﻿502 
  Dr. 
  E. 
  D. 
  Kleeman 
  on 
  some 
  

  

  surface-tension 
  has 
  been 
  determined 
  over 
  a 
  limited 
  range 
  

   o£ 
  temperatures 
  in 
  some 
  cases 
  so 
  that 
  a 
  corresponding 
  tem- 
  

   perature 
  referring 
  to 
  each 
  liquid 
  cannot 
  be 
  found, 
  and 
  the 
  

   values 
  of 
  Ca 
  for 
  a 
  number 
  of 
  atoms 
  cannot 
  therefore 
  be 
  

   obtained 
  under 
  this 
  restriction. 
  A 
  formula 
  involving 
  S<?„ 
  

   will 
  be 
  developed 
  at 
  a 
  later 
  stage 
  which 
  is 
  not 
  restricted 
  to 
  

   the 
  same 
  extent 
  in 
  its 
  application. 
  

  

  Similarly, 
  the 
  values 
  of 
  (k^')2C„ 
  for 
  a 
  number 
  of 
  atoms 
  have 
  

  

  been 
  calculated 
  from 
  the 
  equation 
  (Ac")(Sca)^= 
  — 
  2~5 
  ^^^^ 
  are 
  

  

  given 
  in 
  the 
  fourth 
  column 
  of 
  Table 
  IX. 
  (p. 
  501). 
  As 
  before, 
  

   the 
  first 
  four 
  liquids 
  supplied 
  the 
  data 
  which 
  were 
  taken 
  at 
  fTc. 
  

  

  Tiie 
  second 
  column 
  gives 
  the 
  values 
  of 
  obtained 
  from 
  

  

  P 
  

   experiment, 
  while 
  tlie 
  third 
  column 
  gives 
  the 
  theoretically 
  

   equivalent 
  values 
  of 
  {jc")i 
  Xca- 
  The 
  two 
  columns 
  agree 
  fairly 
  

   well. 
  The 
  last 
  column 
  of 
  the 
  table 
  gives 
  the 
  values 
  of 
  c„, 
  

   that 
  for 
  H 
  being 
  put 
  equal 
  to 
  unity. 
  These 
  values 
  agree 
  

   fairly 
  well 
  with 
  those 
  obtained 
  in 
  Table 
  YIII., 
  except 
  

   for 
  oxygen. 
  If 
  the 
  values 
  of 
  Ca 
  were 
  in 
  both 
  cases 
  

   determined 
  from 
  a 
  larger 
  number 
  of 
  liquids 
  by 
  a 
  method 
  

   of 
  least 
  squares 
  the 
  agreement 
  would 
  probably 
  be 
  much 
  

   better. 
  

  

  The 
  equation 
  (4) 
  \ 
  = 
  - 
  — 
  ^- 
  (Sca)^ 
  is 
  further 
  interesting 
  

  

  since 
  it 
  can 
  be 
  connected 
  with 
  other 
  investigations 
  in 
  capil- 
  

   larity. 
  An 
  expression 
  for 
  the 
  surface-tension 
  of 
  a 
  liquid 
  is 
  

   usually 
  given 
  in 
  text-books 
  on 
  physics 
  deduced 
  from 
  the 
  

   work 
  necessary 
  to 
  produce 
  a 
  new 
  liquid 
  surface. 
  

  

  Consider 
  the 
  work 
  required 
  to 
  separate 
  two 
  portions 
  of 
  a 
  

   liquid 
  A 
  and 
  B, 
  the 
  resulting 
  surfaces 
  to 
  be 
  plane. 
  Let 
  B 
  be 
  

   divided 
  up 
  into 
  slices 
  parallel 
  to 
  the 
  interface, 
  then 
  the 
  work 
  

   done 
  in 
  removing 
  the 
  slice 
  whose 
  thickness 
  is 
  dz, 
  and 
  whose 
  

   height 
  above 
  the 
  plane 
  is 
  ^, 
  is 
  per 
  unit 
  of 
  area 
  equal 
  to 
  

  

  pHz\ 
  

  

  ylrQv) 
  da;, 
  

  

  where 
  p'^ijxi) 
  denotes 
  the 
  attraction 
  due 
  to 
  a 
  mass 
  of 
  liquid 
  

   of 
  density 
  p 
  bounded 
  by 
  a 
  flat 
  surface 
  on 
  unit 
  mass 
  placed 
  

   at 
  a 
  distance 
  x 
  above 
  the 
  surface. 
  The 
  w^ork 
  required 
  to 
  

   remove 
  the 
  whole 
  of 
  the 
  liquid 
  B 
  standing 
  on 
  unit 
  area 
  is 
  

  

  r 
  

  

  p^v 
  dz, 
  where 
  v 
  = 
  \ 
  

  

  yjr(x)dx. 
  

  

  