388 DR THOMAS MUIR ON THE 
where 
0 0 
cp es Ie eters 
ik ey Ae Ty!’ 
i caste 4!) \ eee ole) 
are used for 
| Abe, ls Si Gohrs ly 
| aybofg 1, | Byeo93 |, | Cth |, [egohs |, | Alofg |, | OFo9s |, 
| G93 |, | Peete |, | ets |, | Cyhots |, | F931, | OGohs |, 
| aybotg |, | dyofs |, | Cds |, | Fo9s |, | 49o%3 |, |Ohoss |, 
respectively. 
(42) There is, however, a second form of invariance which it is convenient now to 
consider. Looking at the equations we at once see that the performance of the 
we @ i 
iG b a 
leaves them unaltered, and that the same is true of either of the interchanges 
C b S j Cait 
1 © Ibs > Nw @ ae 
From this it follows that the eliminant is invariant to each one of the three interchanges 
ye ee 
Taking the first of these and observing its effect on our twenty determinants 
the third order we find that it is equivalent to the substitution 
interchange 
Oe ee ey 8, A BS 6S. 1B 2 ON I eee. ea ec ee 
(ee J) 2G Slee Sense 0, = a6G=0, alba S.= 9 <7, 
of each determinant may be changed with impunity, this substitution has the same 
effect as the simpler substitution 4 
or the interchange 
Similarly we have 
eae 0, 1;' 2,8, 4, S86" Fi 8. 79: OF 1% 05 “85 a oe 
Veh =o a, oe eee _0',-6',-5',- 4-3-2, — 1 9 rn 
