﻿208 
  Dr. 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry. 
  

  

  where 
  the 
  B 
  coefficients 
  vary 
  with 
  the 
  nature 
  of 
  the 
  glass. 
  

   Doubtless 
  (7) 
  is 
  convergent 
  for 
  the 
  restricted 
  values 
  of 
  t 
  

   occurring 
  in 
  our 
  problem 
  ; 
  but 
  it 
  would 
  not 
  be 
  safe 
  to 
  assume 
  

   that 
  B 
  is 
  always 
  the 
  most 
  important 
  term. 
  For 
  instance, 
  if 
  

   we 
  neglect 
  all 
  constants 
  with 
  suffixes 
  greater 
  than 
  2, 
  we 
  

   reduce 
  (6) 
  to 
  

  

  g 
  =«(100-0(l 
  + 
  «it 
  + 
  a^*)- 
  1 
  { 
  ^^S 
  ~' 
  2 
  + 
  «i«} 
  , 
  (8) 
  

  

  and 
  conceivably 
  <? 
  1 
  (a 
  1 
  + 
  100a 
  2 
  ) 
  ~ 
  e 
  2 
  might 
  be 
  very 
  small. 
  

  

  It 
  is 
  important 
  to 
  notice 
  that 
  even 
  if 
  mercury 
  and 
  glass 
  

   had 
  both 
  a 
  linear 
  law 
  of 
  expansion, 
  on 
  the 
  hydrogen 
  scale, 
  x 
  

   would 
  not 
  vanish, 
  but 
  would 
  be 
  given 
  as 
  a 
  first 
  approximation 
  

  

  by 
  

  

  x=a 
  1 
  t(100-t) 
  (9) 
  

  

  This 
  is 
  a 
  relation 
  of 
  the 
  same 
  form 
  as 
  that 
  proposed 
  by 
  

   Callendar 
  for 
  the 
  difference 
  between 
  the 
  platinum-resistance 
  

   and 
  air-thermometer 
  scales. 
  

  

  The 
  divergences 
  between 
  actual 
  glass-mercury 
  and 
  hy- 
  

   drogen 
  scales 
  depend 
  partly 
  on 
  the 
  departures 
  of 
  glass 
  from 
  

   our 
  ideal 
  ; 
  their 
  discussion 
  is 
  thus 
  postponed 
  until 
  the 
  

   properties 
  of 
  glass 
  have 
  been 
  dealt 
  with. 
  

  

  Properties 
  of 
  Real 
  Glass. 
  

  

  § 
  3. 
  The 
  principal 
  departure 
  of 
  real 
  glass 
  from 
  our 
  ideal 
  is 
  

   that 
  its 
  volume 
  at 
  a 
  given 
  temperature 
  is 
  not 
  invariable. 
  It 
  

   is 
  well 
  known 
  that 
  if 
  a 
  mercury-thermometer 
  employed 
  at 
  

   ordinary 
  temperatures 
  be 
  tested 
  at 
  intervals 
  in 
  ice 
  it 
  usually 
  

   reads 
  higher 
  as 
  time 
  progresses, 
  i. 
  e. 
  its 
  zero 
  rises. 
  Its 
  

   behaviour 
  is 
  explicable 
  on 
  the 
  hypothesis 
  of 
  a 
  secular 
  con- 
  

   traction 
  of 
  the 
  bulb, 
  becoming 
  gradually 
  slower 
  as 
  time 
  

   elapses. 
  By 
  properly 
  annealing 
  the 
  tubes, 
  and 
  storing 
  them 
  

   for 
  several 
  years 
  before 
  dividing 
  them, 
  this 
  defect 
  may 
  be 
  

   very 
  largely 
  if 
  not 
  entirely 
  got 
  rid 
  of 
  ; 
  and 
  it 
  can 
  in 
  any 
  but 
  

   a 
  very 
  new 
  thermometer 
  be 
  easily 
  allowed 
  for 
  in 
  reducing 
  

   observations. 
  This 
  change 
  of 
  zero, 
  be 
  it 
  noticed, 
  is 
  believed 
  

   to 
  occur 
  however 
  uniform 
  be 
  the 
  temperature 
  at 
  which 
  a 
  

   thermometer 
  is 
  kept. 
  

  

  When 
  we 
  expose 
  a 
  thermometer 
  to 
  changes 
  of 
  temperature 
  

   a 
  further 
  defect 
  presents 
  itself, 
  which 
  for 
  thermometry 
  of 
  the 
  

   highest 
  accuracy 
  is 
  much 
  more 
  troublesome. 
  Within 
  certain 
  

   limits, 
  the 
  increase 
  of 
  volume 
  in 
  glass 
  accompanying 
  rise 
  of 
  

   temperature 
  from, 
  say, 
  t 
  to 
  t' 
  does 
  not 
  wholly 
  disappear 
  at 
  

   once 
  when 
  the 
  temperature 
  is 
  rapidly 
  reduced 
  to 
  t. 
  A 
  

   thermometer 
  taken 
  through 
  such 
  a 
  cycle 
  reads 
  lower 
  on 
  the 
  

   second 
  exposure 
  to 
  the 
  lower 
  temperature. 
  This 
  phenomenon 
  

  

  