85 
.1903-4.] Dr Muir on General Determinants. 
where six equations are again intended to be specified, viz., 
a , a n 
X, x. 
I Vi V % 
a Y 
a z 
X 1 
I 5 
h 
Vi 
Vz 
each determinant of the one group of six being meant to be equal 
to the corresponding determinant of the other group. 
The example actually employed by Cayley is a result of the 
multiplication-theorem, and fully justifies the usage. It is 
\a + A. a + • • • , XJ3 + A . /3 + • • • , 
= 
X fJL • • • 
* I 
a /3 • • * 
jxa + yd a + • • • , y/3 + fjd/3' + • • • , 
X' yd • • • 
a /3’ • • • 
where, of course, the number of columns in the multiplier must 
be greater than the number in the determinant which is its 
cofactor. 
It may be worth adding that the Memoir e sur les hyper- 
determinants affords the first instance of the occurrence of Cayley’s 
vertical-line notation in Crelle's Journal .* 
De Ferussac (1845). 
[Sur la resolution d’un systeme general de m equations du 
premier degre entre m inconnues. Nouv. Annales de 
Math., iv. pp. 28-32.] 
This is a belated contribution, having no connection with any 
of those immediately preceding it. The author in all probability 
knew nothing of the subject, with the exception of Cramer’s rule, 
which by this time was almost a century old. 
The theorem which he seeks to establish is : — 
‘ ‘ Connaissant les valeurs des inconnues d’un systeme de n 
equations a n inconnues, pour avoir le denominates commun 
des valeurs d’un systeme de n + 1 equations a n + 1 inconnues, 
on multiplie le denominates du vales du premier systeme, 
par le coefficient de la nouvelle inconnue dans la nouvelle 
equation. Puis on en retranche les produits respectifs des 
* In Liouvillds Journal brackets, [ ] or { } , were used in Cayley’s own 
papers of the year 1845. See vol. x. 
