﻿270 
  

  

  PROCEEDINGS 
  OF 
  THE 
  GEOLOGICAL 
  SOCIETY. 
  

  

  Table 
  III. 
  — 
  Oocygeyi-proportions 
  of 
  the 
  Constituent 
  Minerals 
  of 
  the 
  

   Granite 
  of 
  Donegal 
  (Table 
  XI. 
  loc. 
  cit.). 
  

  

  

  Quartz. 
  

  

  Orthoclase. 
  

  

  Oligoclase. 
  

  

  Black 
  Mica. 
  

  

  Silica 
  

  

  51-92 
  

  

  3281 
  

   8-91 
  

   3-55 
  

  

  31-11 
  

  

  11-41 
  

  

  3-61 
  

  

  18-78 
  

  

  16-28 
  

  

  3-94 
  

  

  Peroxides 
  

  

  Protoxides 
  

  

  

  

  

  Totals 
  

  

  51-92 
  

  

  45-27 
  

  

  46-13 
  

  

  39-00 
  

  

  

  The 
  problem 
  to 
  be 
  solved 
  with 
  respect 
  to 
  the 
  foregoing 
  fifteen 
  

   granites 
  may 
  be 
  thus 
  stated 
  : 
  — 
  " 
  Given 
  the 
  chemical 
  analysis 
  of 
  a 
  

   compound 
  rock, 
  and 
  the 
  chemical 
  analyses 
  of 
  its 
  supposed 
  constituent 
  

   minerals, 
  it 
  is 
  required 
  to 
  find 
  its 
  mineralogical 
  composition 
  ex- 
  

   pressed 
  in 
  terms 
  of 
  those 
  minerals." 
  At 
  first 
  sight 
  nothing 
  is 
  easier 
  

   than 
  the 
  mathematical 
  statement 
  of 
  this 
  problem 
  ; 
  for 
  each 
  com- 
  

   ponent 
  of 
  the 
  rock-analysis 
  gives 
  us 
  an 
  equation 
  of 
  condition, 
  which 
  

   is 
  linear, 
  and 
  the 
  whole 
  problem 
  is 
  reduced 
  to 
  the 
  solution 
  of 
  a 
  

   number 
  of 
  simultaneous 
  linear 
  equations. 
  

  

  In 
  practice, 
  however, 
  the 
  number 
  of 
  equations 
  thus 
  furnished 
  is 
  

   generally 
  greater 
  than 
  the 
  number 
  of 
  minerals, 
  and 
  the 
  supernu- 
  

   merary 
  equations 
  may 
  be 
  regarded 
  as 
  test-equations, 
  and 
  used 
  to 
  

   ascertain 
  whether 
  our 
  hypothesis 
  as 
  to 
  the 
  constituent 
  minerals 
  be 
  

   physically 
  correct 
  or 
  not. 
  

  

  Let 
  us 
  consider 
  this 
  question 
  somewhat 
  in 
  detail 
  as 
  to 
  the 
  Donegal 
  

   granites. 
  

  

  The 
  hypothesis 
  I 
  make 
  respecting 
  them 
  is, 
  that 
  they 
  are 
  composed 
  

   of 
  four 
  minerals, 
  whose 
  chemical 
  composition 
  is 
  contained 
  in 
  Table 
  II. 
  

   The 
  equations 
  at 
  my 
  disposal 
  are 
  seven 
  in 
  number, 
  derived 
  from 
  the 
  

   following 
  components 
  : 
  — 
  Silica, 
  Alumina, 
  Iron 
  and 
  Manganese, 
  Lime, 
  

   Magnesia, 
  Soda, 
  Potash. 
  

  

  It 
  is 
  therefore 
  evident 
  that 
  I 
  have 
  three 
  supernumerary 
  equations, 
  

   which 
  may 
  be 
  used 
  as 
  tests 
  of 
  the 
  accuracy 
  of 
  the 
  fundamental 
  

   hypothesis, 
  when 
  the 
  mineral 
  composition 
  of 
  the 
  granite 
  has 
  been 
  

   deduced 
  from 
  any 
  four 
  of 
  the 
  seven 
  equations 
  at 
  my 
  disposal. 
  Of 
  

   the 
  seven 
  equations, 
  those 
  deduced 
  from 
  silica 
  and 
  alumina 
  are 
  the 
  

   most 
  trustworthy, 
  because 
  they 
  deal 
  with 
  the 
  largest 
  quantities, 
  and 
  

   because 
  these 
  elements 
  enter 
  into 
  the 
  composition 
  of 
  the 
  constituent 
  

   minerals 
  in 
  a 
  more 
  precise 
  and 
  definite 
  manner 
  than 
  the 
  protoxide 
  

   bases. 
  

  

  In 
  addition 
  to 
  the 
  seven 
  equations 
  derived 
  from 
  the 
  components 
  

   of 
  the 
  rock, 
  there 
  is 
  an 
  eighth, 
  which 
  expresses 
  the 
  self-evident 
  fact 
  

   that 
  the 
  whole 
  rock 
  is 
  equal 
  in 
  weight 
  to 
  the 
  weights 
  of 
  all 
  its 
  con- 
  

   stituent 
  minerals 
  ; 
  so 
  that 
  we 
  have 
  in 
  reality 
  eight 
  equations 
  to 
  de- 
  

   termine 
  four 
  supposed 
  unknown 
  quantities. 
  

  

  Instead, 
  however, 
  of 
  employing 
  these 
  equations, 
  I 
  prefer, 
  in 
  the 
  

   first 
  instance, 
  to 
  use 
  three 
  equations 
  derived 
  from 
  the 
  oxygen-ratios 
  

   of 
  the 
  silica, 
  the 
  peroxides, 
  and 
  the 
  protoxides, 
  together 
  with 
  the 
  

   equation 
  depending 
  on 
  weights 
  — 
  a 
  method 
  which 
  will 
  give 
  me 
  four 
  

   reliable 
  equations 
  to 
  find 
  four 
  unknown 
  quantities 
  ; 
  and 
  when 
  these 
  

  

  