﻿600 
  Mr. 
  I. 
  Williams 
  on 
  the 
  Absolute 
  

  

  Let 
  

  

  Q 
  = 
  quantity 
  of 
  heat 
  transmitted 
  radially 
  per 
  second 
  

  

  through 
  unit 
  length 
  of 
  the 
  glass 
  cylinder 
  AA 
  X 
  ; 
  

   i\ 
  = 
  interna] 
  radius 
  of 
  AA 
  } 
  ; 
  

   r 
  2 
  = 
  external 
  ,, 
  „ 
  ; 
  

  

  6 
  i 
  = 
  temperature 
  of 
  the 
  inner 
  surface 
  of 
  the 
  glass 
  tube 
  

  

  AA 
  i; 
  

   6 
  2 
  = 
  temperature 
  of 
  the 
  outer 
  surface 
  of 
  the 
  glass 
  tube 
  

  

  AA,; 
  

   E 
  = 
  potential 
  difference 
  in 
  volts 
  at 
  the 
  ends 
  of 
  a 
  mercury 
  

  

  column 
  of 
  length 
  I; 
  

   = 
  heating 
  current 
  in 
  amperes; 
  

   J 
  = 
  4-18xl0 
  7 
  ergs; 
  

  

  k 
  = 
  coefficient 
  of 
  thermal 
  conductivity 
  of 
  glass. 
  

   The 
  energy 
  generated 
  per 
  second 
  in 
  a 
  length 
  I 
  cm. 
  of 
  

  

  mercury 
  by 
  the 
  electric 
  current 
  is 
  EC 
  joules 
  or 
  j— 
  ^ 
  calories. 
  

  

  It 
  can 
  easily 
  be 
  shown 
  that 
  for 
  an 
  infiuite 
  cylinder 
  

  

  Q= 
  27Tk(0 
  l 
  -0 
  a 
  ) 
  

  

  log,- 
  

  

  If 
  

  

  Ex 
  = 
  P.D. 
  in 
  volts 
  at 
  the 
  ends 
  of 
  the 
  mercury 
  column 
  BC, 
  

   E 
  2 
  = 
  P.D. 
  in 
  volts 
  at 
  the 
  ends 
  of 
  the 
  mercury 
  column 
  B^, 
  

  

  then 
  the 
  quantities 
  of 
  heat 
  energy 
  generated 
  in 
  BC 
  and 
  BjCi 
  

   are 
  respectively 
  E 
  X 
  C 
  and 
  E 
  2 
  C. 
  

  

  Assuming 
  that 
  the 
  end 
  corrections 
  for 
  the 
  two 
  lengths 
  BC 
  

   and 
  BiCi 
  are 
  identical, 
  it 
  follows 
  that 
  the 
  heat 
  energy 
  trans- 
  

   mitted 
  through 
  a 
  length 
  BC 
  — 
  B^ 
  is 
  equal 
  to 
  (E 
  x 
  — 
  E 
  2 
  )C. 
  

  

  . 
  , 
  (E 
  1 
  -E,)C 
  . 
  r, 
  1 
  

  

  4^18 
  ^n^TT^-y^-^) 
  

  

  = 
  A(E 
  1 
  -E 
  2 
  )C 
  

   @i 
  — 
  2 
  

   where 
  A 
  is 
  a 
  constant, 
  BC 
  = 
  Zi 
  and 
  B 
  1 
  C 
  1 
  = 
  Z 
  2 
  . 
  

  

  § 
  4. 
  For 
  the 
  purpose 
  of 
  measuring 
  the 
  potential 
  differences 
  

   E 
  x 
  and 
  E 
  2 
  , 
  electrodes 
  were 
  inserted 
  into 
  the 
  mercury 
  column 
  

   through 
  holes 
  drilled 
  into 
  the 
  capillary 
  at 
  B, 
  C, 
  B 
  1? 
  and 
  Ci. 
  

   Outside 
  the 
  tube 
  these 
  electrodes 
  were 
  coated 
  with 
  a 
  thick 
  

   layer 
  of 
  varnish 
  to 
  insulate 
  them 
  from 
  the 
  water 
  in 
  which 
  

   the 
  apparatus 
  stood. 
  E 
  x 
  and 
  E 
  2 
  were 
  measured 
  with 
  a 
  milli- 
  

   voltmeter 
  calibrated 
  by 
  means 
  of 
  a 
  cadmium 
  cell. 
  

  

  The 
  measurement 
  of 
  the 
  temperature 
  difference 
  presents 
  

   rather 
  more 
  difficulty. 
  In 
  the 
  earlier 
  experiments 
  a 
  tube 
  

  

  