﻿364 
  Mr. 
  R. 
  A. 
  Lehfeldt 
  on 
  a 
  Numerical 
  Evaluation 
  of 
  

  

  to 
  the 
  fact 
  that 
  if 
  the 
  other 
  data 
  required 
  were 
  investigated 
  

   with 
  equal 
  care 
  and 
  thoroughness, 
  we 
  could 
  now 
  know 
  the 
  

   absolute 
  scale 
  as 
  accurately 
  as 
  we 
  know 
  the 
  hydrogen 
  or 
  the 
  

   mercury 
  scale. 
  

  

  The 
  problem 
  consists 
  of 
  two 
  parts 
  : 
  first, 
  taking 
  the 
  interval 
  

   between 
  the 
  freezing- 
  and 
  boiling-points 
  as 
  100°, 
  it 
  is 
  ne- 
  

   cessary 
  to 
  determine 
  the 
  absolute 
  temperature 
  corresponding 
  

   to 
  one 
  of 
  those 
  fixed 
  points 
  ; 
  second, 
  knowing 
  that 
  value, 
  we 
  

   can 
  proceed 
  to 
  compare 
  the 
  absolute 
  scale 
  with 
  some 
  actual 
  

   scale, 
  such 
  as 
  that 
  of 
  the 
  constant-volume 
  hydrogen 
  ther- 
  

   mometer, 
  throughout 
  its 
  range, 
  so 
  far 
  as 
  experimental 
  infor- 
  

   mation 
  extends. 
  On 
  the 
  first 
  of 
  these 
  points 
  no 
  substantial 
  

   advance 
  can 
  as 
  yet 
  be 
  made 
  on 
  the 
  result 
  published 
  by 
  

   Thomson 
  and 
  Joule 
  several 
  decades 
  ago. 
  The 
  freezing-point 
  

   is 
  approximately 
  273° 
  absolute, 
  and 
  the 
  uncertainty 
  amounts 
  

   to 
  one 
  or 
  two 
  tenths 
  of 
  a 
  deo-ree 
  on 
  each 
  side 
  of 
  that 
  number. 
  

   But 
  I 
  think 
  it 
  is 
  at 
  least 
  certain 
  that 
  the 
  higher 
  values 
  

   obtained 
  by 
  some 
  later 
  German 
  writers 
  (some 
  as 
  high 
  as 
  

   274°*5) 
  are 
  wrong. 
  On 
  the 
  second 
  point 
  very 
  varying 
  results 
  

   have 
  been 
  found 
  ; 
  but 
  I 
  think 
  it 
  is 
  possible 
  to 
  show 
  that 
  the 
  

   existing 
  data 
  are 
  in 
  good 
  accord 
  with 
  the 
  comparisons 
  between 
  

   the 
  three 
  gas 
  thermometers 
  made 
  at 
  the 
  Bureau 
  International. 
  

  

  Theory 
  of 
  the 
  Method. 
  

  

  In 
  order 
  to 
  determine 
  the 
  relation 
  between 
  the 
  absolute 
  and 
  

   an 
  arbitrary 
  scale 
  of 
  temperature, 
  it 
  is 
  not 
  sufficient 
  to 
  know 
  

   the 
  characteristic 
  equation 
  of 
  a 
  gas, 
  but, 
  as 
  has 
  recently 
  been 
  

   pointed 
  out 
  afresh 
  by 
  Boltzmann 
  *, 
  calorimetric 
  data 
  are 
  also 
  

   necessary; 
  consequently 
  any 
  reduction 
  that 
  does 
  not 
  explicitly 
  

   make 
  use 
  of 
  such 
  data 
  must 
  do 
  so 
  implicitly. 
  The 
  form 
  in 
  

   which 
  the 
  calorimetric 
  data 
  usually 
  occur 
  is 
  that 
  of 
  the 
  differ- 
  

   ence 
  between 
  the 
  two 
  specific 
  heats 
  of 
  a 
  gas 
  ; 
  consequently 
  

   the 
  evaluation 
  of 
  the 
  absolute 
  scale 
  is 
  closely 
  bound 
  up 
  with 
  

   the 
  determination 
  of 
  the 
  difference, 
  or 
  the 
  ratio 
  of 
  the 
  specific 
  

   heats. 
  But 
  all 
  direct 
  determinations 
  of 
  K 
  P 
  — 
  K 
  v 
  , 
  by 
  mea- 
  

   suring 
  K 
  P 
  and 
  K 
  v 
  , 
  or 
  by 
  measuring 
  K 
  P 
  and 
  the 
  ratio 
  7, 
  are, 
  

   I 
  believe, 
  insufficiently 
  accurate. 
  The 
  difference 
  is, 
  however, 
  

   nearly 
  equal 
  to 
  the 
  principal 
  gas 
  constant 
  (K 
  P 
  — 
  K 
  V 
  = 
  R), 
  

   and 
  it 
  is 
  the 
  small 
  outstanding 
  discrepancy 
  between 
  these 
  

   two 
  quantities 
  which 
  is 
  the 
  subject 
  of 
  Joule 
  and 
  Thomson's 
  

   experiments 
  on 
  the 
  cooling 
  by 
  free 
  expansion, 
  so 
  that 
  those 
  

   experiments 
  afford 
  the 
  most 
  satisfactory 
  means 
  of 
  determining 
  

   the 
  difference 
  between 
  the 
  specific 
  heats. 
  

  

  The 
  argument 
  runs 
  as 
  follows 
  : 
  — 
  Let 
  a 
  gram 
  of 
  hydrogen 
  

  

  * 
  Boltzmann, 
  Wied. 
  Ann. 
  vol. 
  liii. 
  p. 
  948 
  (1804). 
  

  

  