﻿792 
  Mr. 
  T. 
  H. 
  Laby 
  : 
  A 
  Recalculation 
  of 
  

  

  Reduction 
  of 
  Observations. 
  

  

  The 
  logarithms 
  of 
  the 
  observed 
  pressures 
  of 
  the 
  last 
  table 
  

   were 
  plotted 
  against 
  the 
  temperatures 
  on 
  squared 
  paper 
  

   600 
  by 
  300 
  mm., 
  and 
  a 
  (log 
  p, 
  t) 
  curve 
  was 
  drawn 
  through 
  

   the 
  points. 
  The 
  final 
  curve, 
  or 
  rather 
  formulae, 
  were 
  then 
  

   obtained 
  by 
  the 
  following 
  successive 
  approximations. 
  

  

  The 
  most 
  probable 
  values 
  for 
  p 
  at 
  50° 
  and 
  250° 
  were 
  

   found 
  from 
  the 
  above 
  diagram, 
  and 
  a 
  Kirchhoff-Rankine- 
  

   Dupre 
  formula 
  (B) 
  of 
  the 
  form 
  

  

  logp 
  = 
  A 
  + 
  B/0 
  + 
  Clog 
  (6 
  = 
  £ 
  + 
  273) 
  ' 
  

  

  was 
  deduced 
  from 
  these 
  values, 
  and 
  the 
  boiling-point 
  356 
  0, 
  7. 
  

   The 
  observed 
  values 
  of 
  t 
  and 
  log 
  p 
  were 
  replotted 
  (diagram 
  B) 
  

   on 
  a 
  larger 
  scale, 
  giving 
  a 
  curve 
  about 
  1100 
  mm. 
  long 
  when 
  

   the 
  graph 
  of 
  formula 
  B 
  was 
  drawn 
  in. 
  This 
  figure 
  enabled 
  

   (as 
  is 
  described 
  below) 
  six 
  points 
  to 
  be 
  found 
  from 
  which 
  a 
  

   three-constants 
  Kirchhoff 
  formula 
  was 
  calculated 
  by 
  the 
  

   method 
  of 
  least 
  squares. 
  

  

  The 
  46 
  observations 
  from 
  15° 
  to 
  the 
  boiling-point, 
  at 
  the 
  

   following 
  temperatures, 
  were 
  arranged 
  thus 
  : 
  — 
  

  

  15°, 
  16°, 
  30°, 
  40° 
  (reduced 
  to 
  16°) 
  ; 
  

  

  50°, 
  56°-3, 
  60°, 
  70° 
  

  

  (reduced 
  to 
  60°) 
  ; 
  

  

  89°-4, 
  98 
  c 
  '8, 
  117°, 
  129° 
  

  

  (reduced 
  to 
  120°) 
  ; 
  

  

  154°% 
  to 
  224°-5 
  

  

  (reduced 
  to 
  190°).; 
  

  

  230°*5, 
  236°, 
  ... 
  to 
  315° 
  

  

  (reduced 
  to 
  270°) 
  ; 
  

  

  B.P. 
  356 
  

  

  D 
  -7. 
  

  

  One 
  value 
  of 
  p 
  was 
  deduced 
  for 
  each 
  group 
  (namely, 
  the 
  

   values 
  of 
  p 
  at 
  16°, 
  60°, 
  120°, 
  190°, 
  270°) 
  by 
  the 
  process 
  

   indicated 
  in 
  fig. 
  1, 
  in 
  which 
  so 
  much 
  of 
  the 
  curve 
  B 
  (one- 
  

   eighteenth) 
  is 
  drawn 
  as 
  the 
  second 
  group 
  covers. 
  Lines 
  

   parallel 
  to 
  B 
  were 
  drawn 
  through 
  the 
  observed 
  points 
  50°, 
  

   56°-3, 
  60°, 
  70° 
  to 
  cut 
  the 
  isotherm 
  60° 
  in 
  a, 
  b, 
  c, 
  d. 
  The 
  

   mean 
  position 
  of 
  these 
  four 
  points 
  gave 
  the 
  value 
  of 
  p 
  

   at 
  60°. 
  The 
  other 
  groups 
  were 
  similarly 
  treated, 
  and 
  it 
  was 
  

   found 
  that 
  logp 
  for 
  the 
  different 
  groups 
  is 
  : 
  — 
  

  

  16° 
  ... 
  

  

  .. 
  4-994 
  

  

  60° 
  ... 
  

  

  ... 
  2-333 
  

  

  120° 
  .... 
  

  

  .. 
  1-875 
  

  

  190° 
  

  

  .. 
  1-1072 
  

  

  270° 
  ... 
  

  

  ... 
  2-0965 
  

  

  356°-7 
  . 
  

  

  .. 
  2-8808 
  

  

  But 
  the 
  logp 
  — 
  A 
  + 
  B/0 
  + 
  Clog 
  formula, 
  calculated 
  by 
  

   the 
  method 
  of 
  least 
  squares 
  from 
  these 
  observations, 
  gave 
  too 
  

   much 
  weight 
  to 
  the 
  fewer 
  and 
  less 
  accurate 
  low-temperature 
  

  

  