908 Proceedings of Royal Society of Edinburgh. [sess. 
The Theory of General Determinants in the Historical 
Order of Development up to 1852. By Thomas 
Muir, LL.D. 
(MS. received June 12, 1905. Read July 3, 1905.) 
Cauchy (1844). 
[Memoire sur les arrangements qne Ton peut former avec des 
lettres donnees, et sur les permutations ou substitutions a 
l’aide desquelles on passe d’un arrangement a un autre. 
Exercices d’ Analyse et de Phys. Math., iii. pp. 151-252.] 
The nature of the connection of this with the theory of deter- 
minants is evident from the title. Some of the elementary 
portions of the memoir had in fact already appeared in Cauchy’s 
determinant papers of the years 1812, 1840, 1841, and have been 
noted in our accounts of the latter. In these papers, as was 
natural, only such isolated properties were given as might be of 
immediate application to the main subject : here we have a 
methodically arranged and lucidly written treatise. As, however, 
in dealing with permutations the question of signature is not taken 
up, there is no explicit reference to determinants : and all that is 
therefore necessary is to direct attention to a storehouse of informa- 
tion regarding a subject closely connected with them. 
Cauchy (1844). 
[Memoire sur quelques proprietes des resultantes a deux termes. 
Exercices d’ Analyse et de Phys. Math., iii. pp. 274-304.] 
By “ resultantes a deux termes ” are meant determinants of the 
second ord.er. The expression recalls “resultantes a deux lettres,” 
used by Binet in his memoir of November 1812 ; and as the said 
memoir is here referred to by Cauchy and contains the foundation 
of the latter’s results, it is not improbable that the one expression 
suggested the other. 
