﻿Dr. 
  C 
  Chree's 
  Notes 
  on 
  Thermometry. 
  213 
  

  

  almost 
  exactly 
  o, 
  l 
  C. 
  lower 
  than 
  that 
  answering 
  to 
  0° 
  C. 
  

   Thus 
  from 
  (18) 
  

  

  100(6/ 
  + 
  100 
  W 
  + 
  ...)(! 
  + 
  100 
  a 
  x 
  -f 
  100 
  2 
  a 
  2 
  + 
  ..Q 
  1 
  

  

  « 
  l 
  +iootf 
  1 
  +...+(v+ioov+-.-) 
  "~ro* 
  

  

  Having 
  regard 
  to 
  the 
  small 
  value 
  found 
  above 
  for 
  

   lOOai 
  + 
  lOO' 
  2 
  ^, 
  we 
  thence 
  deduce 
  as 
  a 
  close 
  approximation 
  

  

  (V 
  + 
  1006/ 
  + 
  . 
  ..)/(«!+ 
  100 
  * 
  + 
  .. 
  .) 
  = 
  1/1000, 
  

  

  and 
  so, 
  from 
  above, 
  6/ 
  +100 
  6/+ 
  . 
  . 
  . 
  = 
  1/6300000 
  roughly. 
  

  

  The 
  size 
  of 
  a 
  x 
  seems 
  fairly 
  uniform 
  in 
  different 
  kinds 
  of 
  

   glass, 
  so 
  that 
  e\ 
  never 
  differs 
  much 
  from 
  the 
  value 
  160 
  x 
  10~ 
  6 
  

   found 
  above. 
  The 
  size 
  of 
  a 
  2 
  and 
  e 
  2 
  is 
  probably 
  much 
  more 
  

   variable, 
  but 
  100 
  e 
  2 
  /ei 
  is, 
  doubtless, 
  in 
  all 
  cases 
  a 
  small 
  fraction. 
  

   Similarly 
  the 
  size 
  of 
  (6/ 
  + 
  100 
  &/ 
  + 
  . 
  . 
  .)/(*! 
  + 
  100 
  e 
  2 
  + 
  . 
  . 
  is 
  

   certainly 
  somewhat 
  variable 
  ; 
  it 
  may 
  be 
  as 
  large 
  in 
  some 
  

   kinds 
  of 
  glass 
  as 
  1/300, 
  but 
  we 
  are 
  unlikely 
  to 
  commit 
  any 
  

   serious 
  error 
  if 
  we 
  treat 
  it 
  as 
  a 
  quantity 
  of 
  the 
  order 
  1/1000 
  

   in 
  English 
  glass. 
  

  

  § 
  7. 
  Thus 
  in 
  neglecting 
  6/+ 
  100 
  b 
  2 
  +... 
  in 
  the 
  denominator 
  

   of 
  (19) 
  we 
  should 
  only 
  make 
  an 
  error 
  of 
  the 
  order 
  1/1000 
  in 
  the 
  

   value 
  of 
  y. 
  Now 
  between 
  0° 
  C. 
  and 
  100° 
  C. 
  the 
  largest 
  value 
  

   of 
  y 
  seldom 
  approaches 
  o, 
  5 
  0., 
  so 
  throughout 
  at 
  least 
  this 
  

   range 
  the 
  neglect 
  is 
  abundantly 
  justified, 
  even 
  when 
  accuracy 
  

   of 
  the 
  order 
  o, 
  001 
  C. 
  is 
  aimed 
  at. 
  At 
  temperatures 
  much 
  

   above 
  100° 
  C. 
  the 
  neglect 
  of 
  6/ 
  + 
  100 
  V 
  + 
  » 
  • 
  • 
  would 
  require 
  

   more 
  consideration. 
  Neglecting 
  it 
  provisionally, 
  we 
  deduce 
  

   from 
  (6) 
  and 
  (19) 
  

  

  y-(l+a 
  1 
  t+...)(e 
  1 
  + 
  100e 
  2 
  + 
  ...)' 
  ' 
  ' 
  W 
  

  

  As 
  we 
  have 
  already 
  seen, 
  a, 
  is 
  of 
  the 
  order 
  2 
  x 
  10 
  _5 
  ,.and 
  

   bi/e-i 
  appears 
  seldom 
  to 
  approach 
  1/400. 
  Thus 
  for 
  values 
  of 
  

   * 
  between 
  0° 
  and 
  100° 
  

  

  a^/^lOO-O-K 
  1 
  *^ 
  • 
  • 
  0(^1 
  + 
  100 
  e 
  2 
  . 
  . 
  .) 
  

  

  is 
  a 
  quantity 
  of 
  the 
  order 
  o, 
  0001 
  C, 
  and 
  so 
  may 
  be 
  neglected. 
  

   For 
  the 
  same 
  range 
  of 
  temperature 
  os—y 
  is 
  a 
  small 
  fraction 
  

   of 
  a 
  degree, 
  and 
  we 
  may 
  thus 
  write 
  1 
  for 
  1 
  +a 
  1 
  t 
  + 
  . 
  . 
  . 
  in 
  (20). 
  

   Thus 
  we 
  conclude 
  that 
  for 
  practical 
  purposes 
  — 
  so 
  long 
  at 
  

   least 
  as 
  t 
  is 
  not 
  considerably 
  in 
  excess 
  of 
  100 
  — 
  we 
  may 
  re- 
  

   place 
  (20) 
  by 
  

  

  a! 
  -.y 
  = 
  t(lQ0-t)b 
  2 
  '+(e 
  1 
  + 
  100e 
  2 
  + 
  ...). 
  . 
  . 
  (21) 
  

  

  Our 
  reasoning 
  does 
  not 
  necessarily 
  imply 
  that 
  b 
  2 
  )a^){ 
  is 
  

  

  