﻿Dr. 
  0. 
  Ghree's 
  Notes 
  on 
  Thermometry. 
  319 
  

  

  generally 
  suffice 
  for 
  accuracy 
  of 
  the 
  order 
  o, 
  05 
  0. 
  to 
  

   replace 
  (30) 
  by 
  

  

  x'=eTt, 
  (31) 
  

  

  where 
  e 
  is 
  the 
  mean 
  value 
  between 
  0° 
  and 
  100° 
  of 
  the 
  co- 
  

   efficient 
  of 
  expansion 
  of 
  the 
  mercury 
  relative 
  to 
  the 
  glass 
  of 
  

   the 
  thermometer. 
  

  

  Our 
  calculation 
  assumed 
  the 
  thermometer 
  to 
  read 
  correctly 
  

   in 
  its 
  final 
  state, 
  and 
  our 
  conclusion 
  shows 
  that 
  in 
  order 
  that 
  

   this 
  may 
  be 
  the 
  case 
  it 
  should 
  in 
  the 
  preliminary 
  state 
  

   read 
  t 
  degrees 
  too 
  high 
  in 
  ice, 
  and 
  show 
  an 
  error 
  increasing 
  

   er 
  per 
  degree 
  as 
  we 
  pass 
  up 
  the 
  scale. 
  In 
  other 
  words, 
  in 
  

   the 
  preliminary 
  state 
  its 
  scale 
  must 
  be 
  too 
  short 
  for 
  the 
  

   quantity 
  of 
  mercury 
  then 
  present 
  by 
  lOO^r 
  scale-divisions 
  in 
  

   100 
  ; 
  the 
  quantity 
  lOOeT 
  may 
  be 
  conveniently 
  called 
  the 
  

   percentage 
  contraction. 
  

  

  For 
  the 
  mean 
  coefficient 
  of 
  expansion 
  of 
  mercury 
  between 
  

   0° 
  and 
  1C0° 
  C. 
  Stewart 
  and 
  Gee 
  * 
  give 
  -0001815. 
  What 
  the 
  

   mean 
  coefficient 
  of 
  expansion 
  for 
  the 
  glass 
  in 
  English 
  thermo- 
  

   meters 
  may 
  be 
  is 
  somewhat 
  uncertain, 
  but 
  it 
  is 
  unlikely 
  to 
  

   differ 
  much 
  from 
  the 
  value 
  '000025, 
  given 
  by 
  Stewart 
  and 
  

   Gee 
  (/. 
  c. 
  p. 
  120) 
  for 
  the 
  mean 
  from 
  nine 
  different 
  kinds 
  

   of 
  glass. 
  

  

  Taking 
  these 
  values 
  provisionally 
  we 
  have 
  

  

  e= 
  -000156 
  f, 
  

   100 
  <?t= 
  -0156 
  xt. 
  

   In 
  Welch's 
  example 
  r= 
  72*2, 
  in 
  centigrade 
  degrees, 
  whence 
  

   100 
  er= 
  1-13. 
  

  

  The 
  instruction 
  to 
  the 
  optician 
  in 
  this 
  case 
  would 
  thus 
  be 
  : 
  

   make 
  the 
  scale 
  1*13 
  per 
  cent, 
  too 
  contracted 
  for 
  the 
  quantity 
  

   of 
  mercury 
  originally 
  present 
  ; 
  or, 
  more 
  simply, 
  tell 
  him 
  that 
  

   the 
  following 
  table 
  of 
  relations 
  applies 
  : 
  — 
  

  

  True 
  temperature 
  (Fahrenheit) 
  42° 
  52° 
  62° 
  72° 
  82° 
  

   Reading 
  of 
  thermometer 
  in 
  pre- 
  

   liminary 
  state 
  171-55 
  181-66 
  191-77 
  201-89 
  212. 
  

  

  . 
  For 
  simplicity 
  it 
  should 
  be 
  noticed 
  that 
  all 
  w~e 
  have 
  to 
  

   consider 
  is 
  the 
  absolute 
  value 
  of 
  er 
  in 
  (31), 
  so 
  long 
  as 
  we 
  

   measure 
  aj 
  and 
  t 
  on 
  the 
  same 
  scale, 
  whether 
  centigrade 
  or 
  

   Fahrenheit. 
  In 
  other 
  words 
  the 
  suitable 
  contraction 
  of 
  

   scale 
  depends 
  only 
  on 
  the 
  amount 
  of 
  mercury 
  thrown 
  oft. 
  

   The 
  mistake, 
  however, 
  of 
  supposing 
  that 
  throwing 
  over 
  

  

  * 
  ' 
  Elementary 
  Practical 
  Physics/ 
  vol. 
  i. 
  p, 
  118. 
  

  

  t 
  For 
  verre 
  dur 
  and 
  59 
  m 
  the 
  values 
  -000158 
  and 
  -0001645 
  respectively 
  

   "are 
  found 
  at 
  the 
  Keichsanstalt 
  ( 
  Wiss. 
  Abhandl. 
  vol. 
  ii. 
  pp. 
  9, 
  17,), 
  

  

  Z 
  2 
  

  

  