﻿Relations 
  in 
  Capillarity. 
  499 
  

  

  follo^vs 
  from 
  this 
  that 
  — 
  -A^ 
  — 
  r:, 
  must 
  be 
  a 
  constant 
  h 
  for 
  all 
  

   pcK^Cay 
  

  

  liquids 
  in 
  order 
  that 
  

  

  ^'=M-4}' 
  

  

  which 
  makes 
  tc' 
  assume 
  the 
  same 
  value 
  for 
  all 
  liquids 
  at 
  

   corresponding 
  states. 
  

  

  Similarly 
  the 
  function 
  represented 
  by 
  k'^ 
  can 
  be 
  deter- 
  

   mined. 
  From 
  equations 
  (4) 
  and 
  (6) 
  and 
  the 
  relation 
  \ 
  = 
  /jl\q 
  

   we 
  have 
  

  

  Since 
  k'^ 
  must 
  be 
  a 
  function 
  which 
  has 
  the 
  same 
  value 
  for 
  

   different 
  liquids 
  at 
  corresponding 
  states, 
  then 
  — 
  ^ 
  ^ 
  ^ 
  must 
  

  

  p2''{2,Cay 
  

  

  be 
  equal 
  to 
  some 
  constant 
  k 
  which 
  is 
  the 
  same 
  for 
  all 
  liquids. 
  

   Thus 
  we 
  have 
  

  

  'c"=^-^i=^, 
  (8) 
  

  

  and 
  this 
  is 
  the 
  same 
  for 
  all 
  liquids 
  at 
  corresponding 
  

   states. 
  

  

  From 
  equation 
  (2) 
  we 
  see 
  that 
  any 
  change 
  in 
  k' 
  is 
  due 
  to 
  

   ■p 
  

   a 
  change 
  in 
  — 
  ^, 
  since 
  m 
  and 
  (XcaY 
  are 
  constants 
  which 
  do 
  

  

  r 
  

  

  not 
  vary 
  under 
  any 
  conditions. 
  In 
  Table 
  VII. 
  (p. 
  500) 
  the 
  

   values 
  of 
  -^ 
  are 
  calculated 
  for 
  five 
  liquids 
  at 
  temperatures 
  

  

  differing 
  by 
  10^ 
  over 
  a 
  range 
  of 
  about 
  140° 
  C. 
  The 
  constancy 
  

  

  E 
  E 
  . 
  

  

  of 
  -^^ 
  shows 
  that 
  -7, 
  is 
  proportional 
  to 
  T, 
  or 
  the 
  function 
  /c' 
  

   p-T 
  P^ 
  ^ 
  

  

  is 
  proportional, 
  at 
  least 
  approximately 
  so, 
  to 
  the 
  absolute 
  

  

  temperature. 
  This 
  is 
  a 
  more 
  convenient 
  expression 
  for 
  

  

  the 
  variation 
  of 
  «' 
  with 
  temperature 
  than 
  that 
  given 
  

  

  above. 
  

  

  The 
  values 
  of 
  {'^')ka 
  for 
  a 
  number 
  of 
  atoms 
  have 
  been 
  

  

  calculated 
  from 
  the 
  equation 
  /c'(Sc«)- 
  = 
  — 
  j-, 
  and 
  are 
  given 
  

  

  