﻿Relations 
  in 
  Capillarity. 
  497 
  

  

  for 
  each 
  set 
  of 
  corresponding 
  temperatures 
  it 
  varies 
  con- 
  

   siderably 
  from 
  set 
  to 
  set. 
  

  

  E 
  

  

  The 
  relation 
  — 
  = 
  constant 
  for 
  corresponding 
  temperatures 
  

  

  which 
  has 
  just 
  been 
  proved, 
  can 
  be 
  deduced 
  from 
  a 
  well- 
  

   known 
  relation 
  connecting 
  surface-tension 
  with 
  other 
  quan- 
  

   tities. 
  The 
  deduction 
  will 
  also 
  bring 
  some 
  other 
  important 
  

   relations 
  to 
  light. 
  

  

  Ramsav, 
  following 
  Eotvos, 
  has 
  shown 
  that 
  

  

  Xe=x^=A(T,-T-a), 
  .... 
  (5) 
  

  

  where 
  A 
  is 
  a 
  constant 
  whose 
  value 
  is 
  about 
  2*1 
  for 
  all 
  

   liquids, 
  and 
  a 
  is 
  another 
  constant 
  whose 
  value 
  is 
  about 
  6. 
  

   Let 
  pQ 
  and 
  Xq 
  denote 
  the 
  density 
  and 
  fictitious 
  surface-tension 
  

   at 
  absolute 
  zero. 
  Then 
  

  

  Xo=^^(T,-a) 
  = 
  ^:AT., 
  

  

  since 
  a 
  is 
  small 
  in 
  comparison 
  with 
  Tc. 
  If 
  po 
  is 
  P^if 
  equal 
  

   to 
  bpc 
  we 
  have 
  

  

  For 
  any 
  temperature 
  other 
  than 
  absolute 
  zero 
  equation 
  (5) 
  

   may 
  be 
  written 
  

  

  We 
  may 
  neglect 
  a 
  except 
  when 
  we 
  are 
  dealing 
  with 
  tempe- 
  

   ratures 
  quite 
  close 
  to 
  the 
  critical 
  temperature. 
  Omitting 
  a, 
  

   and 
  combining 
  this 
  equation 
  with 
  the 
  one 
  preceding, 
  we 
  

   obtain 
  

  

  /x=^,(l-^) 
  (6) 
  

  

  For 
  different 
  liquids 
  a 
  and 
  jS 
  are 
  the 
  -same 
  at 
  corresponding 
  

   states, 
  and 
  since 
  absolute 
  zero 
  is 
  a 
  corresponding 
  state 
  for 
  

   all 
  liquids 
  h 
  is 
  the 
  same, 
  hence 
  /jl 
  is 
  the 
  same 
  for 
  all 
  liquids 
  

   under 
  the 
  same 
  circumstances. 
  This 
  leads 
  to 
  the 
  conclusion 
  

  

  