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

DETERMINANTS IN GENERAL (STOCKWELL, 1860)

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for beginners. Todhunter's plan and style are quite similar to
Ferrers', and his three chapters are therefore still more helpful.
Tait's also resembles Ferrers', and is of the same extent.
STOCKWELL, J. N. (1860, July).
[On the resolution of symmetrical equations with indeterminate
coefficients. (Gould's) Astron. Journ., vi. pp. 145-149.]
Stockwell's subject being the equation of the secular inequalities,
he opens with a very short account of determinants. His mode
of writing the final expansion of 100-11221, 100.11-22.331,.... is
that which would be reached by using Cauchy's rule of 1841; for
example,
100-11.221
=00-11-22-21-12-00-20-0211- 10-01-22 +21.10-02 +20-01-12.
In specifying the number of terms of each type in the expansion,
he gives for the number of terms in a zero-axial determinant of
the 3rd, 4th, 5th,.... orders the expressions.:
1 3-1,
(1-3-1) 4+1,
{(13 -1) 4+1}5- 1,
CAYLEY, A. (1860, December).
[Note on the theory of determinants. Philos. Magazine, (4), xxi.
pp. 180-185; or Collected Math. Papers, v. pp. 45-49.]
Cayley's 'mode of arrangement of the developed expression of
a determinant ' is in its result the same as Stockwell's, and is not
therefore essentially different from Cauchy's of the year 1841;
as written, however, his development is more compendious than
Cauchy's, and deserves attention. For all three it is necessary that
the elements of the determinant be specified by their row and
column numbers.
He denotes
11, 22,...; 122, 12331, 12 3-32-2,...
by 111, 121|...; 1121, 11231, 11321,...,