﻿Minors 
  of 
  an 
  Axisymmetnc 
  Determinant. 
  

  

  415 
  

  

  showing 
  that 
  the 
  two 
  components 
  differ 
  only 
  in 
  sign. 
  Thus 
  

   the 
  fifteen- 
  termed 
  aggregate 
  

  

  H 
  

  

  i. 
  e. 
  2 
  

   = 
  2 
  

  

  12456 
  [ 
  

   3789r|' 
  

  

  12456 
  1,^1 
  12467 
  

   3789 
  r 
  + 
  ^I3589r 
  

  

  12453 
  | 
  1 
  12435 
  

  

  6789 
  r 
  

   0: 
  

  

  | 
  (5789 
  r 
  | 
  ' 
  

  

  and 
  the 
  twenty-termed 
  aggregate 
  

   fij', 
  i.e. 
  2 
  2389 
  r 
  ' 
  

  

  v 
  I 
  14567 
  

  

  ^2389- 
  

  

  14678 
  

   2359- 
  

  

  14523J 
  _ 
  1142351 
  

   6789r 
  6789- 
  ' 
  

  

  = 
  0. 
  

  

  The 
  35-termed 
  aggregate 
  /x 
  ?> 
  and 
  the 
  70-termed 
  aggregate 
  

   fju± 
  are 
  seen 
  to 
  resemble 
  the 
  M's 
  in 
  their 
  constitution, 
  the 
  one 
  

   being 
  the 
  sum 
  of 
  two 
  zeros 
  and 
  the 
  other 
  the 
  sum 
  of 
  four. 
  

  

  7. 
  Finally, 
  let 
  it 
  be 
  noted 
  that 
  two 
  lines 
  of 
  generalization 
  

   are 
  herein 
  marked 
  out. 
  The 
  first 
  is 
  indicated 
  in 
  the 
  series 
  of 
  

   identities 
  — 
  

  

  y 
  o 
  

   I 
  a 
  ,3 
  y 
  

  

  I 
  c 
  e 
  'C 
  

  

  I 
  a 
  /3 
  y 
  S 
  

   I 
  e 
  £ 
  ?7 
  6 
  

  

  a 
  (3 
  y 
  c 
  6 
  

  

  

  =2 
  

   =2 
  

  

  y 
  £_£ 
  I 
  

  

  a 
  ?> 
  y 
  e 
  | 
  

  

  d 
  Z 
  y 
  e 
  I 
  

  

  a, 
  fi 
  y 
  o 
  £ 
  

  

  e 
  r) 
  6 
  i 
  k 
  

  

  s? 
  j 
  a 
  S 
  e 
  

  

  a 
  /3 
  e 
  '( 
  I 
  _y 
  I 
  a 
  e 
  £ 
  r\ 
  I 
  . 
  

   y 
  I 
  n 
  d 
  | 
  " 
  A 
  I 
  j8 
  ySel' 
  

  

  ^ 
  | 
  a 
  /3 
  7 
  £ 
  // 
  I 
  ^ 
  I 
  a 
  /3 
  £ 
  v 
  ft 
  

  

  where 
  the 
  opening 
  identity 
  in 
  each 
  line 
  is 
  Kronecker's. 
  The 
  

  

  