﻿JAN. 
  4, 
  1922 
  

  

  WILLIAMSON 
  : 
  ANNEALING 
  OF 
  GLASS 
  

  

  possible 
  under 
  the 
  conditions 
  of 
  the 
  problem. 
  An 
  example 
  of 
  how 
  

   the 
  cooling 
  rate 
  changes 
  is 
  found 
  in 
  table 
  1. 
  

  

  The 
  problem 
  may 
  now 
  be 
  restated. 
  t^ 
  is 
  a 
  function 
  of 
  ^o 
  and 
  ^N^, 
  

   and 
  t^ 
  can 
  also 
  be 
  expressed 
  in 
  terms 
  of 
  these 
  by 
  means 
  of 
  equation 
  (1) 
  

   and 
  the 
  proper 
  value 
  of 
  ho 
  , 
  that 
  is, 
  provided 
  the 
  necessary 
  integrations 
  

   can 
  be 
  carried 
  out. 
  Can 
  values 
  of 
  Ao 
  and 
  AN^ 
  be 
  chosen 
  so 
  that 
  

   {io 
  + 
  ^c) 
  iii^y 
  t)e 
  a 
  minimum? 
  

  

  Now/,= 
  -- 
  

  

  huth^ 
  

  

  ANJ 
  

  

  {'■-'¥) 
  

  

  10 
  

  

  From 
  the 
  latter, 
  taking 
  the 
  logarithm 
  of 
  each 
  side 
  and 
  differentiating 
  

  

  20hdh 
  

  

  dd= 
  - 
  

  

  (--'-f) 
  

  

  In 
  2 
  

  

  Therefore 
  L 
  = 
  

  

  20 
  

  

  dh 
  

  

  10 
  c 
  

  

  ln2\ 
  _AiV„ 
  

  

  ANJn2 
  

  

  In 
  

  

  ho 
  

  

  h 
  + 
  

  

  AN. 
  

  

  In 
  actual 
  practice 
  the 
  cooling 
  proceeds 
  over 
  a 
  range 
  of 
  several 
  hundred 
  

   degrees. 
  By 
  this 
  time 
  h 
  is 
  large 
  compared 
  with 
  ANJc 
  so 
  that 
  the 
  

   upper 
  limit 
  of 
  the 
  integral 
  may 
  be 
  taken 
  as 
  containing 
  In 
  1 
  and 
  hence 
  

   is 
  zero. 
  

  

  The 
  result 
  therefore 
  is 
  

  

  t 
  = 
  

  

  10c 
  

  

  he 
  

  

  AN^ 
  In 
  2 
  

  

  In 
  

  

  c 
  

  

  ho 
  — 
  — 
  

   c 
  

  

  in 
  which 
  ho 
  has 
  yet 
  to 
  be 
  determined 
  by 
  the 
  condition 
  

  

  V 
  

  

  