﻿582 
  MR 
  W. 
  J. 
  M. 
  RANKLNE 
  ON 
  THE 
  

  

  Com. 
  log 
  2 
  b 
  = 
  2-1101845 
  ; 
  log 
  ~ 
  . 
  — 
  = 
  2-4017950 
  ; 
  

  

  and 
  these 
  values 
  suit 
  any 
  scale 
  of 
  temperatures. 
  

  

  In 
  calculating, 
  for 
  use 
  in 
  these 
  formulae, 
  the 
  densities 
  ^ 
  from 
  the 
  observed 
  

  

  pressures, 
  it 
  is 
  sufficiently 
  near 
  the 
  truth, 
  in 
  the 
  case 
  of 
  air, 
  to 
  use 
  the 
  approxi- 
  

   mate 
  equation 
  

  

  1 
  T 
  

  

  =j5- 
  = 
  — 
  • 
  P 
  (in 
  atmospheres). 
  

  

  The 
  common 
  logarithm 
  of 
  t 
  , 
  the 
  absolute 
  temperature 
  of 
  melting 
  ice, 
  for 
  the 
  

   centigrade 
  scale, 
  is 
  24387005. 
  

  

  The 
  constant 
  N 
  for 
  atmospheric 
  air 
  is 
  0*4 
  nearly 
  ; 
  therefore 
  

  

  Com. 
  log 
  (N 
  x 
  hyp. 
  log 
  10) 
  = 
  1-9642757. 
  

  

  The 
  following, 
  therefore, 
  is 
  the 
  approximate 
  value 
  of 
  the 
  formula 
  (103), 
  to 
  be 
  

   used 
  (with 
  the 
  numerical 
  constants 
  already 
  given) 
  in 
  reducing 
  the 
  experiments 
  of 
  

   Mr 
  Joule 
  and 
  Professor 
  Thomson 
  on 
  atmospheric 
  air, 
  so 
  as 
  to 
  obtain 
  approximate 
  

   values 
  of 
  the 
  absolute 
  temperature 
  of 
  total 
  privation 
  of 
  heat 
  : 
  — 
  

  

  «={»*.(£?■ 
  fr) 
  H 
  A.(P*)-»ft)*A.-<rt)-C-AT) 
  } 
  

  

  -r- 
  N 
  hyp. 
  log 
  10 
  x 
  A 
  . 
  com. 
  log 
  -^ 
  (108.) 
  

  

  In 
  using 
  this 
  formula, 
  the 
  mean 
  absolute 
  temperature 
  should 
  be 
  taken 
  as 
  the 
  

   value 
  of 
  t. 
  

  

  The 
  following 
  table 
  shews 
  the 
  values 
  of 
  the 
  quantity 
  k, 
  computed 
  from 
  ten 
  

   mean 
  experimental 
  data, 
  taken 
  respectively 
  from 
  the 
  first 
  ten 
  series 
  of 
  experi- 
  

   ments 
  described 
  in 
  the 
  recent 
  paper 
  of 
  Messrs 
  Joule 
  and 
  Thomson, 
  in 
  the 
  supple- 
  

   mentary 
  number 
  of 
  the 
  Philosophical 
  Magazine 
  for 
  December 
  1852. 
  The 
  tempe- 
  

   ratures 
  in 
  the 
  table, 
  for 
  the 
  sake 
  of 
  convenience, 
  are 
  reduced 
  to 
  the 
  centigrade 
  

   scale, 
  because 
  that 
  scale 
  has 
  been 
  used 
  throughout 
  the 
  previous 
  sections 
  of 
  this 
  

   paper. 
  

  

  The 
  final 
  pressure 
  in 
  each 
  case 
  was 
  that 
  of 
  the 
  atmosphere. 
  

  

  