﻿540 
  Wright 
  — 
  Graphical 
  Plot 
  for 
  Use 
  in 
  Microscopical 
  

  

  Art. 
  XLYII. 
  — 
  A 
  Graphical 
  Plot 
  for 
  Use 
  in 
  the 
  Microscop- 
  

   ical 
  Dete?*?ninatio?i 
  of 
  the 
  Plagioclase 
  Feldspars 
  ; 
  by 
  

   Fred. 
  Eugene 
  Wright. 
  With 
  Plate 
  X. 
  

  

  In 
  1901 
  the 
  writer 
  plotted 
  on 
  a 
  small 
  sheet 
  (12 
  cm 
  x 
  30 
  cm 
  ) 
  of 
  

   millimeter 
  cross 
  section 
  paper 
  the 
  most 
  important 
  optical 
  

   properties 
  of 
  the 
  plagioclase 
  feldspars 
  together 
  with 
  their 
  

   chemical 
  composition. 
  Blue 
  prints 
  of 
  this 
  sheet 
  were 
  used 
  by 
  

   his 
  students 
  at 
  the 
  Michigan 
  College 
  of 
  Mines 
  and 
  later 
  by 
  

   some 
  of 
  the 
  members 
  of 
  the 
  Federal 
  Geological 
  Survey. 
  The 
  

   suggestion 
  has 
  been 
  made 
  at 
  different 
  times 
  that 
  the 
  plot 
  be 
  

   published, 
  but 
  this 
  has 
  been 
  postponed 
  from 
  time 
  to 
  time, 
  

   chiefly 
  in 
  the 
  hope 
  of 
  adding 
  to 
  the 
  data 
  of 
  measurement 
  on 
  the 
  

   plagioclases. 
  It 
  has 
  now 
  been 
  decided 
  to 
  delay 
  no 
  longer 
  but 
  

   to 
  revise 
  the 
  table 
  so 
  far 
  as 
  possible 
  with 
  the 
  best 
  existing 
  data, 
  

   and 
  to 
  publish 
  it 
  even 
  though 
  it 
  is 
  not 
  equally 
  correct 
  in 
  all 
  

   particulars. 
  The 
  effort 
  has 
  been 
  made 
  to 
  give 
  only 
  the 
  more 
  

   important 
  data, 
  which 
  the 
  working 
  microscopist 
  actually 
  needs. 
  

  

  On 
  Plate 
  X 
  there 
  are 
  represented 
  graphically 
  : 
  

  

  Curves 
  1. 
  The 
  chemical 
  composition 
  of 
  the 
  plagioclases. 
  

  

  Curve 
  2. 
  A 
  curve 
  showing 
  the 
  relation 
  between 
  chemical 
  

   composition 
  and 
  molecular 
  proportions. 
  The 
  use 
  of 
  this 
  curve 
  

   may 
  be 
  illustrated 
  by 
  an 
  example 
  : 
  Find 
  the 
  molecular 
  per- 
  

   centage 
  of 
  anorthite 
  which 
  the 
  feldspar 
  Ab 
  2 
  An 
  x 
  contains. 
  

   This 
  is 
  indicated 
  on 
  curve 
  2 
  at 
  the 
  point 
  33*3 
  where 
  the 
  

   horizontal 
  line 
  through 
  the 
  ordinate 
  2 
  cuts 
  the 
  curve. 
  Curve 
  

   2a 
  is 
  similar 
  to 
  curve 
  2 
  except 
  that 
  the 
  unit 
  of 
  its 
  vertical 
  

   scale 
  is 
  ten 
  times 
  greater. 
  Both 
  curves 
  are 
  parabolas. 
  Similar 
  

   parabolic 
  curves 
  result 
  when, 
  instead 
  of 
  the 
  molecular 
  percent- 
  

   ages 
  of 
  the 
  two 
  end 
  members, 
  the 
  weight 
  percentages 
  are 
  

   plotted. 
  

  

  The 
  derivation 
  of 
  the 
  equation 
  for 
  the 
  molecular 
  proportion 
  

   curves 
  is 
  simple. 
  Thus 
  to 
  find 
  the 
  percentage 
  corresponding 
  

   to 
  the 
  molecular 
  proportions 
  Ab^Au^ 
  we 
  note 
  that 
  in 
  the 
  sub- 
  

   stance 
  there 
  are 
  x 
  molecules 
  of 
  Ab 
  to 
  every 
  molecule 
  of 
  An. 
  

   The 
  ratio 
  of 
  one 
  An 
  molecule 
  to 
  the 
  complete 
  molecule 
  

  

  is 
  evidently:, 
  . 
  The 
  percentage 
  composition 
  is, 
  therefore, 
  

  

  JL 
  "t" 
  tL> 
  

  

  100 
  

  

  y 
  ~ 
  T~+x 
  

  

  Similarly, 
  if 
  we 
  wish 
  to 
  express 
  the 
  weight 
  percentage 
  of 
  

   An 
  in 
  the 
  plagioclase 
  Ab^An^ 
  we 
  note 
  that 
  if 
  the 
  molecular 
  

   weight 
  of 
  An 
  be 
  m 
  n 
  that 
  of 
  Ab, 
  m„ 
  then 
  the 
  total 
  weight 
  of 
  

   the 
  composition 
  Ab^A^ 
  is 
  x.n\ 
  + 
  l.m, 
  and 
  the 
  percentage 
  

   composition 
  is 
  

  

  