﻿492 
  Dr. 
  R. 
  D. 
  Kleeman 
  on 
  some 
  

  

  usually 
  done 
  in 
  gravitational 
  investigations. 
  Thus 
  

  

  where 
  v 
  denotes 
  the 
  molecular 
  volume. 
  This 
  expression, 
  

   on 
  transforming 
  the 
  integral 
  to 
  rectangular 
  coordinates, 
  

   becomes 
  

  

  (Sn 
  "12 
  C"^ 
  C^ 
  r* 
  

  

  •J 
  — 
  ao«y— 
  oo«./— 
  00 
  

  

  or, 
  if 
  we 
  denote 
  the 
  integral 
  by 
  k 
  

  

  P=P.-^(2c.)^. 
  

  

  Einstein 
  then 
  expresses 
  the 
  potential 
  energy 
  of 
  a 
  liquid 
  of 
  

   volume 
  V 
  and 
  surfaces 
  S 
  as 
  

  

  P 
  = 
  P„-^(2c„)^V-^^(2cvyS, 
  . 
  . 
  . 
  (1) 
  

   where 
  

  

  zi=l 
  3/1 
  = 
  1 
  zi=0 
  x=x) 
  y=oo 
  2^=00 
  

  

  ''=^ 
  \ 
  ^ 
  ^ 
  ^ 
  J^^'i 
  ^yi 
  dz, 
  dx 
  dy 
  dz 
  fx/{.v-a;,f 
  + 
  {y-yif 
  + 
  (^-^^i)'. 
  

  

  ^1 
  = 
  yi=0 
  ■^1 
  = 
  00 
  z=— 
  CO 
  y 
  = 
  — 
  00 
  z=0 
  

  

  The 
  potential 
  energy 
  E 
  per 
  unit 
  surface 
  is 
  the 
  coefficient 
  of 
  

   S 
  in 
  (1), 
  or 
  

  

  E=^(Sc.)^=^'(2c«)^ 
  .... 
  (2) 
  

  

  since 
  v= 
  — 
  , 
  where 
  p 
  is 
  the 
  density 
  and 
  m 
  the 
  molecular 
  

  

  weight 
  o£ 
  the 
  liquid. 
  

  

  The 
  potential 
  energy 
  of 
  the 
  surface-film 
  of 
  a 
  liquid 
  is 
  also 
  

  

  given 
  by 
  ( 
  X 
  — 
  T-^ 
  J 
  where 
  X 
  is 
  the 
  surface-tension 
  at 
  the 
  tem- 
  

   perature 
  T. 
  This 
  follows 
  from 
  thermodynamics. 
  When 
  the 
  

   surface 
  is 
  increased 
  by 
  1 
  cm.^ 
  the 
  external 
  work 
  done 
  on 
  the 
  

   film 
  is 
  X 
  and 
  the 
  heat 
  absorbed, 
  according 
  to 
  the 
  Helmholtz 
  

   free-energy 
  equation, 
  to 
  keep 
  the 
  temperature 
  constant, 
  is 
  

  

  — 
  T-i?p, 
  and 
  thus 
  the 
  potential 
  energy 
  is 
  increased 
  by 
  

  

  