

  

  With 
  perfect 
  semipermeability 
  ir 
  is 
  a 
  function 
  of 
  C 
  and 
  T, 
  

   provided 
  £> 
  is 
  constant, 
  and 
  then 
  we 
  see 
  that 
  if 
  the 
  ideal 
  equi- 
  

   librium 
  pressure 
  can 
  be 
  defined 
  by 
  equation 
  3, 
  ijr 
  must 
  be 
  

   such 
  a 
  function 
  of 
  k 
  x 
  k 
  2 
  ... 
  k 
  m 
  that 
  for 
  Z 
  — 
  Z 
  = 
  and 
  \ 
  = 
  the 
  

   quantities 
  dependent 
  on 
  the 
  membrane 
  must 
  disappear. 
  And 
  

   consequently, 
  if 
  i|r 
  is 
  continuous 
  with 
  regard 
  to 
  the 
  leaks 
  up 
  

   to 
  the 
  point 
  of 
  ideality, 
  we 
  must 
  have 
  that 
  the 
  influence 
  of 
  the 
  

   membrane 
  upon 
  the 
  reversion 
  pressure 
  actually 
  measured 
  must 
  

   disappear 
  with 
  the 
  leak. 
  

  

  Let 
  us, 
  on 
  the 
  other 
  hand, 
  assume 
  that 
  the 
  membrane 
  has 
  

   such 
  properties 
  that 
  when 
  the 
  leaks 
  diminish 
  the 
  pressure 
  

   7T(/ 
  approaches 
  a 
  value 
  7r 
  " 
  where 
  

  

  