﻿14 
  W. 
  P. 
  White 
  — 
  Silicate 
  Specific 
  Heats. 
  

  

  urinations, 
  18 
  at 
  500°, 
  nearly 
  3 
  times, 
  and 
  this 
  is 
  the 
  

   possible 
  error 
  of 
  almost 
  any 
  value 
  based 
  on 
  these 
  deter- 
  

   minations. 
  The 
  further 
  error 
  due 
  to 
  inadequacy 
  of 
  a 
  4th 
  

   degree 
  equation 
  is 
  probably 
  small 
  by 
  comparison. 
  

  

  This 
  method 
  evidently 
  does 
  not 
  give 
  results 
  for 
  the 
  

   highest 
  or 
  lowest 
  interval 
  heat 
  in 
  the 
  series, 
  since 
  there 
  

   are 
  not 
  first 
  differences 
  on 
  both 
  sides 
  of 
  these. 
  At 
  the 
  

   lower 
  end 
  of 
  the 
  scale 
  an 
  arbitrary 
  but 
  quite 
  unsubjective 
  

   procedure 
  was 
  adopted 
  to 
  get 
  the 
  true 
  heat. 
  A 
  2nd- 
  

   degree 
  equation 
  was 
  passed 
  through 
  the 
  3 
  lower 
  values, 
  

   a 
  cubic 
  through 
  the 
  lower 
  four, 
  the 
  true 
  heats 
  taken 
  at 
  0°, 
  

   100°, 
  and 
  300° 
  were 
  the 
  means 
  of 
  those 
  obtained 
  from 
  the 
  

   two 
  equations. 
  The 
  uncertainty 
  due 
  to 
  the 
  computation 
  

   is 
  probably 
  under 
  3 
  per 
  mille 
  at 
  100° 
  and 
  300°, 
  perhaps 
  

   6 
  per 
  mille 
  at 
  0°. 
  At 
  the 
  upper 
  end 
  of 
  the 
  scale, 
  where 
  

   the 
  rate 
  of 
  variation 
  is 
  less, 
  a 
  slight 
  extrapolation 
  is 
  not 
  

   out 
  of 
  the 
  question 
  for 
  the 
  present 
  results. 
  At 
  1100° 
  the 
  

   total 
  effect 
  on 
  the 
  true 
  heat 
  of 
  a 
  third 
  difference 
  of 
  the 
  

   interval 
  heat 
  is 
  only 
  about 
  2 
  per 
  mille, 
  so 
  an 
  estimated 
  

   value 
  could 
  be 
  safely 
  used. 
  For 
  the 
  diopside 
  first 
  dif- 
  

   ference 
  from 
  1100° 
  to 
  1350°, 
  a 
  200-degree 
  interval 
  was 
  

   constructed 
  by 
  multiplying 
  the 
  observed 
  difference 
  by 
  

   4/3, 
  and 
  then 
  diminishing 
  this 
  result 
  to 
  fit 
  the 
  hypothesis 
  

   that 
  the 
  3rd 
  difference 
  was 
  constant 
  from 
  900° 
  to 
  1300°. 
  

   The 
  error 
  from 
  the 
  assumption 
  is 
  demonstrably 
  neg- 
  

   ligible, 
  but 
  the 
  effect 
  of 
  the 
  accidental 
  error 
  of 
  the 
  short 
  

   interval 
  is 
  increased. 
  A 
  similar 
  procedure 
  was 
  used 
  in 
  

   getting 
  the 
  three 
  values 
  at 
  1300°. 
  For 
  silica 
  glass 
  at 
  

   900° 
  a 
  value 
  for 
  the 
  difference 
  900°-1100° 
  (namely 
  4370) 
  

   was 
  derived 
  from 
  several 
  silicates 
  whose 
  first 
  differences 
  

   below 
  900° 
  were 
  close 
  to 
  that 
  of 
  silica 
  glass, 
  but 
  in 
  other 
  

   cases 
  it 
  has 
  been 
  regarded 
  as 
  unsatisfactory 
  to 
  attempt 
  

   by 
  extrapolation 
  to 
  get 
  a 
  value 
  of 
  the 
  true 
  heat 
  for 
  the 
  

   highest 
  temperature 
  observed. 
  

  

  The 
  above 
  method, 
  as 
  carried 
  out 
  -in 
  this 
  case, 
  reduces 
  

   the 
  effect 
  of 
  accidental 
  error 
  by 
  basing 
  each 
  final 
  value 
  

   mainly 
  on 
  three 
  original 
  results, 
  covering 
  an 
  interval 
  

   of 
  400°, 
  but 
  this 
  involves 
  assuming 
  the 
  validity 
  of 
  a 
  reg- 
  

   ular 
  law 
  over 
  this 
  wide 
  interval. 
  It 
  is 
  also 
  possible 
  to 
  

   obtain 
  a 
  true 
  heat 
  mainly 
  from 
  two 
  adjacent 
  readings, 
  

   which 
  is 
  thus 
  less 
  dependent 
  on 
  the 
  assumption 
  of 
  a 
  

  

  w 
  This 
  of 
  course 
  implies 
  that 
  all 
  the 
  errors 
  are 
  of 
  the 
  same 
  size 
  and 
  that 
  

   their 
  signs 
  are 
  distributed 
  in 
  a 
  certain 
  one, 
  out 
  of 
  32 
  different 
  ways. 
  But 
  

   an 
  error 
  nearly 
  as 
  large 
  might 
  occur 
  1 
  time 
  in 
  8. 
  

  

  