﻿494 
  Dr. 
  R. 
  D. 
  Kleeman 
  on 
  some 
  

  

  The 
  assumption 
  made 
  by 
  Einstein 
  that 
  the 
  potential 
  energy 
  

   of 
  the 
  surface-film 
  of 
  a 
  liquid 
  is 
  independent 
  of 
  the 
  tempe- 
  

   rature 
  is, 
  however, 
  not 
  true. 
  The 
  potential 
  energy 
  for 
  

   different 
  substances 
  over 
  a 
  wide 
  range 
  of 
  temperature 
  has 
  

   been 
  calculated 
  by 
  Whittaker* 
  from 
  surface-tension 
  values. 
  

   He 
  finds 
  that 
  the 
  potential 
  energy 
  decreases 
  with 
  increase 
  of 
  

   temperature, 
  the 
  decrease 
  being 
  about 
  20 
  to 
  25 
  per 
  cent, 
  

   over 
  a 
  range 
  of 
  100°. 
  If 
  the 
  potential 
  energy 
  E 
  in 
  equation 
  

   (2) 
  is 
  assumed 
  constant, 
  then 
  /c' 
  cannot 
  be 
  constant, 
  for 
  there 
  

   is 
  no 
  other 
  quantity 
  in 
  the 
  equation 
  to 
  balance 
  the 
  variations 
  

   in 
  p 
  as 
  m 
  and 
  ^Ca 
  are 
  from 
  their 
  nature 
  absolute 
  constants. 
  

   It 
  is 
  very 
  unlikely 
  then 
  that 
  k! 
  should 
  be 
  a 
  constant. 
  

  

  It 
  is 
  now 
  necessary, 
  from 
  the 
  above 
  considerations, 
  to 
  

   modify 
  Einstein's 
  formula. 
  Let 
  us 
  assume 
  that 
  ac' 
  in 
  equa- 
  

   tion 
  (2) 
  is, 
  if 
  not 
  a 
  constant, 
  a 
  function 
  which 
  is 
  the 
  same 
  

   for 
  all 
  liquids 
  at 
  corresponding 
  states. 
  We 
  shall 
  then 
  com- 
  

   pare 
  the 
  results 
  of 
  this 
  assumption 
  with 
  experimental 
  results. 
  

   Integrating 
  the 
  equation, 
  we 
  have 
  

  

  X=CT-?^,(2c„)^r^'<iT, 
  

  

  where 
  C 
  is 
  an 
  arbitrary 
  constant. 
  Let 
  us 
  write 
  p 
  = 
  upc 
  and 
  

   T 
  = 
  /3Te 
  where, 
  as 
  usual, 
  pc 
  and 
  Tc 
  denote 
  the 
  critical 
  density 
  

   and 
  the 
  critical 
  temperature. 
  

   On 
  substitution 
  we 
  have 
  

  

  

  Making 
  use 
  of 
  the 
  fact 
  that 
  X 
  = 
  when 
  T 
  = 
  Tc 
  we 
  obtain 
  the 
  

   value 
  of 
  the 
  constant 
  

  

  ?7r 
  Ic 
  

   where 
  k 
  is 
  another 
  constant. 
  

   Therefore 
  

  

  

  With 
  the 
  aid 
  oi 
  p 
  = 
  ap, 
  and 
  T=/3T<„ 
  

  

  where 
  /c" 
  involves 
  only 
  quantities 
  relating 
  to 
  corresponding 
  

   states. 
  For 
  different 
  liquids 
  at 
  corresponding 
  states 
  k!' 
  is 
  

   therefore 
  the 
  same. 
  The 
  expression 
  for 
  A, 
  given 
  by 
  equation 
  

   (4) 
  is, 
  it 
  will 
  be 
  observed, 
  similar 
  to 
  the 
  expression 
  for 
  E 
  

   given 
  by 
  equation 
  (2). 
  

  

  * 
  Proc. 
  Ptoy. 
  Soc. 
  A. 
  vol. 
  Ixxxi. 
  p. 
  21 
  (1908). 
  

  

  