﻿1 
  1 
  

  

  — 
  + 
  — 
  

  

  a 
  7 
  

  

  1 
  1 
  

  

  — 
  + 
  — 
  

   a 
  y 
  

  

  528 
  F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  cos 
  (d 
  + 
  #') 
  (21) 
  

  

  V") 
  cos 
  (#*-#') 
  (22) 
  

  

  The 
  computations 
  required 
  for 
  the 
  solution 
  of 
  these 
  equa- 
  

   tions 
  can 
  be 
  readily 
  made 
  by 
  use 
  of 
  Table 
  II 
  and 
  Plate 
  YI. 
  The 
  

  

  values 
  

  

  and 
  

  

  can 
  be 
  derived 
  

   1/1 
  1 
  \. 
  

  

  from 
  the 
  data 
  of 
  Table 
  II, 
  and 
  the 
  value 
  of 
  

  

  2 
  \ 
  a 
  7 
  

  

  cos 
  (■& 
  — 
  #') 
  can 
  then 
  be 
  read 
  off 
  directly 
  from 
  Plate 
  Y, 
  for 
  

   this 
  expression 
  can 
  be 
  written 
  

  

  1/1 
  1 
  

  

  x 
  T 
  

  

  sin 
  [90 
  - 
  (3 
  - 
  i>')] 
  

  

  (23) 
  

  

  The 
  solution 
  of 
  this 
  equation 
  by 
  Plate 
  Y 
  is 
  indicated 
  in 
  fig. 
  5, 
  

   the 
  principle 
  involved 
  being 
  identical 
  with 
  that 
  of 
  the 
  preced- 
  

  

  Fig. 
  5. 
  

  

  sin[9CM£Hy 
  

  

  ing 
  methods. 
  The 
  numerical 
  value 
  of 
  the 
  right-hand 
  side 
  of 
  

   equation 
  (21) 
  having 
  been 
  thus 
  obtained, 
  the 
  value 
  of 
  a' 
  can 
  be 
  

   read 
  off 
  directly 
  from 
  Table 
  II. 
  Similarly 
  we 
  find 
  the 
  value 
  

   of 
  7 
  ; 
  . 
  The 
  difference, 
  <y' 
  — 
  a', 
  is 
  then 
  the 
  correct 
  measure 
  of 
  

   the 
  birefringence 
  for 
  the 
  given 
  section. 
  In 
  minerals 
  of 
  weak 
  

   birefringence 
  this 
  result 
  is 
  not 
  sensibly 
  different 
  from 
  that 
  

   derived 
  directly 
  from 
  the 
  simpler 
  equation 
  4. 
  But 
  in 
  more 
  

   strongly 
  birefracting 
  substances, 
  this 
  difference 
  between 
  the 
  

   two 
  results 
  is 
  perceptible 
  and 
  for 
  accurate 
  work 
  equations 
  21 
  

   and 
  22 
  should 
  be 
  used. 
  

  

  