Dr Muir on General Determinants. 
685 
1907-8.] 
established and the results deduced are absolutely the same as those 
published by himself in 1844. He says (p. 127), “ Les clefs algebriques de 
M. Cauchy ne sont au fond que les unites relatives ; et ses facteurs 
symboliques conviennent, du moins dans un certain rapport, aux quantites 
extensives telles que je les ai definies. La difference ne consiste qu’en ce 
que M. Cauchy regarde les clefs algebriques seulement comme un moyen 
pour resoudre divers problemes de l’analyse et de la mecanique et qui, les 
problemes etant resolus, disparaissent, tandis que d’apres les principes 
etablis par moi, on est en etat, a chaque pas du procede, d’attribuer une 
signification independante aux unites relatives et aux quantites qui en sont 
composees, quelle que soit d’ailleurs la marche que Ion suive.” 
Majo, L. de (1854, March). 
[Metodi e formole generali per Y eliminazione nelle equazioni di primo 
grado. Memorie . . . Accad. delle Sci. (Napoli), i. pp. 101-116.] 
This is a carefully written but curiously belated exposition, the author 
apparently being quite out of touch with the writers of his own time, and 
possibly not familiar with any of the older writers save Cramer, Bezout, and 
Hindenburg. In the first six pages he defines “ il polinomio P m (a 1 b i ,c 3 . . . s m ) ” 
after the fashion of Bezout (1764), and gives one or two very ele- 
mentary properties of it. The remaining ten pages are occupied with 
simultaneous linear equations, and are notable as containing (§§ 15-19) a 
clear exposition of Bezout ’s peculiar rule-of-thumb process of 1779. Herein 
lies the value of the paper, Majo being not only the first since Hindenburg 
to recall attention to a neglected process of real practical value, but also the 
first to give (§ 16) a reason for its validity. 
Cayley, A. (1854, May). 
[Remarques sur la notation des fonctions algebriques. Crelles 
Journal, 1. pp. 282-285 : or Collected Math. Papers, ii. pp. 185- 
188.] 
The notation referred to is that of matrices, and is exemplified by 
( cq a 2 a 3 ) 
^1 @2 fi 3 
7i 72 7s » 
a matrix being defined as a system of quantities arranged in the form of a 
square, but otherwise quite independent. With its help the set of equations 
