﻿514 
  F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  The 
  position 
  of 
  this 
  line 
  can 
  be 
  readily 
  ascertained 
  by 
  assum- 
  

   ing 
  first 
  that 
  

  

  log 
  B 
  = 
  then 
  

  

  log 
  A 
  = 
  log 
  C. 
  

  

  These 
  two 
  equations 
  represent 
  the 
  line 
  OjQ. 
  If 
  now 
  we 
  

   assume 
  that 
  

  

  log 
  C 
  = 
  then 
  

  

  log 
  A 
  = 
  log 
  B. 
  

  

  The 
  last 
  two 
  equations 
  represent 
  the 
  straight 
  line 
  2 
  P. 
  

  

  Since 
  the 
  value 
  log 
  A 
  is 
  common 
  to 
  both 
  lines 
  it 
  is 
  at 
  their 
  

   intersection 
  and 
  the 
  vertical 
  line 
  3 
  passes 
  through 
  the 
  point 
  

   thus 
  found. 
  This 
  construction 
  holds 
  good 
  for 
  any 
  two 
  values 
  

   of 
  log 
  B 
  and 
  log 
  O, 
  whose 
  sum 
  is 
  equal 
  to 
  log 
  A. 
  In 
  case 
  the 
  

   scales 
  of 
  log 
  B 
  and 
  log 
  G 
  are 
  of 
  the 
  same 
  unit, 
  then 
  the 
  line 
  

   3 
  K 
  is 
  located 
  midway 
  between 
  O 
  a 
  M 
  and 
  0,N 
  and 
  the 
  scale 
  

   of 
  log 
  A 
  is 
  half 
  that 
  of 
  log 
  B, 
  and 
  of 
  log 
  C* 
  

  

  On 
  applying 
  this 
  method 
  of 
  plotting 
  to 
  some 
  of 
  the 
  equa- 
  

   tions 
  above, 
  notably 
  the 
  refractive 
  index 
  equation 
  1 
  and 
  the 
  

   transformation 
  equation, 
  sin 
  A 
  = 
  sin 
  B 
  sin 
  C, 
  I 
  have 
  found 
  

   that 
  the 
  distortion 
  in 
  the 
  logarithmic 
  trigonometric 
  functions 
  

   is 
  so 
  great 
  that 
  it 
  renders 
  this 
  general 
  method 
  of 
  little 
  value 
  in 
  

   the 
  graphical 
  solution 
  of 
  trigonometric 
  formulas. 
  The 
  first 
  

   methods 
  outlined 
  above 
  are, 
  therefore, 
  better 
  adapted 
  for 
  the 
  

   purpose. 
  The 
  logarithmic 
  principle 
  is, 
  however, 
  invaluable 
  in 
  

   certain 
  problems 
  ; 
  on 
  it 
  the 
  slide 
  rule 
  is 
  based. 
  

  

  Refractive 
  index 
  formula. 
  — 
  Plates 
  II, 
  III, 
  and 
  IV 
  are 
  

   given 
  to 
  illustrate 
  how 
  the 
  same 
  equation 
  can 
  be 
  treated 
  so 
  

   that 
  the 
  relative 
  accuracy 
  of 
  different 
  parts 
  of 
  the 
  plot 
  is 
  

  

  greatly 
  changed. 
  Plate 
  II 
  is 
  based 
  on 
  the 
  formula 
  = 
  

  

  (fig. 
  4a), 
  Plate 
  III, 
  on 
  the 
  equation 
  — 
  = 
  (fig. 
  4b) 
  and 
  

  

  n 
  i 
  

  

  sin^ 
  i 
  

   Plate 
  IV, 
  on 
  the 
  equation 
  -7-5 
  — 
  = 
  — 
  (fig. 
  4c). 
  

  

  It 
  is 
  of 
  interest 
  to 
  note 
  that, 
  in 
  Plate 
  II, 
  the 
  distance 
  between 
  

   i 
  = 
  0° 
  and 
  i 
  = 
  5° 
  is 
  larger 
  than 
  that 
  of 
  any 
  other 
  5° 
  interval, 
  

   while 
  the 
  distance 
  between 
  i 
  = 
  85° 
  and 
  i 
  = 
  90° 
  is 
  so 
  small 
  

   that 
  the 
  intervening 
  degrees 
  cannot 
  be 
  properly 
  represented 
  

   on 
  the 
  diagram. 
  In 
  Plate 
  III, 
  on 
  the 
  other 
  hand, 
  the 
  distance 
  

   between 
  successive 
  degrees 
  in 
  the 
  lower 
  part 
  of 
  the 
  projection 
  

  

  * 
  The 
  general 
  principles, 
  on 
  which 
  this 
  construction 
  is 
  based, 
  are 
  discussed 
  

   at 
  length 
  by 
  C. 
  Eunge, 
  in 
  Graphical 
  Methods, 
  p. 
  88-92, 
  1912. 
  

  

  