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  YII. 
  The 
  Determination 
  of 
  a 
  Constant 
  in 
  Capillarity. 
  By 
  

   R. 
  D. 
  Kleeman, 
  D.Sc, 
  B.A,^ 
  Research 
  Student 
  of 
  

   Emmanuel 
  College^ 
  Cambridge* 
  . 
  

  

  WHEN 
  the 
  area 
  of 
  the 
  surface 
  of 
  a 
  liquid 
  is 
  increased 
  

   the 
  increase 
  in 
  the 
  amount 
  of 
  energy 
  in 
  the 
  surface- 
  

   film 
  of 
  the 
  liquid 
  is 
  equal 
  to 
  the 
  sum 
  of 
  the 
  external 
  work 
  

   done 
  and 
  the 
  amount 
  of 
  heat 
  absorbed 
  from 
  the 
  surrounding 
  

   bodies 
  to 
  keep 
  the 
  temperature 
  constant 
  during 
  the 
  process. 
  

   The 
  relation 
  between 
  these 
  quantities 
  can 
  be 
  immediately 
  

   obtained 
  by 
  means 
  of 
  Helmholtz's 
  free 
  energy 
  equation 
  

   conaectmg 
  the 
  total 
  energy 
  with 
  the 
  free 
  energy, 
  which 
  

   gives 
  

  

  E 
  + 
  T^=X, 
  (1) 
  

  

  a 
  

  

  where 
  \ 
  denotes 
  the 
  surface-tension 
  and 
  E 
  the 
  total 
  energy 
  

   corresponding 
  to 
  the 
  temperature 
  T. 
  X 
  is 
  equal 
  to 
  the 
  ex- 
  

   ternal 
  work 
  done, 
  and 
  —T-^ 
  is 
  therefore 
  equal 
  to 
  the 
  amount 
  

  

  of 
  heat 
  absorbed 
  from 
  the 
  surrounding 
  bodies. 
  This 
  formula 
  

   was 
  first 
  given 
  by 
  Lord 
  Kelvin. 
  

  

  Wbittakerf 
  has 
  calculated 
  the 
  values 
  of 
  E, 
  the 
  total 
  energy 
  

   for 
  different 
  temperatures, 
  for 
  a 
  number 
  of 
  liquids, 
  using 
  

   the 
  surface-tension 
  determinations 
  of 
  Ramsay 
  and 
  Shields 
  J. 
  

   He 
  found 
  that 
  the 
  energy 
  E 
  per 
  cm.^ 
  of 
  the 
  film 
  of 
  a 
  

   liquid 
  is 
  proportional 
  to 
  the 
  product 
  of 
  the 
  internal 
  latent 
  

   heat 
  of 
  evaporation 
  into 
  the 
  absolute 
  temperature 
  of 
  the 
  

   liquid, 
  or 
  

  

  E 
  = 
  KTL, 
  (2) 
  

  

  where 
  L 
  is 
  the 
  internal 
  latent 
  heat 
  of 
  evaporation 
  corre- 
  

   sponding 
  to 
  the 
  temperature 
  T, 
  and 
  K 
  is 
  a 
  constant. 
  The 
  

   constant 
  K 
  was 
  found 
  to 
  be 
  different 
  for 
  the 
  various 
  liquids. 
  

   The 
  extent 
  of 
  the 
  agreement 
  of 
  this 
  empirical 
  law 
  with 
  the 
  

   experimental 
  facts 
  is 
  shown 
  by 
  the 
  following 
  tables 
  taken 
  

   from 
  Whittaker^s 
  paper. 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  Proc. 
  Roy. 
  Soc. 
  A. 
  vol. 
  Ixxxi. 
  p. 
  21 
  (1908). 
  

  

  I 
  Phil. 
  Trans. 
  A. 
  vol. 
  clxxxiv. 
  p. 
  647 
  (1893). 
  

  

  