﻿Determination 
  of 
  a 
  Constant 
  in 
  Capillarity. 
  43 
  

  

  constant 
  for 
  different 
  liquids 
  at 
  corresponding 
  states. 
  Writing 
  

  

  -^- 
  =B, 
  where 
  B= 
  -^ 
  -^ 
  R, 
  and 
  substituting 
  for 
  L 
  in 
  

  

  equation 
  (4) 
  we 
  obtain 
  

  

  Expressing 
  p 
  and 
  T 
  in 
  terms 
  of 
  the 
  critical 
  density 
  and 
  

   temperature, 
  we 
  obtain 
  

  

  where 
  p 
  = 
  iypc. 
  

  

  Let 
  us 
  write 
  the 
  equation 
  in 
  the 
  form 
  

  

  ^_ 
  Mm'^'iTe-a)p,'f^ 
  

  

  ^— 
  I 
  2 
  » 
  

  

  J 
  c 
  

  

  where 
  M 
  = 
  ^y 
  ^ 
  • 
  Now 
  it 
  is 
  know^i 
  that 
  K 
  is 
  a 
  constant 
  

   X) 
  a"* 
  

  

  for 
  a 
  given 
  liquid, 
  therefore 
  M 
  must 
  be 
  a 
  constant 
  for 
  the 
  

   liquid. 
  Further, 
  in 
  obtaining 
  K 
  for 
  different 
  liquids 
  we 
  

   may 
  suppose 
  the 
  liquids 
  taken 
  at 
  corresponding 
  states, 
  so 
  

   that 
  the 
  values 
  of 
  «, 
  /5, 
  y, 
  are 
  the 
  same 
  for 
  each 
  liquid. 
  Then 
  

   it 
  follows 
  that 
  since 
  M 
  is 
  a 
  function 
  of 
  a, 
  /3, 
  and 
  y 
  only, 
  it 
  

   must 
  be 
  the 
  same 
  for 
  each 
  liquid. 
  

  

  Further, 
  since 
  a 
  is 
  equal 
  to 
  about 
  5 
  and 
  To 
  of 
  the 
  order 
  

  

  500, 
  ^2 
  ^^^-^y 
  b® 
  neglected 
  in 
  comparison 
  with 
  ^r 
  • 
  ^Ve 
  

  

  have 
  then, 
  finally, 
  

  

  ^^Mm_E^^ 
  .... 
  (5) 
  

  

  where 
  M 
  is 
  a 
  constant 
  which 
  is 
  the 
  same 
  for 
  every 
  liquid. 
  

   The 
  following 
  table 
  contains 
  the 
  values 
  of 
  10* 
  „i 
  

  

  for 
  a 
  few 
  liquids 
  calculated 
  from 
  the 
  data 
  given 
  in 
  the 
  second, 
  

   third, 
  and 
  fourth 
  columns 
  of 
  the 
  table, 
  the 
  value 
  of 
  M 
  being 
  

   put 
  equal 
  to 
  5*57 
  X 
  10~^ 
  in 
  each 
  case. 
  The 
  values 
  of 
  10* 
  K, 
  

   contained 
  in 
  the 
  fitth 
  column 
  of 
  the 
  tible, 
  are 
  the 
  means 
  of 
  

   the 
  values 
  contained 
  in 
  the 
  preceding 
  tables. 
  It 
  will 
  be 
  seen 
  

   that 
  the 
  values 
  of 
  K 
  given 
  by 
  equation 
  (5) 
  agree 
  fairly 
  well 
  

  

  E 
  

  

  with 
  the 
  values 
  given 
  by 
  the 
  equation 
  K 
  = 
  =r— 
  . 
  Abetter 
  

  

  agreement 
  can 
  scarcely 
  be 
  expected 
  since 
  the 
  critical 
  constants 
  

   cannot 
  be 
  determined 
  with 
  any 
  grea.t 
  accuracy. 
  

  

  