﻿510 
  F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  tion, 
  but 
  it 
  lacks 
  the 
  straight 
  equidistant 
  zone 
  lines 
  and 
  is 
  

   inferior 
  in 
  this 
  and 
  other 
  respects 
  to 
  the 
  gnomonic 
  projection 
  

   for 
  actual 
  crystallographic 
  work. 
  For 
  other 
  purposes, 
  how- 
  

   ever, 
  it 
  is 
  superior 
  to 
  the 
  gnomonic 
  projection 
  chiefly 
  because 
  

   it 
  represents 
  a 
  less 
  distorted 
  image 
  of 
  the 
  hemisphere. 
  Other 
  

   projections, 
  notably 
  the 
  equidistant 
  and 
  the 
  angle, 
  distort 
  still 
  

   less 
  and 
  are, 
  therefore, 
  superior 
  to 
  the 
  stereographic 
  projection 
  

   for 
  certain 
  purposes. 
  No 
  single 
  projection, 
  however, 
  is 
  supe- 
  

   rior 
  to 
  all 
  others 
  in 
  eveiw 
  detail, 
  and 
  for 
  this 
  reason 
  a 
  number 
  

   of 
  different 
  projections 
  are 
  in 
  common 
  use 
  and 
  will 
  continue 
  

   to 
  be 
  used, 
  notwithstanding 
  their 
  defects, 
  because 
  for 
  each 
  

   given 
  type 
  of 
  problem 
  there 
  is 
  a 
  projection 
  which 
  best 
  meets 
  

   the 
  situation, 
  and 
  which, 
  therefore, 
  should 
  be 
  adopted, 
  even 
  

   though 
  it 
  may 
  be 
  unsuited 
  for 
  other 
  kinds 
  of 
  problems 
  involv- 
  

   ing 
  projection. 
  

  

  In 
  graphical 
  plots 
  for 
  the 
  solution 
  of 
  equations 
  the 
  principle 
  

   of 
  uniformity 
  in 
  relative 
  accuracy 
  over 
  the 
  entire 
  plot 
  is 
  

   equally 
  important 
  and 
  often 
  leads 
  the 
  observer 
  to 
  modify 
  an 
  

   equation, 
  which 
  he 
  wishes 
  to 
  solve, 
  in 
  such 
  a 
  way 
  that 
  the 
  

   amount 
  of 
  distortion 
  or 
  lack 
  of 
  uniformity 
  in 
  plotting 
  scale 
  is 
  

   decreased. 
  This 
  can 
  be 
  done 
  either 
  by 
  taking 
  some 
  function 
  

   of 
  the 
  values 
  in 
  question, 
  as 
  the 
  logarithmic 
  function, 
  or 
  by 
  

   raising 
  the 
  values 
  to 
  some 
  power. 
  Experience 
  is 
  required 
  to 
  

   enable 
  the 
  observer 
  to 
  select 
  such 
  functions 
  skilfully. 
  This 
  

   principle 
  is 
  well 
  illustrated 
  in 
  Plate 
  III 
  (based 
  on 
  the 
  equation 
  

   sin 
  2 
  i 
  = 
  n 
  2 
  sin 
  2 
  r) 
  which 
  shows 
  considerably 
  less 
  distortion 
  than 
  

   Plate 
  II, 
  although 
  both 
  plates 
  furnish 
  solutions 
  of 
  the 
  ordinary 
  

   refractive 
  index 
  equation 
  sin 
  i 
  — 
  n 
  sin 
  r. 
  

  

  The 
  second 
  principle, 
  that 
  of 
  ease 
  of 
  application, 
  concerns 
  

   itself 
  with 
  the 
  efficiency 
  of 
  the 
  method, 
  both 
  in 
  the 
  solution 
  of 
  

   problems 
  and 
  in 
  the 
  preparation 
  of 
  the 
  diagrams 
  for 
  such 
  solu- 
  

   tions. 
  It 
  is, 
  however, 
  obvious 
  and 
  requires 
  no 
  further 
  com- 
  

   ment. 
  

  

  In 
  the 
  following 
  pages 
  illustrations 
  of 
  these 
  and 
  other 
  

   principles 
  will 
  be 
  given 
  and 
  several 
  new 
  graphical 
  plots 
  will 
  

   be 
  described 
  briefly. 
  

  

  Graphical 
  solution 
  of 
  the 
  equations 
  used 
  in 
  microscopical 
  

   petrography. 
  — 
  The 
  most 
  important 
  equations 
  which 
  the 
  

   petrographer 
  has 
  to 
  solve 
  in 
  his 
  work 
  with 
  thin 
  sections 
  and 
  

   crystal 
  plates 
  are 
  the 
  following 
  : 
  

  

  1. 
  Refractive 
  index 
  formula 
  

  

  sinz 
  = 
  rosin?* 
  (1) 
  

  

  wherein 
  i 
  is 
  the 
  angle 
  of 
  incidence, 
  r, 
  the 
  angle 
  of 
  refraction, 
  

   and 
  ro, 
  the 
  refractive 
  index 
  (Plates 
  II, 
  III, 
  and 
  TV). 
  

  

  2. 
  Minimum 
  deviation 
  prism 
  formula 
  

  

  