﻿214 
  Dr. 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry. 
  

  

  large. 
  There 
  may 
  be 
  cases 
  where 
  it 
  is 
  not 
  large 
  ; 
  only 
  for 
  

   them 
  x— 
  y 
  is 
  negligible. 
  

  

  § 
  8. 
  As 
  our 
  treatment 
  of 
  the 
  movable 
  zero 
  method 
  rests 
  

   on 
  (10), 
  it 
  is 
  desirable 
  to 
  indicate 
  the 
  experimental 
  basis 
  for 
  

   this 
  formula, 
  especially 
  as 
  by 
  doing 
  so 
  we 
  shall 
  see 
  more 
  

   clearly 
  how 
  to 
  obtain 
  numerical 
  results 
  for 
  bj, 
  b 
  2 
  ', 
  and 
  x 
  — 
  y. 
  

  

  The 
  experimental 
  basis 
  is 
  simply 
  that 
  in 
  ordinary 
  thermo- 
  

   meters 
  used 
  in 
  a 
  definite 
  way 
  the 
  depression 
  D^ 
  in 
  the 
  zero 
  

   reading, 
  after 
  exposure 
  to 
  moderate 
  temperature 
  t, 
  is 
  given 
  

   satisfactorily 
  by 
  a 
  formula 
  of 
  the 
  type 
  

  

  D 
  f 
  =cZ 
  L 
  t 
  + 
  cfet 
  8 
  +..., 
  (22) 
  

  

  where 
  d 
  v 
  d 
  2 
  are 
  constants 
  for 
  the 
  particular 
  thermometer. 
  

  

  If 
  v 
  ' 
  be 
  the 
  volume 
  of 
  a 
  scale-division, 
  and 
  V 
  that 
  of 
  the 
  

   bulb 
  up 
  to 
  the 
  fixed 
  zero 
  mark 
  after 
  prolonged 
  exposure 
  to 
  

   0° 
  C, 
  we 
  have 
  

  

  i> 
  'D,=V, 
  j0 
  -V„, 
  

  

  where 
  V^ 
  is 
  the 
  volume 
  of 
  the 
  bulb 
  after 
  sudden 
  cooling 
  

   from 
  t° 
  to 
  0°. 
  Hence 
  by 
  (22) 
  

  

  Vt,o=V 
  {l 
  + 
  (d 
  1 
  v 
  '/Y 
  )t 
  + 
  (d 
  z 
  v 
  '/Y 
  )t* 
  + 
  ...\. 
  • 
  (23) 
  

  

  This 
  is 
  a 
  formula 
  of 
  the 
  assumed 
  type 
  (10), 
  with 
  

  

  «W/V.=V, 
  <W/Vo=V, 
  to. 
  • 
  • 
  (24) 
  

  

  In 
  practice, 
  as 
  explained 
  above, 
  v 
  f 
  may 
  differ 
  from 
  v 
  , 
  the 
  

   value 
  corresponding 
  to 
  prolonged 
  exposure 
  to 
  0° 
  C. 
  The 
  

   divergence 
  is, 
  however, 
  negligible 
  in 
  (23) 
  for 
  values 
  of 
  t 
  not 
  

   exceeding 
  100°. 
  Neglecting 
  it 
  also 
  in 
  (24), 
  we 
  clearly 
  have 
  

   &/ 
  and 
  6 
  2 
  / 
  determined 
  in 
  terms 
  of 
  v 
  Q 
  /V 
  , 
  a 
  quantity 
  known 
  

   when 
  the 
  glass 
  is 
  known, 
  and 
  of 
  d 
  l 
  and 
  d 
  2j 
  constants 
  deter- 
  

   mined 
  by 
  experiments 
  on 
  the 
  depressed 
  zero 
  readings 
  after 
  a 
  

   series 
  of 
  temperatures. 
  

  

  In 
  deducing 
  (21) 
  from 
  (20) 
  we 
  neglected 
  (a 
  l 
  t 
  + 
  a 
  2 
  t 
  2 
  ')/l. 
  

   Thus 
  to 
  this 
  degree 
  of 
  accuracy 
  we 
  may 
  also 
  neglect 
  

   100 
  a-i 
  + 
  100 
  2 
  c/ 
  2 
  + 
  . 
  . 
  . 
  ; 
  and 
  when 
  we 
  do 
  so 
  we 
  have 
  from 
  (4) 
  

  

  v 
  /Y 
  =c 
  1 
  + 
  100e 
  2 
  + 
  ... 
  

  

  Hence, 
  referring 
  to 
  (24), 
  we 
  see 
  that 
  (21) 
  is 
  equivalent 
  to 
  

  

  x-y=t 
  (100 
  -*)<*» 
  ( 
  25 
  ) 
  

  

  In 
  reality 
  100% 
  + 
  100% 
  + 
  . 
  . 
  • 
  is 
  of 
  the 
  order 
  1/400, 
  while, 
  

   for 
  values 
  of 
  t 
  between 
  and 
  100, 
  D 
  t 
  or 
  t 
  (100 
  —t)d 
  2 
  is 
  of 
  the 
  

   order 
  1/10 
  ; 
  thus 
  their 
  product 
  is 
  negligible. 
  

   If 
  d 
  2 
  be 
  zero, 
  i.e. 
  if 
  D^ 
  be 
  a 
  linear 
  function 
  of 
  t, 
  

  

  