﻿414 
  

  

  Dr. 
  T. 
  Muir 
  : 
  Aqqreqates 
  of 
  

  

  and 
  the 
  still 
  more 
  recent 
  aggregates 
  

  

  12356 
  

  

  4789r 
  

  

  12567 
  

   3489 
  r 
  

  

  12456 
  

   3789 
  r 
  

  

  13456 
  

  

  2789 
  r 
  

  

  V 
  

  

  Pl, 
  1*2, 
  f*>%, 
  

  

  the 
  following 
  partition 
  of 
  the 
  126 
  terms 
  of 
  2 
  

   make 
  clear 
  the 
  various 
  relationships 
  involved. 
  

  

  p±; 
  

  

  12345 
  

  

  6789 
  r 
  

  

  will 
  

  

  LL 
  = 
  

  

  M 
  3 
  = 
  { 
  

  

  L 
  

  

  H 
  

  

  {fa 
  (15 
  terms), 
  

  

  _ 
  ( 
  fa 
  f 
  (15 
  terms), 
  

  

  ^ 
  ~\fa 
  (20 
  terms), 
  

  

  r„>- 
  Oi'' 
  (15 
  terms), 
  

  

  = 
  y* 
  ~~ 
  W 
  (20 
  terms), 
  

  

  J 
  /* 
  2 
  " 
  (20 
  terms), 
  

  

  I 
  

  

  ^ 
  ~ 
  W 
  (15 
  terms). 
  

   Of 
  course 
  for 
  perfect 
  completeness 
  we 
  should 
  have 
  started 
  

   with 
  the 
  252 
  terms 
  of 
  the 
  aggregate 
  2 
  

   and 
  2 
  

  

  into 
  2 
  

  

  12345 
  

  

  6789 
  r 
  

  

  23456 
  

   1789 
  r 
  

  

  12345 
  

  

  6789 
  r 
  

  

  ? 
  dividing 
  it 
  

  

  -that 
  is 
  to 
  say, 
  into 
  M 
  3 
  and 
  

  

  M 
  8 
  ': 
  but 
  nothing 
  would 
  thereby 
  have 
  been 
  gained, 
  as 
  the 
  

   difference 
  between 
  the 
  one 
  half 
  and 
  the 
  other 
  is 
  made 
  to 
  

   disappear 
  by 
  row-and-column 
  interchange. 
  

  

  The 
  fundamental 
  aggregates 
  in 
  the 
  collection 
  are 
  seen 
  to 
  be 
  

   K, 
  fa, 
  /x 
  2 
  ; 
  that 
  is 
  to 
  say, 
  

  

  <« 
  ! 
  12345 
  

  

  ^ 
  16789 
  - 
  

  

  ^ 
  i 
  12356 
  I 
  

  

  Z 
  \47S9t\ 
  

  

  ^ 
  I 
  12567 
  

  

  ^|3489r 
  

  

  the 
  others 
  on 
  the 
  extreme 
  right 
  being 
  variants 
  of 
  two 
  of 
  these 
  

   and 
  therefore 
  indicated 
  by 
  the 
  same 
  letters 
  with 
  one 
  or 
  more 
  

   dashes. 
  The 
  common 
  characteristic 
  of 
  the 
  three 
  is 
  the 
  inva- 
  

   riability 
  of 
  four 
  line-numbers, 
  all 
  the 
  possible 
  distributions 
  of 
  

   four 
  such 
  numbers 
  among 
  rows 
  and 
  columns 
  being 
  

  

  4 
  + 
  0, 
  

  

  3 
  + 
  1, 
  

  

  2 
  + 
  2. 
  

  

  6. 
  The 
  proof 
  that 
  fa 
  and 
  fa 
  vanish 
  on 
  the 
  imposition 
  of 
  

   axisymmetry 
  is 
  accomplished 
  by 
  continuing 
  in 
  each 
  case 
  the 
  

   process 
  of 
  fission 
  by 
  which 
  they 
  themselves 
  arose, 
  and 
  then 
  

  

  