﻿210 
  Dr. 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry. 
  

  

  slowly 
  rising, 
  and 
  the 
  zero 
  employed 
  answer 
  really 
  to 
  

   prolonged 
  exposure 
  to 
  the 
  temperature 
  0° 
  0. 
  

  

  The 
  movable 
  zero 
  method 
  is 
  analogous 
  to 
  experiments 
  in 
  

   which 
  the 
  volume 
  v 
  of 
  glass 
  at 
  temperature 
  t 
  is 
  compared 
  

   with 
  a 
  volume 
  v 
  f 
  t 
  ,o 
  obtained 
  after 
  suddenly 
  cooling 
  the 
  glass 
  

   to 
  0° 
  C. 
  Instead 
  of 
  attempting 
  to 
  modify 
  (6) 
  to 
  suit 
  these 
  

   circumstances, 
  I 
  shall 
  develop 
  the 
  theory 
  independently. 
  

  

  § 
  5. 
  If 
  the 
  changes 
  in 
  temperature 
  are 
  slow, 
  as 
  is 
  really 
  

   assumed 
  in 
  the 
  movable 
  zero 
  method, 
  except 
  in 
  zero 
  deter- 
  

   minations, 
  then 
  so 
  long 
  as 
  t 
  is 
  increasing 
  we 
  may 
  regard 
  v 
  t 
  ,o 
  

   as 
  a 
  continuous 
  function 
  of 
  t, 
  which 
  for 
  ordinary 
  values 
  of 
  t 
  

   differs 
  little 
  from 
  a 
  constant. 
  We 
  may 
  thus 
  provisionally 
  

   assume 
  

  

  1 
  /t 
  =t>o(i+V*+V* 
  , 
  +V*'+---); 
  • 
  ■ 
  ( 
  1() 
  ) 
  

  

  where 
  r 
  = 
  v'o,o 
  is 
  the 
  volume 
  answering 
  to 
  prolonged 
  exposure 
  

   to 
  0° 
  C, 
  while 
  bi, 
  b 
  2 
  , 
  &c, 
  are 
  absolute 
  constants 
  for 
  the 
  

   particular 
  glass. 
  

  

  Though 
  not 
  essential 
  for 
  our 
  present 
  purpose, 
  we 
  may 
  

   notice 
  that 
  combining 
  (2) 
  and 
  (10) 
  we 
  deduce 
  a 
  relation 
  of 
  

   the 
  type 
  

  

  v 
  = 
  v't,o(l 
  + 
  b 
  1 
  t 
  + 
  b 
  2 
  t 
  2 
  + 
  b 
  3 
  t* 
  + 
  ...) 
  ; 
  . 
  . 
  (11) 
  

   where 
  

  

  or, 
  iii 
  general, 
  to 
  a 
  first 
  approximation 
  

  

  b 
  1 
  = 
  a 
  1 
  — 
  bi, 
  b 
  2 
  = 
  a 
  2 
  — 
  b 
  2 
  . 
  

  

  Let 
  S 
  represent 
  the 
  volume 
  at 
  100° 
  C. 
  of 
  the 
  bulb 
  and 
  tube 
  

   up 
  to 
  the 
  division 
  100, 
  and 
  at 
  the 
  same 
  temperature 
  let 
  100 
  s 
  

   denote 
  the 
  volume 
  of 
  the 
  fundamental 
  interval. 
  Then 
  the 
  

   mercury 
  at 
  100° 
  C. 
  has 
  a 
  volume 
  S, 
  and 
  at 
  any 
  other 
  tem- 
  

   perature 
  t 
  (on 
  the 
  hydrogen 
  scale) 
  it 
  has 
  by 
  (1) 
  a 
  volume 
  

  

  S(l 
  + 
  Ai* 
  + 
  A 
  2 
  £ 
  2 
  + 
  . 
  . 
  .)+ 
  (1 
  + 
  100 
  Ai 
  + 
  100 
  2 
  A 
  2 
  + 
  . 
  . 
  .). 
  

  

  The 
  volume 
  of 
  the 
  bulb, 
  including 
  the 
  stem 
  up 
  to 
  the 
  

   division 
  0, 
  when 
  the 
  glass 
  has 
  been 
  suddenly 
  cooled 
  to 
  

   0° 
  G. 
  after 
  exposure 
  to 
  100° 
  C, 
  is 
  equal 
  to 
  the 
  volume 
  

   8-r- 
  (1 
  + 
  100 
  A 
  x 
  + 
  100 
  2 
  A 
  2 
  + 
  . 
  . 
  .) 
  of 
  the 
  mercury 
  at 
  0° 
  G. 
  Thus 
  

   its 
  volume 
  at 
  temperature 
  t 
  under 
  the 
  conditions 
  supposed 
  

   is 
  by 
  (2) 
  

  

  S(l 
  + 
  a 
  1 
  £ 
  + 
  a 
  2 
  £ 
  2 
  + 
  ...) 
  

  

  -r 
  {(1 
  + 
  100 
  A 
  1 
  + 
  100 
  2 
  A 
  2 
  + 
  ...) 
  (1 
  + 
  1006 
  1 
  / 
  + 
  100*V 
  + 
  •■ 
  -)\> 
  

  

  Thus 
  supposing 
  the 
  thermometer 
  to 
  read 
  t 
  + 
  y 
  when 
  the 
  

   hydrogen 
  temperature 
  is 
  t 
  we 
  get, 
  reasoning 
  as 
  in 
  § 
  2, 
  

  

  