﻿12 
  W. 
  P. 
  White 
  — 
  Silicate 
  Specific 
  Heats. 
  

  

  This 
  formula 
  is 
  well 
  adapted 
  for 
  computation 
  ; 
  m. 
  1 
  was 
  

   determined 
  from 
  the 
  values 
  for 
  0-100,° 
  0-300°, 
  0-500°, 
  by 
  

   assuming 
  that 
  a 
  quadratic 
  equation 
  in 
  represented 
  the 
  

   interval 
  specific 
  heat 
  from 
  0° 
  to 
  500°. 
  The 
  required 
  

   equation 
  must 
  of 
  course 
  be 
  satisfied 
  by 
  the 
  values 
  which 
  

   result 
  from 
  its 
  application 
  to 
  the 
  experimental 
  values; 
  

   it 
  was 
  very 
  easily 
  reached 
  by 
  a 
  process 
  of 
  successive 
  

   approximation. 
  As 
  to 
  the 
  possible 
  error 
  resulting 
  from 
  

   the 
  assumption 
  of 
  a 
  quadratic 
  relation, 
  if 
  we 
  instead 
  

   assume, 
  first, 
  that 
  all 
  the 
  curvature 
  is 
  above 
  300°, 
  and 
  

   second, 
  that 
  all 
  is 
  below 
  300°, 
  the 
  resulting 
  difference 
  in 
  

   the 
  final 
  value 
  for 
  0° 
  — 
  100° 
  is 
  in 
  each 
  case 
  about 
  6 
  units 
  

   in 
  the 
  last 
  place 
  (though 
  of 
  opposite 
  sign 
  in 
  the 
  two 
  cases) 
  

   and 
  is 
  much 
  less 
  at 
  higher 
  temperatures. 
  The 
  error 
  from 
  

   the 
  reduction 
  is 
  therefore 
  almost 
  certainly 
  negligible 
  

   above 
  100° 
  and 
  probably 
  there 
  also. 
  14 
  

  

  The 
  true 
  specific 
  heats 
  were, 
  in 
  an 
  earlier 
  research, 
  

   obtained 
  by 
  a 
  graphic 
  method 
  15 
  which 
  involved 
  drawing 
  a 
  

   tangent 
  to 
  the 
  plotted 
  curve 
  of 
  interval 
  heats. 
  It 
  seemed 
  

   possible 
  to 
  improve 
  this 
  method 
  by 
  drawing 
  chords 
  

   instead 
  of 
  a 
  tangent, 
  but 
  this 
  scheme 
  proved 
  to 
  be 
  merely 
  

   a 
  graphic 
  way 
  of 
  differencing 
  the 
  original 
  values, 
  so 
  that 
  

   the 
  end 
  could 
  be 
  obtained 
  more 
  easily 
  and 
  directly 
  as 
  fol- 
  

   lows: 
  If 
  the 
  interval 
  specific 
  heat 
  is 
  sufficiently 
  well 
  

   expressed 
  by 
  polynomial 
  equations 
  with 
  5 
  constants, 
  

   A 
  + 
  B0 
  + 
  C0 
  2 
  , 
  etc., 
  where 
  is 
  Centigrade 
  temperature, 
  the 
  

   total 
  heat 
  from 
  0°C 
  up 
  is 
  AO 
  + 
  BO 
  2 
  + 
  CO 
  3 
  , 
  etc., 
  and 
  the 
  

   true 
  specific 
  heat 
  at 
  anv 
  temperature, 
  which 
  is 
  the 
  differ- 
  

   ential 
  of 
  the 
  total 
  heat", 
  is 
  16 
  A 
  + 
  2B0 
  + 
  3C# 
  2 
  etc., 
  so 
  that 
  

   the 
  quantity 
  which 
  must 
  be 
  added 
  to 
  the 
  mean 
  specific 
  

   heat 
  to 
  get 
  the 
  true 
  heat 
  is 
  : 
  

  

  B0 
  + 
  2C0 
  2 
  + 
  3D6> 
  s 
  -f4E0\ 
  

  

  But 
  in 
  a 
  series 
  of 
  4th 
  degree 
  polynomials 
  each 
  first 
  

   difference 
  is 
  : 
  

  

  BP 
  + 
  2CP0 
  -1- 
  DP(30 
  2 
  + 
  ^) 
  + 
  EP(46> 
  3 
  + 
  0P 
  2 
  ) 
  ; 
  

  

  14 
  The 
  values 
  can 
  also 
  very 
  easily 
  be 
  adjusted 
  back 
  to 
  a 
  lower 
  temperature 
  

   of 
  20°, 
  by 
  using 
  the 
  same 
  quadratic 
  again, 
  when 
  the 
  remaining 
  error 
  will 
  

   certainly 
  be 
  quite 
  insignificant. 
  

  

  "Walter 
  P. 
  White, 
  this 
  Journal, 
  28, 
  341, 
  1909, 
  op. 
  cit. 
  Also 
  used 
  in 
  

   1909 
  by 
  A. 
  Dumas, 
  Chaleur 
  Specifique 
  des 
  Substances 
  Ferromagnetiques, 
  

   Arch. 
  Sci. 
  Phys. 
  et 
  Nat., 
  27, 
  460. 
  

  

  10 
  Mr. 
  P. 
  D. 
  Foote 
  has 
  kindly 
  called 
  my 
  attention 
  to 
  an 
  error 
  in 
  my 
  former 
  

   paper 
  where 
  I 
  gave 
  this 
  formula 
  as 
  the 
  one 
  for 
  reducing 
  true 
  specific 
  heat 
  

   to 
  interval 
  specific 
  heat. 
  As 
  the 
  relation 
  is 
  simple 
  and 
  well 
  known 
  I 
  may 
  

   hope 
  that 
  my 
  slip 
  has 
  done 
  little 
  harm. 
  

  

  