﻿272 
  

  

  PROCEEDINGS 
  OF 
  THE 
  GEOLOGICAL 
  SOCIETY. 
  

  

  If 
  k 
  denote 
  the 
  quantity, 
  

  

  aa 
  + 
  oft 
  + 
  ey 
  =a'a! 
  + 
  &'/3' 
  + 
  C 
  7 
  ' 
  = 
  a" 
  a" 
  + 
  6' 
  f 
  j3' 
  f 
  + 
  c" 
  y 
  ", 
  

  

  then 
  .r, 
  3/, 
  z 
  are 
  given 
  by 
  the 
  following 
  equations 
  : 
  — 
  

  

  10000(Aa 
  +B/3 
  + 
  Cy 
  )^ 
  

  

  07: 
  

  

  ?/ 
  

  

  _10000(Aa'+B/3'+Cy') 
  

  

  > 
  

  

  __10000(Aa" 
  + 
  B/3" 
  + 
  Cy") 
  

  

  (4) 
  

  

  a 
  = 
  69077 
  

   a' 
  =-113443 
  

   a"= 
  41702 
  

  

  y 
  = 
  196703 
  

   y 
  = 
  79167 
  

   y 
  "= 
  -163140 
  

  

  The 
  constants 
  of 
  the 
  system 
  of 
  equations 
  (3) 
  are 
  found, 
  by 
  actual 
  

   multiplication, 
  to 
  be, 
  

  

  j3 
  =-188220 
  

   fi' 
  = 
  211768 
  

   /3" 
  = 
  — 
  24442 
  

   k 
  =34131692. 
  

  

  In 
  the 
  calculation 
  of 
  the 
  values 
  of 
  x, 
  y, 
  z, 
  it 
  will 
  be 
  found 
  more 
  

   useful 
  to 
  use 
  logarithms, 
  for 
  which 
  reason 
  I 
  here 
  give 
  the 
  logarithmic 
  

   values 
  of 
  the 
  ten 
  constants 
  of 
  the 
  Donegal 
  granites 
  : 
  — 
  

   log 
  (a) 
  =4-8393335 
  log 
  (/3) 
  =5-2746658 
  log 
  (y) 
  =5-2938110 
  

   log 
  («') 
  =5-0547777 
  log 
  (ft) 
  =5-3258604 
  log 
  (y') 
  =4-8985442 
  

   log 
  (a")=4-6201569 
  log 
  (/3")=4-3881367 
  log 
  ( 
  y 
  ")=5-2125605 
  

  

  log 
  (V) 
  = 
  7-5331578576. 
  

  

  In 
  order 
  to 
  apply 
  these 
  multipliers 
  to 
  the 
  analyses 
  recorded 
  in 
  

   Table 
  I., 
  we 
  must 
  first 
  calculate 
  the 
  quantities 
  of 
  oxygen 
  present 
  in 
  

   each 
  constituent 
  of 
  the 
  analyses. 
  This 
  has 
  been 
  done, 
  and 
  the 
  re- 
  

   sults 
  are 
  recorded 
  in 
  the 
  following 
  Table 
  : 
  — 
  

  

  Table 
  IV 
  

  

  . 
  — 
  Oxygen 
  ir 
  

  

  , 
  Constituents 
  

  

  of 
  Donegal 
  Granites. 
  

  

  No. 
  

  

  

  08 
  

  

  a 
  

  

  a3 
  

  

  prot- 
  

   ; 
  and 
  

   anese. 
  

  

  

  08* 
  

  

  <D 
  

  

  

  -d 
  

  

  d 
  

  

  CD 
  

  

  be 
  

   O 
  

  

  

  c3 
  

   o 
  

  

  • 
  fH 
  

  

  jjj 
  

  

  

  

  g 
  

  

  C8 
  

  

  c8 
  

  

  e8 
  

  

  

  

  m 
  

  

  3 
  

  

  

  H 
  O^i 
  

  

  3 
  

  

  £ 
  

  

  o 
  

  

  Pk 
  

  

  H 
  

  

  I. 
  

  

  36-346 
  7-646 
  

  

  0-838 
  

  

  0-017 
  

  

  0-317 
  

  

  0-282 
  

  

  1-289 
  

  

  0-789 
  

  

  47-524 
  

  

  II. 
  

  

  34-164 
  

  

  5-981 
  

  

  1-988 
  

  

  0-039 
  

  

  0-828 
  

  

  0-609 
  

  

  1-297 
  

  

  0-745 
  

  

  45-651 
  

  

  III. 
  

  

  35-804 
  

  

  8-132 
  

  

  0-753 
  

  

  

  0-795 
  

  

  0-162 
  

  

  0-776 
  

  

  0-889 
  

  

  47-311 
  

  

  IV. 
  

  

  30-341 
  

  

  9-348 
  

  

  1-928 
  

  

  0-454 
  

  

  1-341 
  

  

  0-625 
  

  

  0-976 
  

  

  0-477 
  

  

  45-490 
  

  

  V. 
  

  

  36-032 
  

  

  7-478 
  

  

  0-907 
  

  

  0-066 
  

  

  0-649 
  

  

  0-214 
  

  

  1-068 
  

  

  0-756 
  

  

  47-170 
  

  

  VI. 
  

  

  35-306 
  

  

  7-851 
  

  

  1101 
  

  

  0-144 
  

  

  1-151 
  

  

  0-378 
  

  

  1107 
  

  

  0-345 
  

  

  47-383 
  

  

  VII. 
  

  

  35-409 
  

  

  7-459 
  

  

  1-104 
  

  

  0-221 
  

  

  0-828 
  

  

  0-310 
  

  

  0-960 
  0-700 
  

  

  46-991 
  

  

  VIII. 
  

  

  36-677 
  

  

  7-309 
  

  

  0-789 
  

  

  

  0-700 
  

  

  0-058 
  

  

  0-976 
  

  

  0-767 
  

  

  47-276 
  

  

  IX. 
  

  

  37-507 
  

  

  6-967 
  

  

  0-486 
  

  

  0121 
  

  

  0-484 
  

  

  0142 
  

  

  0-899 
  

  

  0-864 
  

  

  47-470 
  

  

  X. 
  

  

  38-214 
  

  

  6-149 
  

  

  0-778 
  

  

  

  0-224 
  

  

  0-199 
  

  

  1079 
  

  

  0-884 
  

  

  47-827: 
  

  

  XI. 
  

  

  35-721 
  

  

  7-664 
  

  

  0-599 
  

  

  0-202 
  

  

  0-497 
  

  

  0-338 
  

  

  0-788 
  

  

  0-894 
  

  

  46-703 
  

  

  XII. 
  

  

  35-929 
  

  

  7-664 
  

  

  0-625 
  

  

  0-221 
  

  

  0-292 
  

  

  0-338 
  

  

  1077 
  

  

  0-884 
  

  

  47030 
  

  

  XIII. 
  

  

  28-660 
  

  

  9010 
  

  

  1-821 
  

  

  0-313 
  

  

  1-443 
  

  

  1-461 
  

  

  1186 
  

  

  0-536 
  

  

  44-430 
  

  

  XIV. 
  

  

  39-065 
  

  

  7-244 
  

  

  0-179 
  

  

  

  0-638 
  

  

  0-054 
  

  

  1-246 
  

  

  0553 
  

  

  48-979 
  

  

  XV. 
  

  

  37923 
  

  

  7-104 
  

  

  

  

  0-454 
  

  

  0027 
  

  

  0-738 
  

  

  1-240 
  

  

  47-486 
  

  

  