﻿and 
  certain 
  Quantities 
  connected 
  with 
  Capillarity. 
  903 
  

  

  To 
  determine 
  C 
  put 
  p, 
  p^ 
  and 
  T 
  equal 
  to 
  their 
  critical 
  values. 
  

   The 
  equation 
  may 
  then 
  be 
  written 
  

  

  or 
  W(2<-„)^(^^y=y.-|^.o, 
  .... 
  (3) 
  

  

  where 
  W 
  is 
  the 
  same 
  for 
  all 
  liquids 
  at 
  corresponding 
  states. 
  

   Putting 
  j9 
  = 
  <^/>c, 
  which 
  is 
  approximately 
  true, 
  we 
  have 
  

  

  P 
  

  

  (^-i)=w(..,(y^ 
  

  

  If 
  we 
  denote 
  by 
  M 
  the 
  quantities 
  which 
  are 
  the 
  same 
  for 
  

   all 
  liquids 
  at 
  corresponding 
  temperatures, 
  we 
  have 
  

  

  7.^^^f=:MXca 
  (4) 
  

  

  At 
  the 
  critical 
  state 
  M 
  is 
  an 
  indeterminate 
  fraction, 
  but 
  its 
  

   limiting 
  value 
  must 
  be 
  finite, 
  because 
  all 
  the 
  other 
  quantities 
  

   in 
  the 
  equation 
  have 
  perfectly 
  definite 
  values 
  at 
  the 
  critical 
  

   temperature. 
  

  

  This 
  equation 
  will 
  now 
  be 
  applied 
  to 
  a 
  number 
  of 
  liquids 
  

   at 
  their 
  critical 
  state. 
  The 
  values 
  of 
  7?i, 
  />c, 
  and 
  pc 
  are 
  given 
  

   in 
  Table 
  I. 
  (p. 
  904). 
  The 
  values 
  of 
  Ca 
  for 
  the 
  eight 
  elements 
  

   involved 
  are 
  obtained 
  from 
  the 
  application 
  of 
  equation 
  (1) 
  * 
  to 
  

   the 
  eight 
  liquids, 
  ether, 
  methyl 
  formate, 
  carbon 
  tetrachloride, 
  

   benzene, 
  fluor-benzene, 
  bromo-benzene, 
  iodo-benzene, 
  and 
  

   stannic 
  chloride. 
  It 
  will 
  be 
  seen 
  that 
  M 
  is 
  approximately 
  a 
  

   constant 
  for 
  all 
  liquids 
  at 
  their 
  critical 
  states. 
  This 
  shows 
  

   that 
  equation 
  (4) 
  is 
  approximately 
  true. 
  The 
  mean 
  value 
  of 
  

   M 
  is 
  116-8. 
  

  

  From 
  the 
  physical 
  behaviour 
  of 
  the 
  liquids, 
  water, 
  methyl 
  

   alcohol, 
  propyl 
  alcohol, 
  and 
  acetic 
  acid, 
  it 
  has 
  been 
  deduced 
  

   that 
  they 
  are 
  polymerized 
  at 
  ordinary 
  temperatures. 
  The 
  

   surface-tension 
  formulae, 
  in 
  particular 
  that 
  of 
  Eotvos, 
  Ramsay 
  

   and 
  Shields, 
  have 
  not 
  been 
  found 
  to 
  apply 
  to 
  these 
  liquids 
  as 
  

   the 
  extent 
  of 
  polymerization, 
  and 
  therefore 
  the 
  molecular 
  

   weight, 
  is 
  not 
  known. 
  In 
  fact, 
  the 
  departure 
  of 
  the 
  surface 
  

   tension 
  from 
  that 
  given 
  by 
  the 
  formula 
  of 
  Eotvos, 
  Ramsay 
  

   and 
  Shields, 
  is 
  regarded 
  as 
  evidence 
  of 
  polymerization, 
  and 
  

   the 
  extent 
  of 
  it 
  has 
  been 
  calculated 
  by 
  means 
  of 
  this 
  

   formula. 
  

  

  * 
  See 
  previous 
  paper, 
  Phil. 
  Mag. 
  Oct. 
  1909. 
  

   2P2 
  

  

  