﻿W. 
  P. 
  White 
  — 
  Silicate 
  Specific 
  Heats. 
  11 
  

  

  intervals 
  are 
  seldom 
  the 
  same 
  for 
  different 
  observers, 
  so 
  

   that 
  their 
  results 
  are, 
  as 
  a 
  rule, 
  comparable 
  only 
  with 
  

   great 
  difficulty. 
  (2) 
  Each 
  result 
  is 
  the 
  average 
  of 
  a 
  

   varying 
  quantity 
  whose 
  law 
  of 
  variation 
  is 
  unknown, 
  so 
  

   that 
  the 
  specific 
  heat 
  at 
  any 
  given 
  temperature, 
  the 
  

   quantity 
  most 
  often 
  really 
  wanted, 
  is 
  much 
  more 
  uncer- 
  

   tain 
  than 
  the 
  result 
  given. 
  To 
  avoid 
  one 
  of 
  these 
  objec- 
  

   tions 
  in 
  the 
  present 
  case, 
  all 
  the 
  results 
  as 
  given 
  are 
  

   reduced 
  to 
  even 
  intervals 
  ; 
  the 
  other 
  is 
  avoided 
  by 
  the 
  

   number 
  and 
  treatment 
  of 
  the 
  results, 
  since 
  the 
  results, 
  

   forming, 
  as 
  they 
  do, 
  regular 
  series, 
  enable 
  the 
  law 
  of 
  

   variation 
  with 
  temperature 
  to 
  be 
  known, 
  and 
  the 
  actual 
  

   specific 
  heat 
  at 
  any 
  given 
  temperature 
  to 
  be 
  found. 
  For 
  

   while 
  a 
  single 
  actual 
  specific 
  heat 
  may 
  be 
  more 
  useful 
  

   than 
  a 
  mean 
  value, 
  a 
  set 
  of 
  mean 
  values 
  for 
  different 
  

   intervals 
  defines 
  the 
  total 
  specific 
  heat 
  function 
  as 
  well, 
  

   theoretically, 
  as 
  a 
  series 
  of 
  actual 
  heats. 
  In 
  practice, 
  

   actual 
  heats 
  are 
  apt 
  to 
  be 
  known 
  more 
  accurately 
  if 
  they 
  

   are 
  determined 
  directly, 
  but 
  in 
  the 
  present 
  case 
  the 
  inter- 
  

   val-heat 
  method, 
  enabling 
  the 
  calorimeter 
  to 
  be 
  operated 
  

   at 
  room 
  temperature, 
  was 
  thought 
  to 
  give 
  even 
  the 
  actual 
  

   heats 
  more 
  accurately 
  than 
  a 
  direct 
  determination 
  in 
  an 
  

   electric 
  furnace 
  and 
  was, 
  in 
  fact, 
  adopted 
  as 
  more 
  

   accurate 
  after 
  the 
  research 
  had 
  been 
  begun 
  with 
  the 
  

   other 
  plan. 
  

  

  In 
  reducing 
  to 
  even 
  intervals, 
  the 
  slight 
  variation 
  of 
  the 
  

   upper 
  temperature 
  from 
  the 
  round 
  number 
  was 
  corrected 
  

   for 
  by 
  interpolating 
  along 
  the 
  curve 
  defined 
  by 
  the 
  series 
  

   of 
  results 
  for 
  widely 
  differing 
  upper 
  temperatures. 
  This 
  

   correction 
  was 
  seldom 
  as 
  much 
  as 
  one 
  unit 
  in 
  the 
  4th 
  

   place, 
  so 
  that 
  no 
  appreciable 
  error 
  can 
  have 
  occurred 
  in 
  it. 
  

  

  The 
  change 
  of 
  specific 
  heat 
  corresponding 
  to 
  a 
  change 
  

   of 
  the 
  lower 
  temperature 
  to 
  zero 
  was 
  very 
  much 
  larger 
  

   than 
  the 
  above 
  and 
  was 
  determined 
  in 
  accordance 
  with 
  the 
  

   following 
  reckoning: 
  13 
  If 
  M 
  n 
  is 
  the 
  observed 
  interval 
  

   heat, 
  for 
  the 
  temperature 
  interval 
  0, 
  to 
  0«, 
  m 
  1 
  the 
  known 
  

   interval 
  heat 
  from 
  C 
  to 
  U 
  and 
  M. 
  the 
  desired 
  heat 
  for 
  

   the 
  total 
  interval 
  — 
  2 
  , 
  then 
  equating 
  total 
  heats, 
  

  

  M 
  2 
  2 
  = 
  m 
  1 
  1 
  -f 
  M 
  o 
  (0 
  2 
  - 
  0,), 
  whence 
  

   M 
  9 
  = 
  M 
  ~(M 
  -m 
  1 
  )|. 
  

  

  Here 
  repeated 
  from 
  the 
  1909 
  paper, 
  loc. 
  cit., 
  this 
  Journal, 
  28, 
  339. 
  

  

  