﻿W. 
  P. 
  White 
  — 
  Specific 
  Heat 
  Determination. 
  15 
  

  

  single, 
  simple 
  law 
  for 
  all 
  temperatures, 
  and 
  can 
  also, 
  

   without 
  serious 
  extrapolation, 
  be 
  obtained 
  for 
  a 
  tempera- 
  

   ture 
  closer 
  to 
  the 
  highest 
  observed. 
  This 
  is 
  often, 
  and 
  

   properly, 
  done 
  for 
  short 
  intervals 
  by 
  assuming 
  a 
  linear 
  

   law. 
  It 
  seems 
  worth 
  while 
  to 
  inquire 
  what 
  error 
  is 
  thus 
  

   incurred, 
  that 
  is, 
  what 
  correction 
  is 
  needed 
  to 
  make 
  the 
  

   result 
  more 
  exact, 
  and 
  how 
  such 
  a 
  method 
  will 
  work 
  out 
  in 
  

   the 
  present 
  case. 
  

  

  If 
  the 
  total 
  heats 
  at 
  temperatures 
  6 
  1 
  and 
  2 
  are 
  m 
  1 
  1 
  and 
  

   m 
  2 
  2 
  , 
  the 
  interval 
  heat 
  between 
  1 
  and 
  2 
  is 
  evidently 
  

  

  iyyi 
  Q 
  ffll 
  

  

  - 
  ? 
  — 
  ^ 
  -£ 
  — 
  - 
  which 
  may 
  crudely 
  be 
  put 
  for 
  the 
  true 
  heat 
  at 
  

  

  6 
  2 
  — 
  1 
  

  

  A 
  I 
  A 
  

  

  1 
  T~ 
  2 
  , 
  the 
  middle 
  of 
  the 
  interval. 
  If 
  we 
  put 
  simply 
  

  

  a 
  I 
  n 
  

  

  for 
  the 
  mean 
  temperature 
  1 
  "T 
  2 
  , 
  and 
  h 
  for 
  half 
  the 
  

  

  A 
  A 
  

  

  interval, 
  or 
  2 
  ■ 
  1 
  , 
  this 
  crude 
  value 
  is 
  easily 
  shown 
  to 
  be 
  

   f 
  m 
  a 
  — 
  m\ 
  m 
  a 
  4- 
  m, 
  

  

  xl 
  2 
  y 
  + 
  2 
  * 
  [) 
  

  

  If 
  we 
  take, 
  as 
  before, 
  m= 
  A 
  + 
  B0 
  + 
  C0 
  2 
  ++ 
  E<9 
  4 
  , 
  it 
  is 
  

   easy 
  to 
  show 
  (1) 
  is 
  equal 
  to 
  

  

  a 
  + 
  2B<9 
  + 
  3C<9 
  2 
  4- 
  4D6> 
  3 
  4- 
  5E<9 
  4 
  

   + 
  A 
  2 
  C 
  + 
  U 
  2 
  6D 
  + 
  (10A 
  2 
  6> 
  2 
  + 
  A 
  4 
  )E 
  

  

  that 
  is, 
  to 
  the 
  true 
  heat 
  at 
  plus 
  

  

  A 
  2 
  C 
  + 
  4A 
  2 
  6>D 
  + 
  (10A 
  2 
  <9 
  2 
  4- 
  A 
  4 
  )E 
  (2) 
  

  

  The 
  first 
  difference 
  across 
  the 
  interval 
  2h 
  between 
  1 
  and 
  

   6 
  2 
  has 
  already 
  been 
  used 
  as 
  m 
  2 
  — 
  m 
  x 
  . 
  The 
  second 
  dif- 
  

   ference 
  as 
  regularly 
  obtained 
  will 
  not 
  come 
  opposite 
  0, 
  

   but 
  opposite 
  8 
  1 
  or 
  2 
  . 
  "We 
  may, 
  however, 
  use 
  the 
  differ- 
  

   ence 
  at 
  ly 
  expressing 
  it 
  in 
  terms 
  of 
  and 
  h. 
  In 
  all 
  the 
  

   differences 
  the 
  interval, 
  P, 
  will 
  be 
  2h. 
  It 
  is 
  now 
  not 
  hard 
  

   to 
  show 
  that 
  if 
  we 
  add: 
  

  

  — 
  the 
  lower 
  second 
  din 
  . 
  

  

  i 
  e 
  (3) 
  

  

  -f 
  — 
  the 
  third 
  + 
  — 
  - 
  - 
  X 
  the 
  third 
  I 
  

   lb 
  4b 
  n 
  J 
  

  

  