Determinant with Factors like those of the Difference-Product. 271 
The latter mode is less readily generalizable than the former. To give 
an indication of the line it takes, it may be stated that in the case of 7 
variables the original equations 
(a+ ■ 
+g)x* 
• +efg)x* 
(abcd-\- . 
are transformed into 
{x 2 +ab){ x* 
+ (abcde-\- . . . J rcdefg)x 2 + 
. J r defg)x 2 + (abcdef-\- . . . - 
-{cdefg) z x 2 +(cdefg) 5 \ = 0} 
-{cdefg) 2 x*+(cdefg)i\=0 (, 
abcdefg 
-bcdefg) 
where, be it remarked as a digression in passing, the trinomial factors in 
the left-hand members are exactly similar to the left-hand members of the 
pair of equations with which we started this paragraph. 
11. As a natural consequence of the result here foreshadowed we are 
led to consider the dialytic eliminant 
5 3 
5 5 • 
5 4 . 
1 
5 2 54 
where 
5 X stands for 
5 2 ... ab-{-ac-\- . . . -{-de, 
and so on. 
Multiplying it column- wise by unity in the form 
1 
— e 
1 
and then multiplying row-wise the resulting product by unity in the form 
1 
e 2 1 
we reach the result 
1 
1 
4 4 
e 4 +5 2 e 2 +5 4 
