﻿Dr. 
  C. 
  Chree 
  s 
  Notes 
  on 
  Thermometry. 
  211 
  

  

  (t 
  I 
  v'V. 
  l 
  + 
  ^i^ 
  + 
  ^ 
  2 
  + 
  ... 
  _ 
  r 
  l 
  + 
  A^ 
  + 
  A 
  2 
  ^ 
  + 
  ... 
  

   v 
  " 
  r 
  « 
  y; 
  1 
  + 
  100« 
  1 
  + 
  100 
  2 
  « 
  2 
  + 
  ... 
  U+l00A 
  1 
  + 
  100 
  2 
  A 
  2 
  + 
  .. 
  

  

  1 
  + 
  Cl\t 
  + 
  a 
  2 
  t" 
  + 
  . 
  . 
  . 
  1 
  /-J 
  qx 
  

  

  (1 
  + 
  100 
  A 
  x 
  + 
  . 
  . 
  .) 
  (1 
  + 
  100 
  W 
  + 
  . 
  . 
  .) 
  J 
  ' 
  l 
  j 
  

   where 
  

  

  */S--fA 
  4- 
  100 
  A 
  + 
  ( 
  % 
  - 
  6/) 
  + 
  100 
  (g 
  2 
  -5 
  2 
  Q 
  + 
  ... 
  -) 
  

   S 
  /b_jA 
  1 
  + 
  100A 
  2 
  + 
  ... 
  1+1006/+.. 
  . 
  j 
  

  

  + 
  (1 
  + 
  100^ 
  + 
  100^ 
  + 
  ...). 
  . 
  (14) 
  

  

  As 
  will 
  be 
  seen 
  presently 
  in 
  §6, 
  1006/ 
  + 
  100 
  2 
  6 
  2 
  ' 
  + 
  . 
  • 
  • 
  is 
  of 
  

   the 
  order 
  1/50,000 
  in 
  ordinary 
  glass, 
  and 
  is 
  hardly 
  likely 
  to 
  

   be 
  worth 
  retaining 
  in 
  the 
  denominator 
  of 
  (s/S) 
  when 
  multi- 
  

   plied 
  by 
  y' 
  . 
  Omitting 
  it 
  

  

  s/S 
  = 
  {A 
  1 
  -a 
  1 
  + 
  b 
  1 
  / 
  +100(A 
  2 
  -a 
  2 
  + 
  b 
  2 
  ') 
  + 
  . 
  . 
  .} 
  

  

  + 
  (1 
  + 
  100 
  A!+100 
  2 
  A 
  2 
  + 
  ...). 
  . 
  . 
  (15) 
  

  

  Using 
  (15) 
  for 
  (s/S) 
  in 
  the 
  coefficient 
  of 
  y' 
  in 
  (13), 
  and 
  

   (11) 
  in 
  the 
  coefficient 
  of 
  t 
  — 
  since 
  t/y 
  1 
  may 
  be 
  very 
  large 
  — 
  

   and, 
  after 
  the 
  substitutions 
  and 
  reductions 
  are 
  effected, 
  

   neglecting 
  1006/ 
  + 
  I00 
  2 
  b 
  2 
  relatively 
  to 
  1, 
  we 
  get 
  

  

  t{100-t)[(A 
  1 
  -a 
  1 
  + 
  b 
  l 
  / 
  )\a 
  1 
  + 
  a 
  i 
  {100 
  + 
  t)\-{A 
  2 
  -a 
  2 
  + 
  b^'){l-l00a 
  2 
  t) 
  . 
  . 
  .] 
  

   (1 
  +ai* 
  + 
  a 
  3 
  * 
  9 
  + 
  ...){ 
  Ax 
  — 
  % 
  + 
  b 
  1 
  ' 
  + 
  100(A 
  2 
  — 
  a 
  2 
  + 
  6/) 
  + 
  . 
  c 
  .} 
  

  

  (ioo-0{&i 
  , 
  + 
  V(ioo 
  + 
  o+...}(if 
  100OJ 
  + 
  100V.0+ 
  (16) 
  

  

  + 
  {A 
  1 
  -a 
  1 
  + 
  6 
  1 
  ' 
  + 
  100(A 
  2 
  -a 
  2 
  + 
  6 
  2 
  ^+...}(l+a 
  1 
  £ 
  + 
  a/ 
  2 
  + 
  ...)' 
  ^ 
  j 
  

  

  Strictly 
  speaking, 
  the 
  terms 
  in 
  6/a 
  2 
  and 
  6 
  2 
  / 
  a 
  2 
  in 
  the 
  first 
  

   line 
  of 
  (16) 
  should 
  be 
  omitted, 
  as 
  others 
  of 
  the 
  same 
  order 
  

   have 
  been 
  neglected. 
  Their 
  retention, 
  however, 
  can 
  do 
  no 
  

   harm, 
  and 
  it 
  facilitates 
  calculation 
  to 
  group 
  bj 
  with 
  A 
  1 
  — 
  a 
  ± 
  

   and 
  b 
  2 
  with 
  A 
  2 
  —a 
  2 
  , 
  the 
  principal 
  terms 
  in 
  their 
  respective 
  

   multipliers 
  being 
  the 
  same. 
  

  

  We 
  must 
  next 
  determine 
  the 
  ice-reading 
  y' 
  tf0 
  taken 
  after 
  

   exposure 
  to 
  temperature 
  t. 
  

  

  Let 
  s' 
  be 
  the 
  volume 
  of 
  the 
  stem-division 
  to 
  1 
  when 
  y' 
  t 
  ,o 
  

   is 
  observed, 
  then 
  obviously 
  

  

  ft 
  _qJi 
  i+&/*+y* 
  8 
  +... 
  i 
  

  

  s 
  y^-*\ 
  L 
  1+1006/+100V+...J 
  

  

  + 
  (1 
  + 
  100 
  Ai 
  + 
  100 
  2 
  A 
  2 
  + 
  ...). 
  . 
  . 
  . 
  (17) 
  

   As 
  the 
  ice-reading 
  is 
  taken 
  very 
  rapidly, 
  and 
  the 
  stem 
  where 
  

  

  