1899-1900.] Dr Muir on the Theory of Skew Determinants. 181 
The Theory of Skew Determinants and PfaflQans in the 
Historical Order of its Development up to 1857. By 
Thomas Muir, LL.D. 
(Read July 16, 1900.) 
Sets of equations of the form 
® 12*^2 
+ 
a iz x z 
+ 
^14*^4 
+ . . . 
• + n x n 
= 
4 
— a 12 x 1 
+ 
+ 
C*24^4 
+ . . . 
• • + a 2 n X n 
= 
& 
— a 1 2 > x 1 
^23*^2 
+ 
^34^4 
+ . . . 
. + a^ n x n 
= 
4 
$ 24*^2 
— 
^34^3 
+ . . . 
. + a in x n 
f 4 
— a ln Xi 
— a 2n x 2 
- 
a 2,n X 3 
- 
a in x 4 
- . . . 
= 
L 
where the coefficient of x r in the s th equation differs only 
in sign from the coefficient of x s in the r ih equation, had often 
made their appearance in analytical investigations before the 
determinant of such a set came to be considered. An instance 
is to he found in a memoir of Poisson’s, read before the Institute 
in October 1809, and printed in the Journal de VEcole Poly- 
technique , viii., pp. 266 — 344* ; and similar instances of an 
earlier date in writings of Lagrange and Laplace therein referred 
to. The mathematician who first referred definitely to the deter- 
minant appears to have been Jacobi. 
JACOBI (1827). 
[Ueher die Pfaffsche Methode, eine gewohnliche lineare Differen- 
tial-gleichung zwischen 2 n V ariabeln durch ein System von 
n Gleichungen zu integriren. CreTle's Journ ., ii. pp. 347- 
357.] 
An essential part of Pfaff’s method is the solution of a set of 
equations which Jacobi writes in the form 
See especially p. 288. 
