﻿Dr. 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry. 
  321 
  

  

  thermometer 
  is 
  possible. 
  The 
  simplest 
  way 
  to 
  break 
  off 
  the 
  

   necessary 
  mercury-column 
  is 
  to 
  heat 
  the 
  bulb 
  with 
  a 
  spirit- 
  

   lamp 
  so 
  as 
  to 
  force 
  a 
  long 
  column 
  into 
  the 
  tube. 
  After 
  it 
  is 
  

   broken 
  off' 
  and 
  measured 
  it 
  must 
  be 
  run 
  into 
  the 
  top 
  chamber, 
  

   and 
  a 
  second 
  column 
  must 
  be 
  broken 
  off 
  in 
  the 
  same 
  way, 
  so 
  

   as 
  to 
  get 
  the 
  complete 
  quantity, 
  200 
  divisions 
  long, 
  that 
  is 
  

   required. 
  

  

  The 
  possible 
  cumulation 
  of 
  errors 
  of 
  measurement 
  may 
  be 
  

   trifling 
  when 
  the 
  operator 
  is 
  skilled 
  : 
  but 
  the 
  very 
  consider- 
  

   able 
  heating 
  of 
  the 
  bulb 
  and 
  mercury 
  renders 
  it 
  appreciably 
  

   uncertain 
  what 
  is 
  the 
  true 
  length 
  of 
  the 
  m 
  ercury-column 
  at 
  

   0°O. 
  

  

  For 
  definiteness 
  and 
  generality 
  let 
  us 
  suppose 
  that 
  the 
  

   mercury 
  thrown 
  off 
  fills 
  r 
  stem-divisions 
  when 
  mercury 
  and 
  

   glass 
  are 
  at 
  a 
  temperature 
  of 
  T 
  (on 
  the 
  hydrogen 
  scale), 
  

   instead 
  of 
  r 
  divisions 
  at 
  0° 
  as 
  was 
  intended. 
  Then 
  in 
  its 
  

   final 
  state 
  the 
  thermometer 
  when 
  at 
  0° 
  has 
  a 
  volume 
  of 
  

   mercury 
  too 
  great 
  by 
  

  

  T 
  6?! 
  + 
  e 
  2 
  T 
  + 
  . 
  . 
  . 
  

  

  1 
  + 
  A 
  1 
  T 
  + 
  A 
  2 
  T 
  2 
  + 
  ../ 
  

  

  Consequently 
  at 
  temperature 
  t 
  the 
  thermometer 
  will 
  read 
  y 
  

   degrees 
  higher 
  than 
  a 
  standard 
  of 
  its 
  own 
  glass, 
  where 
  

  

  _ 
  gl 
  + 
  e 
  2 
  T+... 
  1 
  + 
  A,£ 
  + 
  A 
  2 
  * 
  2 
  + 
  ... 
  

  

  l 
  '~ 
  T 
  1 
  + 
  AJ 
  + 
  A/F 
  + 
  ... 
  l 
  + 
  ai 
  t 
  + 
  a 
  2 
  t 
  2 
  + 
  ... 
  * 
  W 
  

  

  Suppose, 
  for 
  instance, 
  in 
  the 
  case 
  t=200, 
  recently 
  selected, 
  

   that 
  T 
  is 
  100° 
  C, 
  corresponding 
  to 
  an 
  error 
  of 
  about 
  1J 
  per 
  

   cent, 
  in 
  the 
  quantity 
  of 
  mercury 
  thrown 
  off. 
  Using 
  the 
  

   mean 
  values 
  of 
  expansion 
  coefficients 
  between 
  0° 
  and 
  100° 
  C. 
  

   instead 
  of 
  the 
  series 
  — 
  which 
  is 
  quite 
  good 
  enough 
  for 
  our 
  

   present 
  purpose 
  — 
  we 
  get 
  approximately, 
  in 
  degrees 
  centi- 
  

  

  grade 
  

  

  y 
  = 
  3-10(l 
  + 
  -000156*). 
  

  

  This 
  makes 
  the 
  error 
  vary 
  throughout 
  the 
  entire 
  range 
  of 
  

   150° 
  C. 
  only 
  between 
  3°20 
  C. 
  and 
  3°'25 
  C. 
  

  

  Accuracy 
  to 
  O- 
  05 
  C. 
  is, 
  I 
  suspect, 
  at 
  present 
  a 
  high 
  ideal 
  

   in 
  mercury 
  thermometers 
  used 
  above 
  200° 
  0. 
  Thus 
  even 
  in 
  

   the 
  above 
  case 
  it 
  is 
  doubtful 
  whether 
  we 
  can 
  improve 
  on 
  

   Welsh's 
  direction 
  to 
  treat 
  the 
  difference 
  observed 
  at 
  some 
  

   standard 
  point 
  as 
  a 
  constant 
  zero 
  correction. 
  

  

  If, 
  however, 
  the 
  observed 
  error 
  rose 
  to 
  4° 
  or 
  5° 
  C. 
  we 
  

   should 
  certainly 
  expose 
  ourselves 
  to 
  errors 
  of 
  the 
  order 
  o, 
  l 
  C. 
  

   if 
  we 
  followed 
  this 
  direction. 
  

  

  