1899-1900.] Dr Muir on the Theory of Skew Determinants. 217 
a rs in ,f /\ — the identity, that is to say, with which we were in 
clined to start. 
His words are — 
“ Setzt man 
J A = (r, 1,2,..., r-l,r + l...,n) 
= a ri (2,...,n) + a ri (S, . n,l) +. . 
so findet man 
Ir 4 = (s + i. .... »,i, 
OCtrs 
in welchem Cyclus die Suffixe r and s fehlen.” 
In regard to this the reader has, of course, to note that 
(r,l,2, . . ., r- l,r + 1 . . n) being only one of the two values of 
J A , the differential-quotient obtained is also only one of two ; 
in other words, that the result reached is really 
0(r,l,2, . . ., r - 1, r + I, . . ., n)/da rs = (s + 1, . . ., n,l, . . ., s - 1), 
where from 1 to s - 1 and from s + 1 to n the integers appear in 
natural order, save that r is omitted. 
The remainder of the chapter or section, which contains no new 
feature, refers to Cayley’s expansion of a determinant arranged 
according to products of elements of the principal diagonal, and 
the application of this to skew determinants whose diagonal 
elements are each equal to z. 
