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  299 
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  y 
  

  

  XXXV. 
  Notes 
  on 
  Thermometry. 
  By 
  C. 
  Chree, 
  Sc.D., 
  F.R.S. 
  

  

  [Concluded 
  from 
  p. 
  227.] 
  

  

  § 
  20. 
  Lag. 
  m 
  m 
  

  

  21. 
  Freezing-point 
  of 
  water. 
  // 
  L 
  j^ 
  / 
  \J 
  * 
  

  

  22-24. 
  Boiling-point 
  of 
  water. 
  

  

  25. 
  Calibration. 
  

   26-30. 
  External 
  and 
  internal 
  pressure 
  corrections, 
  standard 
  position 
  for 
  

  

  thermometers. 
  

   31, 
  32. 
  Emergent 
  column. 
  

   33-36. 
  Welsh's 
  method 
  of 
  graduation, 
  and 
  its 
  modern 
  developments. 
  

  

  37. 
  Method 
  of 
  finding- 
  mean 
  coefficient 
  of 
  expansion 
  of 
  mercury 
  in 
  

  

  glass. 
  

  

  38. 
  Comparison 
  of 
  thermometric 
  methods. 
  

  

  Lag. 
  

  

  §20. 
  ^LASS-MERCURY 
  thermometers, 
  and 
  probably 
  

   VJ 
  all 
  others, 
  differ 
  from 
  the 
  ideal 
  of 
  our 
  definition 
  

   in 
  requiring 
  a 
  sensible 
  time 
  to 
  follow 
  a 
  change 
  of 
  tempera- 
  

   ture. 
  This 
  lag 
  in 
  a 
  mercury-thermometer 
  increases 
  with 
  the 
  

   mass 
  of 
  the 
  mercury 
  and 
  the 
  thickness 
  of 
  the 
  glass. 
  It 
  also 
  

   depends 
  on 
  the 
  nature 
  of 
  the 
  surrounding 
  medium. 
  A 
  

   clinical 
  thermometer, 
  for 
  instance, 
  initially 
  at 
  15° 
  C, 
  will 
  rise 
  

   to 
  the 
  temperature 
  of 
  the 
  body 
  faster 
  in 
  a 
  moist 
  than 
  in 
  a 
  

   dry 
  mouth, 
  and 
  much 
  faster 
  in 
  a 
  well-stirred 
  bucket 
  of 
  water 
  

   than 
  in 
  either. 
  In 
  still 
  air 
  where 
  temperature 
  is 
  altering 
  

   rapidly, 
  two 
  adjacent 
  thermometers 
  of 
  different 
  sluggishness 
  

   may 
  differ 
  by 
  degrees. 
  

  

  If 
  T 
  denote 
  time, 
  t 
  the 
  thermometer 
  reading, 
  t 
  the 
  tem- 
  

   perature 
  of 
  its 
  surroundings, 
  the 
  formula 
  usually 
  advanced 
  

   to 
  represent 
  the 
  phenomena 
  is 
  * 
  : 
  

  

  r 
  r 
  + 
  M*-T)=o, 
  

  

  where 
  X 
  is 
  a 
  constant. 
  When 
  t 
  — 
  r 
  is 
  small, 
  this 
  is 
  probably 
  

   at 
  least 
  a 
  close 
  approximation 
  to 
  the 
  facts. 
  When, 
  however, 
  

   t 
  — 
  t 
  is 
  considerable 
  — 
  as, 
  for 
  instance, 
  when 
  a 
  thermometer 
  

   initially 
  at 
  15° 
  C. 
  is 
  suddenly 
  exposed 
  to 
  a 
  temperature 
  of 
  

   40° 
  C. 
  — 
  the 
  initial 
  phenomena, 
  in 
  my 
  experience, 
  do 
  not 
  

   follow 
  so 
  simple 
  a 
  law. 
  

   When 
  t 
  is 
  constant, 
  the 
  solution 
  of 
  the 
  differential 
  equation 
  is 
  

  

  t 
  = 
  T 
  +(t 
  -T)e-^, 
  

  

  where 
  t 
  is 
  the 
  value 
  of 
  t 
  when 
  T 
  = 
  0. 
  

  

  * 
  Cf. 
  Guillaume's 
  Thermometrie, 
  p. 
  185. 
  

  

  