﻿Method 
  of 
  Graduating 
  a 
  Thermometer. 
  231 
  

  

  Integrate 
  between 
  the 
  limits 
  ^ 
  and 
  t, 
  

  

  < 
  * 
  *W 
  *V 
  Mo 
  *y 
  

  

  Hence 
  

  

  -(HHKH)-*}- 
  

  

  ■ 
  *'o 
  i^o 
  rA/i 
  ix 
  i 
  

  

  « 
  ^o 
  tt 
  \2\t 
  ^ 
  t) 
  B 
  r 
  

  

  Multiply 
  by 
  ^(t 
  — 
  t^ 
  and 
  we 
  shall 
  have 
  

  

  <*- 
  2) 
  -«*-«-*=*!?=* 
  tt(M)-»}- 
  

  

  Similarly 
  by 
  interchanging 
  f 
  and 
  t' 
  with 
  ^ 
  and 
  v 
  u 
  we 
  

   might 
  obtain 
  

  

  Subtract 
  the 
  equation 
  last 
  but 
  one 
  from 
  the 
  last, 
  

  

  v 
  V 
  r 
  i 
  r 
  oJ 
  l^i 
  to; 
  c 
  + 
  l 
  'i 
  ? 
  o 
  y 
  on 
  — 
  ^ 
  ^ 
  (-r 
  — 
  jy 
  

  

  We 
  may 
  write 
  this 
  

  

  {v—Vo){ti-to)-(v 
  1 
  -v 
  Q 
  )(t--t 
  ) 
  = 
  K 
  - 
  - 
  \j-jY 
  

  

  Divide 
  by 
  Vi 
  — 
  v 
  and 
  transpose, 
  

  

  '-'o 
  - 
  ~ 
  o 
  (Wo) 
  + 
  - 
  t 
  2(v^oj 
  iirh 
  j 
  ' 
  

  

  Finally, 
  

  

  This 
  last 
  expression 
  for 
  t 
  may 
  be 
  said 
  to 
  consist 
  of 
  three 
  

   parts 
  : 
  — 
  

  

  (i.) 
  There 
  is 
  the 
  quantity 
  t 
  , 
  whose 
  absolute 
  value 
  may 
  be 
  

   considered 
  to 
  have 
  been 
  determined 
  once 
  for 
  all 
  by 
  means 
  of 
  

   its 
  own 
  equation. 
  We 
  may 
  regard 
  it 
  as 
  known 
  numerically 
  

   with 
  sufficient 
  accuracy. 
  

  

  (ii.) 
  There 
  is 
  the 
  term 
  — 
  (ti 
  — 
  t 
  ). 
  This 
  term 
  gives 
  us 
  

  

  the 
  degrees 
  above 
  freezing-point 
  on 
  the 
  equi-expansion 
  

   method 
  of 
  graduation. 
  It 
  is 
  what 
  is 
  usually 
  called 
  the 
  

   " 
  temperature." 
  

  

  • 
  (iii.) 
  The 
  quantity 
  ^ffil*'! 
  ^^^ 
  is 
  due 
  entirely 
  

  

  