﻿4 
  JOURNAL 
  OF 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  1 
  

  

  N- 
  AN.=^ 
  -c'X^"^ 
  ^ 
  de. 
  

  

  Making 
  the 
  same 
  substitution 
  as 
  before 
  for 
  dd, 
  and 
  remembering 
  

  

  10 
  

  

  that 
  A 
  = 
  Ao 
  2o 
  , 
  the 
  integration 
  is 
  simple, 
  and 
  yields 
  

  

  20 
  c^Ao[ho 
  

  

  TV 
  - 
  AiV„ 
  = 
  

  

  In 
  2 
  

  

  Taking 
  the 
  value 
  of 
  ho 
  from 
  this 
  and 
  substituting 
  in 
  the 
  value 
  of 
  t, 
  

   we 
  get 
  

  

  c> 
  

  

  tr 
  = 
  

  

  10 
  C 
  

  

  AN 
  a 
  In 
  2 
  

  

  In 
  

  

  "(N 
  - 
  aN^) 
  In 
  2 
  + 
  40 
  cAo 
  AN^ 
  

   {N- 
  AN,) 
  In 
  2 
  

  

  We 
  shall 
  assume 
  that 
  the 
  original 
  strain 
  in 
  the 
  glass 
  is 
  so 
  large 
  that 
  

  

  1 
  

   its 
  reciprocal 
  is 
  negligible 
  compared 
  with 
  "TT7~ 
  Then 
  by 
  equation 
  

  

  {7c) 
  in 
  the 
  previous 
  communication 
  

  

  1 
  

  

  ^^ 
  Ao 
  AN. 
  

  

  Therefore 
  t^-h 
  tc 
  = 
  

  

  + 
  

  

  10c 
  

  

  AoAN. 
  AA^„ln2 
  

  

  In 
  

  

  XN 
  - 
  ANg) 
  In 
  2 
  + 
  40 
  cAo 
  AN, 
  

   {N 
  - 
  AiVJln2 
  

  

  ] 
  

  

  Partial 
  differentiation 
  with 
  respect 
  to 
  ^4© 
  and 
  AN^ 
  yields 
  two 
  equations 
  

   as 
  conditions 
  for 
  (t, 
  + 
  t^) 
  having 
  a 
  minimum 
  value. 
  After 
  a 
  little 
  

   simplification 
  these 
  take 
  the 
  form 
  

  

  580 
  AN^c'^Ao^ 
  = 
  (AT 
  - 
  AN,) 
  In 
  2 
  + 
  40 
  ANMo 
  

  

  and 
  In 
  

  

  (A^ 
  - 
  ANg) 
  In 
  2 
  + 
  40 
  ANMq 
  

   {N 
  - 
  AA^,)ln2 
  

  

  AA^,ln2 
  

  

  {N 
  - 
  AN,) 
  10 
  cA, 
  

  

  The 
  form 
  of 
  the 
  second 
  equation 
  makes 
  it 
  necessary 
  to 
  use 
  an 
  approxi- 
  

  

  