﻿W. 
  P. 
  White 
  — 
  Silicate 
  Specific 
  Heats. 
  13 
  

  

  each 
  3rd 
  difference 
  is 
  6DP 
  3 
  + 
  24EP 
  3 
  0, 
  where 
  P 
  is 
  the 
  tem- 
  

   perature 
  interval 
  between 
  each 
  two 
  successive 
  values 
  in 
  

   the 
  series. 
  It 
  follows 
  at 
  once 
  that 
  by 
  subtracting 
  1/24 
  of 
  

   the 
  3rd 
  difference 
  from 
  the 
  1st, 
  and 
  then 
  multiplying 
  by 
  

   0/P 
  the 
  difference 
  of 
  true 
  and 
  interval 
  heats 
  is 
  obtained. 
  

   The 
  method 
  is 
  exactly 
  equivalent 
  to 
  obtaining 
  a 
  series 
  of 
  

   4th 
  degree 
  equations 
  and 
  thus 
  computing 
  the 
  true 
  specific 
  

   heat, 
  but 
  is 
  much 
  easier. 
  It 
  is 
  also 
  easier 
  17 
  than 
  the 
  

   graphic 
  method, 
  and 
  has 
  over 
  it 
  the 
  further 
  advantages 
  : 
  

   (2) 
  That 
  it 
  is 
  not 
  at 
  all 
  subjective, 
  and 
  (3) 
  that 
  the 
  error 
  

   due 
  to 
  the 
  inadequacy 
  of 
  the 
  4th 
  degree 
  equation 
  is 
  

   almost 
  certain 
  to 
  be 
  less 
  than 
  that 
  involved 
  in 
  drawing 
  

   the 
  curve 
  and 
  tangents. 
  

  

  In 
  practice, 
  the 
  1st 
  differences 
  of 
  course 
  do 
  not 
  apply 
  to 
  

   the 
  temperatures 
  of 
  the 
  original 
  observations, 
  and 
  the 
  

   mean 
  of 
  the 
  differences 
  (for 
  the 
  temperature 
  interval 
  P) 
  

   immediately 
  above 
  and 
  below 
  the 
  temperature 
  is 
  not 
  the 
  

   difference 
  for 
  0, 
  but 
  is 
  rigorously 
  half 
  the 
  1st 
  difference 
  

   at 
  for 
  the 
  interval 
  2P, 
  and 
  was 
  taken 
  as 
  such. 
  But 
  the 
  

   3rd 
  difference 
  contains 
  P 
  3 
  as 
  a 
  factor 
  so 
  that 
  the 
  sum 
  of 
  

   the 
  3rd 
  differences 
  above 
  and 
  below 
  6 
  is 
  1/4 
  the 
  3rd 
  

   difference 
  at 
  for 
  interval 
  2P, 
  and 
  was 
  therefore 
  divided 
  

   by 
  6, 
  not 
  24, 
  before 
  combining 
  it 
  with 
  the 
  1st 
  difference 
  

   for 
  2P. 
  

  

  The 
  experimental 
  error 
  in 
  the 
  true 
  heat 
  thus 
  obtained 
  

   can 
  be 
  found 
  as 
  follows 
  : 
  if 
  a 
  b 
  c 
  d 
  e 
  are 
  the 
  5 
  consecu- 
  

   tive 
  mean 
  heat 
  values 
  which 
  enter 
  into 
  the 
  true 
  heat 
  at 
  

   the 
  temperature 
  of 
  C, 
  the 
  1st 
  differences 
  are 
  b 
  — 
  a, 
  c 
  — 
  b, 
  

   etc., 
  the 
  3rd, 
  e 
  — 
  3d 
  + 
  3c 
  — 
  b, 
  etc. 
  ; 
  the 
  true 
  specific 
  heat 
  

  

  . 
  ~ 
  . 
  (4:(d-b) 
  e-a\6 
  n 
  _ 
  . 
  ,. 
  

  

  is 
  C+ 
  I 
  s 
  — 
  b 
  - 
  jop- 
  ^P 
  m 
  the 
  present 
  case 
  is 
  

  

  400°, 
  so 
  that 
  for 
  C 
  at 
  500° 
  the 
  true 
  heat 
  is 
  : 
  

  

  0.+|(rf- 
  ft) 
  -A 
  (•-«,); 
  for 
  1100°, 
  

  

  C 
  + 
  £(« 
  r 
  ft)-g(«-a). 
  

  

  Hence 
  at 
  1100° 
  the 
  experimental 
  error 
  in 
  the 
  true 
  heat 
  

   may 
  be 
  5 
  times 
  the 
  error 
  in 
  a 
  single 
  one 
  of 
  the 
  deter- 
  

  

  17 
  Of 
  course, 
  it 
  requires 
  evenly 
  spaced 
  values 
  of 
  the 
  mean 
  specific 
  heat. 
  

   When 
  these 
  are 
  absent, 
  graphic 
  methods 
  are 
  easier, 
  as 
  in 
  almost 
  every 
  case 
  

   where 
  the 
  independent 
  variable 
  increases 
  by 
  unequal 
  increments. 
  

  

  