The theory of determinants in the historical order of development, by Sir Thomas Muir.

SKEW DETERMINANTS (ROBERTS, 1879)

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and in similar fashion
I ad, ab$2 bG acC4 C$5 bc$6 abc6t
-1 $ b$3 -b2, c$5 -ce4 -bc$7 bc$6
-&2 3& C& C$7 -CC4 -Co5
-& - t2 -a ac -c6 c5 -ac4
-&4 - 5 - b6 -b7 t b$ b-3
1 5 a4 -ab7 b6 -a$1 -b$3 ab$,
-& a$7 a4 - -a2 - a1e
-C7 -$6 $5 $4 -$3 $-2 1
= ($2+a 2 +ab$22e +b32 +ac$42b C$2 +-bc2 +abcC72)1
Of these two interesting determinants, R4 and R8 say, the former
is seen to include Souillart's of 1860, and the latter Sylvester's of
1867.
Multiplying R4 in row-by-column fashion by the determinant got
from R4 on changing the signs of t, $2, 3 he obtains a determinant
having 2 1
+a +al2+ b2 + ab2
in the places 11, 22, 33, 44, and zeros in all the other places: further,
he asserts that all the primary minors have 2 +a$2 +b22 +ab$s2
for a factor, and that quite similar properties are possessed by Rs.
It may be added that as the result of an investigation* made in
1879 Roberts convinced himself of the non-existence of an R16.
SYLVESTER, J. J. (1879).
[Note on determinants and duadic disynthemes. American Journ.
of Math., ii. pp. 89-90, 214-222.]
[Sur une propriete arithmetique d'une serie de nombres entiers.
Comptes Rendus.... Acad. des Sci. (Paris), lxxxviii. pp. 1297 -1298.]
The greater part of the space here is devoted to the number of
terms in (the 'denumerant' of) skew and zero-axial skew determinants. In the latter case the difference-equation is given as
Un =- (-n1)2,_2 - -(n-1)(n-2)(n-3)u_4,
* See Quart. Journ. of Math., xvi. pp. 159-170. The paper also contains an
interesting sketch of the history of the problem of representing the product of two
sums of 271 squares as a sum of 2n squares.