﻿538 
  F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  gin 
  of 
  the 
  plot 
  being 
  twice 
  that 
  of 
  1° 
  at 
  the 
  center 
  of 
  the 
  pro- 
  

   jection. 
  .Now 
  in 
  optical 
  work 
  with 
  projections, 
  the 
  principle 
  

   emphasized 
  above, 
  that 
  the 
  relative 
  accuracy 
  of 
  the 
  different 
  

   parts 
  of 
  the 
  plot 
  should 
  be 
  as 
  nearly 
  uniform 
  as 
  possible 
  and 
  

   comparable 
  to 
  that 
  in 
  nature 
  (in 
  this 
  case, 
  the 
  sphere), 
  is 
  of 
  

   prime 
  importance, 
  and 
  for 
  this 
  reason 
  several 
  other 
  projections, 
  

   as 
  the 
  equidistant 
  and 
  the 
  angle 
  projections, 
  which 
  distort 
  less, 
  

   are 
  preferable 
  to 
  the 
  stereographic. 
  An 
  angle 
  meridian 
  pro- 
  

   jection 
  plot, 
  20 
  cm 
  in 
  diameter, 
  was 
  published 
  by 
  the 
  writer 
  in 
  

   1911* 
  and 
  is 
  superior 
  as 
  regards 
  distortion 
  to 
  the 
  other 
  projec- 
  

   tions 
  which 
  have 
  been 
  suggested. 
  The 
  equidistant 
  and 
  angle 
  

   meridian 
  projection 
  plots 
  are 
  very 
  similar 
  in 
  form. 
  The 
  details 
  

   of 
  construction 
  of 
  these 
  projection 
  plots 
  are 
  given 
  in 
  the 
  publi- 
  

   cation 
  referred 
  to 
  and 
  need 
  not 
  be 
  repeated 
  here. 
  

  

  Summary. 
  

  

  The 
  equations 
  which 
  the 
  petrographer 
  has 
  to 
  solve 
  in 
  connection 
  

  

  with 
  his 
  microscopic 
  work 
  are 
  all 
  of 
  the 
  general 
  form, 
  A 
  =B.C, 
  

  

  in 
  which 
  A, 
  B, 
  and 
  (J 
  are 
  variables 
  and 
  usually 
  trigonometric 
  

  

  functions. 
  All 
  equations 
  of 
  this 
  form 
  can 
  be 
  solved 
  graphically 
  

  

  by 
  straight 
  line 
  plots, 
  provided 
  the 
  functions 
  be 
  plotted 
  directly. 
  

  

  The 
  plots 
  are 
  based 
  on 
  the 
  properties 
  of 
  similar 
  triangles 
  and 
  

  

  the 
  fact 
  that 
  the 
  above 
  equation 
  can 
  be 
  written 
  in 
  the 
  form 
  

  

  A 
  C 
  

  

  -^ 
  = 
  — 
  • 
  By 
  thus 
  avoiding 
  curves 
  to 
  represent 
  the 
  different 
  

  

  values 
  of 
  the 
  equation, 
  the 
  observer 
  not 
  only 
  increases 
  the 
  

   accuracy 
  of 
  the 
  results 
  obtained 
  but 
  he 
  can 
  also 
  prepare 
  the 
  

   plots 
  with 
  greater 
  facility 
  and 
  in 
  less 
  time. 
  Although 
  this 
  

   principle 
  is 
  important, 
  regard 
  should 
  also 
  be 
  had 
  for 
  the 
  distor- 
  

   tion 
  introduced, 
  the 
  aim 
  in 
  all 
  graphical 
  solutions 
  being 
  to 
  

   have 
  the 
  relative 
  accuracy 
  over 
  the 
  entire 
  plot 
  as 
  uniform 
  as 
  

   possible. 
  

  

  In 
  case 
  the 
  distortion 
  is 
  great 
  for 
  one 
  form 
  of 
  equation, 
  the 
  

   form 
  may 
  often 
  be 
  changed 
  by 
  introducing 
  some 
  function 
  of 
  

   both 
  sides 
  of 
  the 
  equation, 
  so 
  that 
  the 
  plot 
  becomes 
  more 
  

   nearly 
  uniform. 
  

  

  On 
  these 
  principles 
  Plates 
  II 
  to 
  IX 
  have 
  been 
  drawn. 
  With 
  

   them 
  practically 
  all 
  the 
  equations 
  which 
  the 
  petrographer 
  may 
  

   encounter 
  in 
  his 
  work 
  can 
  be 
  solved 
  graphically. 
  In 
  the 
  fore- 
  

   going 
  pages 
  these 
  plates 
  and 
  methods 
  of 
  solution 
  are 
  discussed 
  

   in 
  detail 
  and 
  illustrated 
  by 
  examples. 
  

  

  In 
  a 
  brief 
  section 
  on 
  projection 
  for 
  use 
  in 
  optical 
  work 
  the 
  

   principle 
  of 
  minimum 
  distortion 
  is 
  emphasized. 
  The 
  angle 
  

   and 
  equidistant 
  projection 
  are 
  found 
  to 
  meet 
  these 
  require- 
  

   ments 
  best 
  and 
  are, 
  therefore, 
  recommended 
  for 
  general 
  use 
  in 
  

   petrographic 
  microscopic 
  work. 
  

  

  * 
  Carnegie 
  Institution 
  of 
  Washington, 
  Pub. 
  158, 
  63-67, 
  and 
  Plate 
  XI, 
  1911. 
  

  

  