﻿212 
  Dr» 
  C. 
  Chree's 
  Notes 
  on 
  Thermometry. 
  

  

  read 
  must 
  emerge 
  from 
  the 
  ice, 
  the 
  temperature 
  to 
  which 
  s' 
  

   corresponds 
  is 
  uncertain. 
  In 
  ordinary 
  glass, 
  however, 
  the 
  

   volume 
  at 
  100° 
  C. 
  exceeds 
  that 
  at 
  0° 
  C. 
  by 
  only 
  about 
  1 
  part 
  

   in 
  400, 
  and 
  y'fo 
  — 
  ?/ioo,o 
  is 
  seldom 
  as 
  much 
  as 
  0°'3 
  C. 
  Thus, 
  

   at 
  least 
  within 
  the 
  range 
  0° 
  to 
  100° 
  C, 
  we 
  can 
  hardly 
  

   introduce 
  an 
  error 
  so 
  large 
  as 
  0°'001 
  C. 
  by 
  supposing 
  s' 
  

   in 
  (17) 
  to 
  answer 
  to 
  the 
  temperature 
  t. 
  

  

  Doing 
  so, 
  neglecting 
  lOObJ 
  + 
  100 
  2 
  6 
  2 
  ' 
  : 
  1, 
  and 
  using 
  (15), 
  

   we 
  get 
  

   , 
  (100-0{V 
  + 
  V(100 
  + 
  0+.--Kl 
  + 
  1 
  OOa 
  1 
  + 
  100 
  2 
  a 
  3 
  +...) 
  (lg) 
  

   y 
  t 
  '°~' 
  {A^a. 
  + 
  b,' 
  +lOO(A 
  2 
  -a 
  2 
  + 
  b 
  2 
  ')+. 
  . 
  A(l-^a 
  1 
  t 
  + 
  a^ 
  + 
  . 
  . 
  .) 
  ' 
  

  

  Thus 
  the 
  second 
  line 
  in 
  the 
  expression 
  (16) 
  for 
  y' 
  is 
  simply 
  

   y' 
  t 
  , 
  , 
  and 
  hence 
  for 
  the 
  difference 
  y 
  between 
  the 
  glass 
  and 
  

   hydrogen 
  scales 
  we 
  get 
  

  

  y=y 
  r 
  — 
  y*,o 
  = 
  

  

  t(l00-t)[(A 
  l 
  -a, 
  + 
  b 
  l 
  '){a 
  1 
  + 
  o 
  2 
  {100 
  + 
  t)-h...}-(A 
  2 
  -a 
  2 
  + 
  b 
  2 
  ') 
  (l-100a 
  8 
  fl 
  + 
  ...] 
  

   (l 
  + 
  a 
  1 
  * 
  + 
  o 
  2 
  * 
  3 
  + 
  ...){A 
  1 
  -a 
  1 
  + 
  />i 
  / 
  + 
  .l00(A 
  8 
  -tf 
  8 
  + 
  6 
  8 
  , 
  ) 
  + 
  ...} 
  

  

  (19) 
  

  

  Comparing 
  (19) 
  and 
  (6), 
  we 
  see 
  that 
  to 
  the 
  degree 
  of 
  ap- 
  

   proximation 
  reached 
  in 
  (19), 
  y 
  differs 
  from 
  x 
  only 
  in 
  

   replacing 
  

  

  e 
  1 
  =A 
  1 
  — 
  a 
  l 
  by 
  A 
  1 
  —a 
  i 
  + 
  b 
  1 
  l 
  , 
  or 
  A,— 
  b 
  lf 
  

  

  e 
  8 
  =A 
  2 
  — 
  a 
  2 
  by 
  A 
  2 
  — 
  a 
  8 
  + 
  W> 
  or 
  ^"~h- 
  

  

  Thus 
  (19) 
  might 
  have 
  been 
  arrived 
  at 
  by 
  using 
  (11) 
  instead 
  

   of 
  (2) 
  and 
  following 
  a 
  method 
  more 
  analogous 
  to 
  that 
  by 
  

   which 
  (6) 
  was 
  obtained. 
  

  

  § 
  6. 
  To 
  see 
  more 
  exactly 
  what 
  we 
  are 
  doing 
  it 
  is 
  con- 
  

   venient 
  at 
  this 
  stage 
  to 
  consider 
  the 
  order 
  of 
  magnitude 
  of 
  

   the 
  several 
  constants. 
  For 
  this 
  purpose 
  verve 
  dur 
  may 
  be 
  

   selected 
  as 
  an 
  example, 
  taking 
  the 
  first 
  approximations 
  to 
  the 
  

   constants, 
  which 
  are 
  quoted 
  by 
  Guillaume*, 
  viz.:— 
  

  

  A 
  1 
  = 
  182xl0- 
  6 
  , 
  A 
  3 
  = 
  3xl0" 
  9 
  , 
  

   a 
  x 
  = 
  22x10-*, 
  « 
  2 
  = 
  24xl0" 
  9 
  , 
  

   and 
  hence 
  ^ 
  = 
  160 
  xlO" 
  6 
  , 
  e 
  2 
  =-21xl0" 
  9 
  . 
  

  

  These 
  figures 
  make 
  100 
  e 
  2 
  /e 
  1 
  =—l/S0 
  approximately, 
  

   100a 
  1 
  + 
  100 
  2 
  a 
  2 
  = 
  1/100 
  „ 
  

  

  e, 
  + 
  100e 
  2 
  = 
  1/6300 
  „ 
  

  

  To 
  arrive 
  at 
  an 
  idea 
  of 
  the 
  size 
  of 
  6/ 
  &c. 
  we 
  utilize 
  the 
  

   fact 
  that 
  in 
  verve 
  duv 
  the 
  depressed 
  zero 
  after 
  100° 
  0. 
  is 
  

  

  * 
  < 
  Thermometries 
  p. 
  217. 
  

  

  