392 DR THOMAS MUIR ON THE 
Similarly it may be shown that 
59 BB 
8 De 9225 
4 
69’ 66. 
= (ys eee 3 
oo 
48 47’ 44’ 
6) Oe 6 of. 6 
— 002 + 038 + 03'6 + 056 — 148 — 189 + 224 — 255’ + 3’47' — 4'99' — 559 + 5'7'9’ + 669’ + 6'89 
= cofactor of 4; 
d 2 
and tee = 2 
=i) 9 Or ood 
7 Ue, 
= —004+013+ 
= cofactor of 4’. 
It consequently follows that the eliminant may be put in the form 
, 58’ 59 |. - 59 by 55’ an 28’ 7 99’ | 
Grey or SG ee 
67 69’ 69 66 39’ 33) | 
i! lage te Meas IPE ohne 9 0+5 Oa 
48 Aq 48 aa ee 19 wh 
es es “Ele OR Gs 3 | <a 
or, say, for convenience of future reference, 
(0+0)A, - S4A, — 34’A,. 
shows that it is invariant to the interchange of § 42. Since, therefore, the performance 
of this interchange on the determinant form of it, A,,-where the invariance is not in 
evidence,—cannot make any alteration in substance, we shall obtain thereby a second 
determinant form V,, thus arriving at the unexpected identity 
58’ 59 39’ 38 
0+ 8 a 0+ 9 - 
67 69’ ey 28’ 
Se ee ee ee ee 
48 47’ 19 la 
Further, since the whole eliminant is invariant to the interchange, the removal from 
it of the invariant portion (0+ 0’) 4, must leave a portion which in substance, if n¢ 
in form, is likewise invariant. ‘This consideration gives us the identity 
