﻿318 
  Dr. 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry 
  . 
  

  

  As 
  evidence 
  that 
  Welsh 
  did 
  not 
  confine 
  bis 
  attention 
  to 
  

   this 
  particular 
  case, 
  I 
  may 
  mention 
  that 
  he 
  supplied 
  at 
  least 
  

   one 
  London 
  optician 
  with 
  data 
  applicable 
  to 
  any 
  length 
  of 
  

   redundant 
  column, 
  and 
  that 
  since 
  his 
  time 
  a 
  considerable 
  

   variety 
  of 
  thermometers 
  of 
  the 
  type 
  have 
  been 
  sent 
  to 
  Kew 
  

   Observatory 
  for 
  verification. 
  

  

  The 
  method 
  has 
  gradually 
  extended 
  to 
  thermometers 
  

   intended 
  for 
  other 
  than 
  hypsometric 
  purposes. 
  Thus 
  before 
  

   referring 
  further 
  to 
  Welsh's 
  particular 
  case, 
  it 
  is 
  convenient 
  

   to 
  discuss 
  the 
  general 
  theory. 
  

  

  § 
  34. 
  In 
  the 
  final 
  state 
  suppose 
  that 
  at 
  0° 
  C. 
  the 
  internal 
  

   volume 
  of 
  the 
  thermometer 
  up 
  to 
  the 
  division 
  (or 
  where 
  

   that 
  division 
  would 
  come 
  if 
  it 
  existed) 
  is 
  V 
  , 
  while 
  100 
  v 
  is 
  

   then 
  the 
  volume 
  between 
  the 
  divisions 
  and 
  100. 
  Suppose 
  

   also 
  that 
  the 
  mercury 
  thrown 
  over 
  when 
  measured 
  at 
  0" 
  C. 
  

   occupied 
  r 
  scale-divisions. 
  

  

  In 
  the 
  preliminary 
  state 
  suppose 
  the 
  thermometer 
  reads 
  

   t 
  + 
  r 
  + 
  x 
  when 
  the 
  hydrogen 
  temperature 
  is 
  /, 
  then 
  in 
  the 
  

   notation 
  of 
  (1) 
  and 
  (2) 
  

  

  (V 
  -r 
  tvr)( 
  1 
  + 
  A,t 
  + 
  A 
  2 
  t 
  2 
  + 
  . 
  .) 
  = 
  

  

  {Y 
  + 
  v 
  T 
  + 
  v 
  (t-\-x)}(l 
  + 
  a 
  1 
  t-\-a 
  2 
  t 
  2 
  + 
  . 
  .}, 
  

  

  where 
  r 
  /V 
  is 
  given 
  by 
  (4). 
  

  

  Eliminating 
  v 
  /V 
  , 
  and 
  for 
  brevity 
  retaining 
  only 
  constants 
  

   with 
  suffixes 
  1 
  and 
  2, 
  we 
  get 
  on 
  reduction 
  

  

  ~x 
  — 
  x-rx') 
  . 
  (29) 
  

  

  where 
  

  

  « 
  = 
  t(ioo-o(i+ch*+«,fr^ 
  

  

  x' 
  = 
  Tt(e 
  1 
  +e 
  2 
  t)/(l 
  + 
  a 
  1 
  t 
  + 
  a 
  2 
  t 
  2 
  ). 
  . 
  . 
  . 
  (30). 
  

  

  Referring 
  to 
  (8) 
  we 
  see 
  that 
  x 
  is 
  simply 
  the 
  departure 
  at 
  

   temperature 
  t 
  of 
  the 
  natural 
  scale 
  of 
  the 
  glass 
  of 
  the 
  thermo- 
  

   meter 
  from 
  the 
  hydrogen 
  scale. 
  Thus 
  if 
  we 
  compared 
  the 
  

   thermometer 
  in 
  its 
  preliminary 
  state 
  with 
  an 
  ordinary 
  

   standard 
  thermometer 
  of 
  the 
  same 
  glass, 
  we 
  should 
  find 
  its 
  

   reading 
  to 
  exceed 
  that 
  of 
  the 
  standard 
  by 
  t 
  + 
  x'. 
  

  

  The 
  excess 
  of 
  reading 
  thus 
  consists 
  of 
  a 
  constant 
  part 
  t 
  

   which 
  should 
  equal 
  the 
  number 
  of 
  degree-lengths 
  (measured 
  

   at 
  0° 
  C.) 
  to 
  be 
  thrown 
  over, 
  and 
  of 
  a 
  variable 
  part 
  x' 
  given 
  

   by 
  (30). 
  

  

  The 
  data 
  already 
  laid 
  down 
  as 
  to 
  the 
  magnitudes 
  of 
  the 
  

   constants 
  of 
  expansion 
  point 
  to 
  the 
  conclusion 
  that 
  so 
  long 
  

   as 
  t 
  and 
  t, 
  in 
  the 
  centigrade 
  scale, 
  are 
  less 
  than 
  100, 
  it 
  will 
  

  

  