Dr T. Muir on the Theory of Determinants. 
503 
Ai = 0 
Aj Cj + A2C2 + Ao Cg + . . . . + A,^ c,„ = 0 
and these to the solution of m linear equations in m unknowns. 
[Philosophie de la Technie Algorithmique. Premiere Section, 
contenant la loi supreme et universelle des Mathematiques. 
Par Hoene Wronski, pp. 175-181, &c. Paris.] 
Here as in the Refutation of 1812 “combinatory sums” make 
their appearance, as being necessary for the expression of the “ loi 
supreme.” Wronski’s point of view is unaltered toward them. He 
now, however, calls them 
from the letter formerly introduced to denote them, et “ pour ne 
j)as introduire de noms nouveaux ” ! Two or three pages are 
occupied with the statement of the recurrent law of formation 
(B6zout, 1764). 
Royal de Nancy, . . . . Paris,] 
As far as can be gathered, Desnanot was acquainted with the 
writings of very few of his predecessors in the investigation of 
determinants. The only one he himself mentions is Bezout, and 
the first part of his work is in direct continuation of a topic which 
the latter had begun. His book is a marvel of laboured detail. 
No expositor could take more pains with his reader, space being 
held of no moment if clearness had to be secured. As might be 
expected, therefore, all that is really worth preserving of his work 
is but a small fraction of the 264 pages which he occupies in ex- 
position. 
WRONSKI (1815). 
Schin functions. 
(xv. 5) 
DESNANOT, P. (1819). 
[Complement de la Theorie des Equations du Premier Degre, 
contenant Par P. Desnanot, Censeur an College 
The first chapter bears the heading 
