﻿JAN. 
  4, 
  1922 
  WII.LIAMSON: 
  ANNEALING 
  OF 
  GI^ASS 
  5 
  

  

  mate 
  solution. 
  A 
  sufficiently 
  close 
  one 
  is 
  

  

  cAo 
  = 
  0.075 
  

   A^^ 
  = 
  0.725 
  N. 
  

  

  If, 
  then, 
  we 
  know 
  c, 
  the 
  constant 
  which 
  depends 
  on 
  the 
  elastic 
  prop- 
  

   erties 
  of 
  the 
  glass, 
  and 
  have 
  a 
  table 
  like 
  table 
  3 
  in 
  the 
  older 
  paper 
  

   showing 
  the 
  values 
  of 
  A 
  for 
  various 
  temperatures, 
  the 
  required 
  prob- 
  

   lem 
  is 
  completely 
  solved 
  and 
  one 
  can 
  say 
  definitely 
  that 
  the 
  glass 
  

   must 
  be 
  held 
  a 
  certain 
  temperature 
  for 
  a 
  certain 
  time 
  and 
  be 
  cooled 
  

   at 
  a 
  predetermined 
  rate 
  at 
  every 
  instant 
  of 
  its 
  cooling 
  in 
  order 
  that 
  

   the 
  necessary 
  conditions 
  may 
  be 
  fulfilled. 
  

   The 
  total 
  time 
  necessary 
  for 
  the 
  process 
  is 
  

  

  re 
  c 
  

  

  + 
  ^ 
  ^, 
  ^^^ 
  . 
  =66.9-- 
  

  

  0.075X0.725 
  A 
  0.075X0.275 
  A 
  N 
  

  

  In 
  computing 
  this 
  the 
  value 
  of 
  tc 
  was 
  simplified 
  by 
  means 
  of 
  the 
  second 
  

   conditional 
  equation. 
  

  

  As 
  an 
  illustration 
  the 
  case 
  of 
  a 
  slab 
  of 
  plate 
  glass 
  2 
  cm. 
  thick 
  will 
  

   be 
  treated. 
  This 
  is 
  the 
  same 
  example 
  that 
  was 
  previously 
  used 
  to 
  

   illustrate 
  four 
  different 
  procedures. 
  In 
  this 
  case 
  c 
  is 
  about 
  13 
  and 
  

  

  0.075 
  

  

  we 
  shall 
  suppose 
  A 
  = 
  5 
  as 
  in 
  the 
  older 
  work. 
  Then 
  Ao 
  = 
  

  

  13 
  

  

  0.0058, 
  and 
  reference 
  to 
  figure 
  12, 
  in 
  the 
  original, 
  places 
  this 
  at 
  about 
  

   520° 
  C, 
  which 
  is 
  6° 
  higher 
  than 
  in 
  the 
  fastest 
  previous 
  schedule. 
  

   ANa 
  will 
  be 
  equal 
  to 
  3.625. 
  The 
  glass 
  must 
  be 
  held 
  at 
  this 
  temperature 
  

  

  for 
  = 
  47 
  . 
  6 
  minutes, 
  and 
  the 
  total 
  time 
  will 
  be 
  174 
  

  

  0.0058X3.625 
  

  

  minutes 
  or 
  a 
  little 
  better 
  than 
  15 
  per 
  cent 
  less 
  than 
  in 
  the 
  best 
  previous 
  

   schedule. 
  

  

  ^, 
  ..,.,, 
  , 
  1-7 
  (iV- 
  ANJ\n2 
  + 
  20cAo 
  AN, 
  

  

  The 
  initial 
  rate 
  of 
  cooling 
  ho 
  = 
  ^ 
  

  

  20 
  c~Ao 
  

  

  = 
  (in 
  this 
  case) 
  0.33° 
  per 
  minute. 
  The 
  table 
  shows 
  how 
  that 
  rate 
  

   increases 
  as 
  the 
  temperature 
  drops. 
  

  

  We 
  have 
  been 
  asked 
  recently 
  how 
  long 
  a 
  time 
  is 
  necessary 
  for 
  an- 
  

   nealing 
  a 
  sheet 
  of 
  glass 
  25 
  feet 
  in 
  diameter 
  and 
  2 
  feet 
  thick. 
  If 
  the 
  

   glass 
  be 
  one 
  for 
  which 
  the 
  constants 
  are 
  known 
  the 
  question 
  can 
  be 
  

   easily 
  answered. 
  Suppose 
  the 
  glass 
  is 
  of 
  the 
  same 
  type 
  as 
  in 
  the 
  

   previous 
  example, 
  then 
  c 
  will 
  be 
  approximately 
  13 
  X 
  30". 
  The 
  final 
  

  

  