﻿F. 
  F. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  509 
  

  

  Art. 
  XLYI. 
  — 
  Graphical 
  Methods 
  in 
  Microscopical 
  Petrog- 
  

   raphy 
  • 
  by 
  Fred. 
  Eugene 
  Wright. 
  With 
  Plates 
  II 
  to 
  IX. 
  

  

  Problems 
  can 
  be 
  solved, 
  and 
  relations 
  between 
  data 
  of 
  

   observation 
  can 
  be 
  represented 
  either 
  by 
  analytical 
  methods 
  

   or 
  by 
  graphical 
  plots. 
  Analytical 
  processes, 
  involving 
  ex- 
  

   tended 
  computations, 
  are 
  often 
  cumbersome, 
  but 
  they 
  must 
  be 
  

   used 
  wherever 
  exact 
  results 
  are 
  required. 
  Graphical 
  methods 
  

   of 
  solution 
  and 
  representation, 
  on 
  the 
  other 
  hand, 
  are 
  usually 
  

   easy 
  to 
  apply 
  and 
  frequently 
  aid 
  the 
  observer 
  in 
  obtaining 
  a 
  

   clear 
  picture 
  of 
  the 
  relations 
  which 
  underlie 
  some 
  problem, 
  

   particularly 
  if 
  geometrical 
  conceptions 
  of 
  space 
  be 
  involved. 
  

   They 
  are, 
  therefore, 
  preferable 
  to 
  analytical 
  methods 
  in 
  all 
  

   problems 
  in 
  which 
  a 
  high 
  degree 
  of 
  accuracy 
  is 
  not 
  required 
  

   or 
  possible. 
  They 
  may 
  also 
  serve 
  to 
  verify 
  the 
  results 
  of 
  com- 
  

   putation. 
  

  

  In 
  geology 
  and 
  microscopical 
  petrography 
  the 
  data 
  obtained 
  

   by 
  measurement 
  are 
  not 
  usually 
  of 
  such 
  a 
  high 
  degree 
  of 
  pre- 
  

   cision 
  that 
  analytical 
  methods 
  of 
  exact 
  computation 
  are 
  neces- 
  

   sary 
  ; 
  experience 
  has 
  shown 
  that 
  the 
  results 
  furnished 
  by 
  

   graphical 
  means 
  are, 
  as 
  a 
  rule, 
  sufficiently 
  accurate 
  and 
  in 
  

   accord 
  with 
  the 
  quality 
  of 
  the 
  observational 
  data. 
  Graphical 
  

   methods 
  have, 
  therefore, 
  been 
  generally 
  adopted 
  by 
  petrolo- 
  

   gists 
  and 
  geologists 
  in 
  recent 
  years 
  in 
  place 
  of 
  analytical 
  

   methods. 
  Geologists 
  and 
  petrologists 
  have, 
  moreover, 
  daily 
  to 
  

   do 
  with 
  maps 
  and 
  are 
  trained 
  to 
  picture 
  and 
  to 
  interpret 
  

   spacial 
  relations 
  from 
  flat 
  surface 
  representations. 
  

  

  In 
  microscopical 
  petrography 
  graphical 
  methods 
  serve 
  three 
  

   purposes 
  : 
  (1) 
  to 
  solve 
  certain 
  equations, 
  (2) 
  to 
  represent 
  data 
  

   of 
  observation 
  and 
  (3) 
  to 
  picture 
  certain 
  important 
  crystallo- 
  

   graphic 
  and 
  optical 
  relations. 
  

  

  In 
  all 
  these 
  cases 
  it 
  is 
  essential 
  : 
  (a) 
  that 
  the 
  graphical 
  means 
  

   employed 
  represent 
  the 
  relations 
  adequately 
  and 
  as 
  free 
  from 
  

   distortion 
  as 
  possible, 
  and 
  (b) 
  that 
  they 
  are 
  easy 
  of 
  application. 
  

  

  The 
  first 
  principle 
  requires 
  that, 
  in 
  any 
  graphical 
  represen- 
  

   tation, 
  the 
  relative 
  accuracy 
  over 
  the 
  entire 
  field 
  be 
  uniform 
  

   and 
  comparable 
  to 
  that 
  which 
  obtains 
  in 
  nature. 
  Great 
  distor- 
  

   tion 
  is 
  only 
  to 
  be 
  tolerated 
  when 
  certain 
  advantages 
  are 
  gained 
  

   which 
  more 
  than 
  counterbalance 
  the 
  effects 
  of 
  distortion. 
  

   Thus 
  the 
  gnomonic 
  projection 
  is 
  exceedingly 
  useful 
  in 
  crystal 
  - 
  

   lographic 
  work, 
  notwithstanding 
  its 
  excessive 
  distortion 
  away 
  

   from 
  the 
  pole, 
  because 
  in 
  it 
  all 
  crystallographic 
  faces 
  are 
  

   plotted 
  as 
  points 
  and 
  all 
  zones 
  as 
  straight 
  lines 
  which, 
  more- 
  

   over, 
  are 
  so 
  spaced 
  in 
  the 
  projection 
  that 
  the 
  crystallographic 
  

   indices 
  and 
  elements 
  of 
  all 
  faces 
  can 
  be 
  read 
  off 
  directly. 
  The 
  

   stereograph 
  ic 
  projection, 
  on 
  the 
  other 
  hand, 
  shows 
  less 
  distor- 
  

  

  Am. 
  Jour. 
  Sci.— 
  Fourth 
  Series, 
  Vol. 
  XXXVI, 
  No. 
  215.— 
  November, 
  1913. 
  

   34 
  

  

  