﻿Dr. 
  C. 
  Ohree's 
  Notes 
  on 
  Thermometry. 
  311 
  

  

  If 
  the 
  stem 
  of 
  a 
  thermometer 
  were 
  of 
  very 
  unequal 
  bore, 
  

   and 
  consequently 
  its 
  degree-divisions 
  of 
  very 
  unequal 
  length, 
  

   the 
  adoption 
  of 
  the 
  vertical 
  as 
  the 
  standard 
  position 
  would 
  

   not 
  eliminate 
  the 
  internal 
  pressure-correction 
  satisfactorily. 
  

   It 
  is 
  rare, 
  however, 
  even 
  in 
  the 
  commonest 
  commercial 
  tubes 
  

   to 
  encounter 
  cases 
  where 
  this 
  need 
  be 
  taken 
  into 
  account 
  for 
  

   accuracy 
  of 
  the 
  order 
  o, 
  01 
  C, 
  

  

  § 
  29. 
  There 
  are, 
  however, 
  thermometers 
  — 
  some 
  of 
  the 
  most 
  

   approved 
  patterns 
  — 
  for 
  which 
  the 
  ordinary 
  Kew 
  method 
  of 
  

   avoiding 
  an 
  internal 
  pressure-correction 
  fails. 
  It 
  is 
  becoming 
  

   increasingly 
  common 
  to 
  have 
  one 
  or 
  more 
  auxiliary 
  chambers 
  

   blown 
  on 
  stems 
  of 
  thermometers, 
  with 
  the 
  object 
  of 
  including 
  

   one 
  or 
  both 
  fundamental 
  points 
  in 
  the 
  scale 
  without 
  making 
  

   the 
  stem 
  inconveniently 
  long. 
  Now 
  the 
  difference 
  between 
  the 
  

   mercury-pressures 
  in 
  the 
  bulb 
  for 
  two 
  readings, 
  one 
  occurring 
  

   above, 
  the 
  other 
  below 
  an 
  auxiliary 
  chamber, 
  is 
  no 
  longer 
  

   proportional 
  to 
  the 
  difference 
  in 
  the 
  temperatures. 
  Thus 
  the 
  

   determination 
  of 
  the 
  fundamental 
  points 
  in 
  the 
  vertical 
  

   position, 
  and 
  the 
  subdivision 
  of 
  the 
  stem 
  into 
  equal 
  volumes, 
  

   each 
  one-hundredth 
  of 
  the 
  fundamental 
  interval, 
  fails 
  to 
  

   render 
  readings 
  in 
  the 
  vertical 
  position 
  correct 
  measures 
  of 
  

   temperatura. 
  The 
  remedy 
  is 
  easy 
  enough, 
  at 
  least 
  theoreti- 
  

   cally, 
  as 
  the 
  following 
  investigation 
  shows 
  : 
  — 
  

  

  Let 
  the 
  degree-divisions 
  immediately 
  below 
  and 
  immediately 
  

   above 
  an 
  auxiliary 
  chamber 
  be 
  respectively 
  £ 
  x 
  and 
  £ 
  2 
  , 
  while 
  

   the 
  interval 
  between 
  the 
  two 
  divisions 
  equals 
  the 
  length 
  of 
  t 
  

   degree-divisions, 
  instead 
  of 
  t 
  2 
  — 
  t 
  1 
  divisions 
  as 
  it 
  would 
  in 
  an 
  

   ordinary 
  thermometer. 
  For 
  shortness 
  let 
  

  

  t 
  2 
  — 
  h 
  — 
  t 
  — 
  t 
  ; 
  

  

  in 
  other 
  words 
  let 
  t' 
  denote 
  the 
  number 
  of 
  degree-divisions 
  

   by 
  which 
  the 
  stem 
  is 
  shortened 
  through 
  the 
  existence 
  of 
  the 
  

   chamber. 
  

  

  Let 
  " 
  depression 
  *' 
  temporarily 
  signify 
  lowering 
  of 
  reading 
  

   as 
  the 
  thermometer, 
  its 
  temperature 
  remaining 
  constant, 
  

   changes 
  from 
  the 
  horizontal 
  to 
  the 
  vertical 
  position 
  ; 
  also 
  let 
  

   A 
  represent 
  the 
  depression 
  at 
  the 
  ice-point, 
  and 
  8 
  the 
  de- 
  

   pression 
  due 
  to 
  a 
  column 
  of 
  mercury 
  equal 
  in 
  length 
  to 
  a 
  

   degree-division. 
  

  

  Above 
  the 
  chamber 
  at 
  a 
  reading 
  i, 
  which 
  may 
  exceed 
  

   100° 
  C, 
  

  

  depression 
  = 
  A 
  + 
  8(t 
  — 
  t') 
  ; 
  

  

  below 
  the 
  chamber 
  at 
  a 
  reading 
  t, 
  which 
  may 
  be 
  below 
  zero 
  

  

  depression 
  = 
  A 
  + 
  Bt, 
  

  

  