﻿JOURNAL 
  

  

  OF 
  THE 
  

  

  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  

  

  Vol. 
  12 
  January 
  4, 
  1922 
  No. 
  1 
  

  

  MATHEMATICS. 
  — 
  A 
  mathematical 
  note 
  on 
  the 
  annealing 
  of 
  glass. 
  '^ 
  

   B. 
  D. 
  Williamson, 
  Geophysical 
  Laboratory, 
  Carnegie 
  Insti- 
  

   tution 
  of 
  Washington. 
  

  

  In 
  a 
  recent 
  paper^ 
  Adams 
  and 
  Williamson 
  have 
  discussed 
  at 
  some 
  

   length 
  the 
  annealing 
  of 
  glass. 
  It 
  is 
  not 
  the 
  object 
  of 
  the 
  present 
  note 
  

   to 
  revise 
  the 
  deductions 
  made 
  from 
  the 
  experimental 
  data 
  but 
  rather 
  

   to 
  show 
  how 
  the 
  mathematical 
  treatment 
  of 
  the 
  equations 
  represent- 
  

   ing 
  these 
  deducticns 
  may 
  be 
  made 
  more 
  rigorous. 
  The 
  immediate 
  

   practical 
  aim 
  is 
  to 
  discover 
  whether 
  this 
  course 
  will 
  indicate 
  a 
  possible 
  

   procedure 
  by 
  which 
  the 
  time 
  spent 
  in 
  the 
  annealing 
  process 
  can 
  be 
  

   materially 
  shortened. 
  We 
  shall 
  anticipate 
  by 
  saying 
  that 
  this 
  is 
  

   found 
  to 
  be 
  the 
  case 
  and 
  a 
  fifteen 
  per 
  cent 
  reduction 
  of 
  time 
  can 
  be 
  

   made. 
  A 
  future 
  communication 
  will 
  give 
  detailed 
  schedules 
  for 
  va- 
  

   ious 
  types 
  of 
  glass 
  on 
  this 
  new 
  basis. 
  

  

  The 
  problem 
  to 
  be 
  solved 
  may 
  be 
  stated 
  as 
  follows. 
  A 
  block 
  of 
  

   glass 
  is 
  found 
  to 
  be 
  in 
  a 
  condition 
  of 
  internal 
  strain. 
  By 
  holding 
  it 
  

   at 
  a 
  temperature 
  somewhat 
  below 
  the 
  softening 
  point 
  the 
  strain 
  may 
  

   be 
  removed 
  at 
  a 
  rate 
  depending 
  on 
  that 
  temperature. 
  Further 
  strain 
  

   will 
  be 
  added 
  during 
  the 
  cooling 
  process 
  due 
  to 
  temperature 
  differences 
  

   set 
  up 
  in 
  cooling. 
  It 
  is 
  required 
  to 
  find 
  at 
  what 
  temperature 
  to 
  hold 
  

   the 
  glass, 
  how 
  long 
  to 
  hold 
  it 
  at 
  that 
  temperature 
  (or, 
  what 
  is 
  the 
  

   same 
  thing, 
  to 
  what 
  degree 
  of 
  completeness 
  to 
  remove 
  the 
  strain) 
  

   and 
  how 
  rapidly 
  to 
  cool 
  at 
  every 
  point 
  in 
  the 
  course 
  of 
  cooling 
  so 
  that 
  

   the 
  least 
  possible 
  time 
  be 
  taken 
  consistent 
  with 
  the 
  final 
  strain 
  being 
  

   inside 
  the 
  allowable 
  limits. 
  

  

  The 
  notation 
  used 
  is 
  that 
  of 
  the 
  paper 
  already 
  cited. 
  

  

  ^ 
  = 
  temperature 
  in 
  degrees 
  Centigrade. 
  

  

  do 
  = 
  temperature 
  at 
  which 
  glass 
  is 
  held 
  to 
  remove 
  strain. 
  

  

  * 
  Received 
  November 
  15, 
  192L 
  

  

  * 
  L. 
  H. 
  Adams 
  and 
  E. 
  D. 
  Wiluamson. 
  Journ. 
  Franklin 
  Inst. 
  190: 
  597-631; 
  835-870. 
  

   1920. 
  

  

  