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

ALTERNANTS (HAEDENKAMP, 1841) 15R
HAEDENKAMP, H. (1841).
['Ueber Transformation vielfacher Integrale. Crelle's Jouvrb.,
xxii. pp. 184-192.*]
The transformation referred to in the title has its origin in a
special equation of the n", degree in y, viz.+i X2 Xn
a1Y C2 Y a -y
and, as Haedenkamp gives the values of x1 X2,...I xn in terms
of the n roots Y, y2,..., Yn of this equation he may of course
be viewed as having solved the set of linear equationsxi 2 Xn
x1 __ __ _ x - ~ ~ ~ ~ - -i
+ +...~ flI
a. y?1 a2 Y?1anY
a-Y, - I2 a2 - Y2 (Cn Y
which Binet had explicitly dealt with four years before.
BORCHARDT, C. W. (1845, Jan.).
[Neue Eigenschaft der Gleichung, mit deren Miilfe man die
seculdren Stbrungeu der Planeten bestimmt. Crelle's
Jomrn., xxx. pp. 38-45;' or, in extended form, Journ.
(de Liouville) de Math., xii. pp. 50-67; or Gesammelte
Ierke, pp. 3-13.]
For the present this paper is only noteworthy as containing
the square of the difference-product in the form of a determinant
of the particular type soon after to be named "persymmetric"
by Sylvester. M being used to stand for
{ g~2 3..n)2f
*See also Crelle's Journ., xxv. pp. 178-183 (1842), and Grunert's Archiv d.
Math. it. Phyi., xxiii. pp. 235, 236 (1854).