﻿356 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  the 
  Effect 
  0j 
  

  

  situated 
  in 
  the 
  infinitesimal 
  volumes 
  au 
  x 
  r,...au 
  m 
  T 
  at 
  Pi,...P 
  TO 
  , 
  

   or 
  

  

  v 
  , 
  = 
  Kn 
  e 
  ~ 
  t'^auxT 
  . 
  . 
  . 
  au 
  m 
  r 
  . 
  

  

  A 
  similar 
  expression 
  holds 
  for 
  v. 
  2 
  except 
  that 
  both 
  </> 
  and 
  the 
  

   us 
  are 
  infinitesimally 
  different 
  : 
  

  

  Equating 
  v 
  x 
  and 
  v 
  2 
  we 
  get 
  

  

  4^-^} 
  = 
  ... 
  = 
  ^J^«4=0. 
  . 
  (7) 
  

  

  !Now, 
  if 
  we 
  write 
  (f> 
  in 
  the 
  form 
  

  

  <j> 
  = 
  fa 
  + 
  fa' 
  = 
  fa 
  + 
  fa', 
  

  

  where 
  </>l 
  is 
  the 
  mutual 
  energy 
  of 
  Ai 
  with 
  all 
  the 
  rest, 
  fa' 
  the 
  

   mutual 
  energy 
  of 
  all 
  the 
  ra 
  — 
  1 
  ions 
  other 
  than 
  A 
  lt 
  fa 
  that 
  

   of 
  A 
  2 
  with 
  all 
  the 
  rest, 
  &c, 
  we 
  see 
  that 
  the 
  only 
  part 
  of 
  <f> 
  

   which 
  is 
  affected 
  by 
  d/dx 
  x 
  is 
  fa, 
  and 
  similarly 
  for 
  each 
  of 
  

   the 
  other 
  ions. 
  Consequently, 
  integrating 
  (7), 
  we 
  see 
  that 
  

   the 
  conditions 
  which 
  must 
  be 
  satisfied 
  in 
  order 
  that 
  the 
  

   distribution 
  may 
  not 
  be 
  disturbed 
  are 
  

  

  M!e 
  _cpl 
  ^ 
  T 
  = 
  const., 
  

  

  u 
  2 
  e~^ 
  kT 
  = 
  const., 
  &c. 
  

  

  The 
  constant 
  is 
  independent 
  of 
  x, 
  that 
  is, 
  of 
  fa, 
  fa, 
  &c, 
  

   and 
  is 
  equal 
  to 
  the 
  velocity 
  with 
  which 
  an 
  ion 
  will 
  move 
  

   when 
  it 
  is 
  so 
  far 
  away 
  from 
  the 
  others 
  that 
  its 
  mutual 
  energy 
  

   with 
  them 
  is 
  zero. 
  In 
  these 
  circumstances 
  the 
  velocity 
  will 
  

   be 
  conditioned 
  simply 
  by 
  the 
  friction 
  of 
  the 
  water, 
  and 
  it 
  is 
  

   clearly 
  the 
  same 
  for 
  all 
  ions 
  of 
  the 
  same 
  sign. 
  Calling 
  it 
  u 
  

   in 
  unit 
  field, 
  we 
  shall 
  then 
  have 
  for 
  the 
  mobility 
  u 
  l9 
  which 
  an 
  

   ion 
  must 
  be 
  reckoned 
  to 
  possess 
  when 
  it 
  exists 
  in 
  a 
  place 
  

   where 
  its 
  mutual 
  energy 
  with 
  other 
  ions 
  is 
  fa, 
  

  

  Mi=W( 
  /i/*t 
  (8) 
  

  

  Effect 
  on 
  Osmotic 
  Pressure. 
  — 
  In 
  the 
  method 
  of 
  the 
  kinetic 
  

   theory 
  of 
  considering 
  the 
  pressure 
  of 
  a 
  gas 
  as 
  the 
  rate 
  at 
  

   which 
  momentum 
  is 
  transferred 
  through 
  a 
  unit 
  plane 
  within 
  

   it, 
  a 
  careful 
  distinction 
  must 
  be 
  made 
  between 
  " 
  internal 
  " 
  

   and 
  " 
  external 
  " 
  pressure. 
  Consider 
  a 
  gas 
  in 
  which 
  — 
  say 
  by 
  

   impressed 
  mechanical 
  forces 
  — 
  the 
  potential 
  energy 
  of 
  a 
  

  

  