﻿2 
  JOURNAL 
  OF 
  the; 
  WASHINGTON 
  ACADEMY 
  OF 
  SClENCEvS 
  VOL. 
  12, 
  NO. 
  1 
  

  

  /i 
  = 
  cooling 
  rate 
  in 
  degrees 
  per 
  minute. 
  

  

  ho 
  = 
  initial 
  cooling 
  rate 
  at 
  60 
  . 
  

  

  A/^ 
  = 
  total 
  strain 
  allowable 
  in 
  optical 
  units. 
  

  

  AA^a 
  = 
  strain 
  left 
  in 
  glass 
  after 
  holding 
  at 
  do. 
  

  

  AA/^c 
  = 
  strain 
  introduced 
  by 
  temperature 
  differences 
  in 
  cooling. 
  

  

  /a 
  = 
  annealing 
  time 
  = 
  time 
  the 
  glass 
  is 
  held 
  at 
  60. 
  

  

  /c 
  = 
  time 
  spent 
  in 
  cooling. 
  

  

  A 
  = 
  annealing 
  constant 
  as 
  found 
  in 
  table 
  3, 
  op. 
  cit. 
  

  

  Ao 
  = 
  value 
  of 
  A 
  at 
  60. 
  

  

  c 
  = 
  constant, 
  depending 
  on 
  the 
  type 
  of 
  glass, 
  defined 
  by 
  equation 
  

   (10), 
  page 
  841, 
  op. 
  cit. 
  

  

  The 
  last 
  part 
  of 
  the 
  problem 
  will 
  be 
  solved 
  first. 
  That 
  is, 
  if 
  the 
  

   glass 
  has 
  been 
  held 
  at 
  do 
  till 
  the 
  strain 
  is 
  reduced 
  to 
  AN^ 
  how 
  must 
  

   it 
  be 
  cooled 
  so 
  that 
  t^ 
  may 
  be 
  a 
  minimum 
  consistent 
  with 
  the 
  final 
  

   strain 
  being 
  A'', 
  or 
  in 
  other 
  words, 
  having 
  ANc 
  = 
  N— 
  AN 
  J 
  

  

  tc= 
  -\ 
  —r- 
  and 
  A^ 
  - 
  AN^ 
  = 
  AAT, 
  = 
  -cM 
  A 
  

  

  J 
  w 
  ^ 
  h 
  

  

  the 
  latter 
  being 
  the 
  integral 
  of 
  equation 
  12 
  in 
  the 
  previous 
  paper 
  

   which 
  depends 
  on 
  the 
  experimental 
  results 
  set 
  forth 
  there. 
  Applying 
  

   the 
  calculus 
  of 
  variations 
  to 
  find 
  /j 
  as 
  a 
  function 
  of 
  d 
  yields 
  

  

  const 
  — 
  ( 
  — 
  

   6h\h 
  

  

  h'--^\^ 
  constant 
  = 
  Ao 
  Uo 
  ' 
  - 
  —^ 
  j 
  (1) 
  

  

  Now 
  it 
  is 
  shown 
  in 
  the 
  previous 
  paper 
  that 
  

  

  e 
  -0o 
  

  

  A=Ao.2 
  

  

  10 
  

  

  Therefore 
  (/.- 
  ^'U 
  (^/.o-^^^ 
  2 
  ^'. 
  

  

  (• 
  

  

  c' 
  J 
  V 
  c' 
  

  

  Equation 
  (1) 
  shows 
  how 
  the 
  rate 
  may 
  be 
  increased 
  as 
  the 
  temperature 
  

   drops, 
  and 
  ho, 
  the 
  initial 
  rate, 
  may 
  be 
  found 
  by 
  the 
  condition 
  that 
  

   ANc 
  = 
  N— 
  AN^. 
  The 
  time 
  consumed 
  will 
  then 
  be 
  the 
  minimum 
  

  

  