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

472 HISTORY OF THE THEORY OF DETERMINANTS

ENNEPER, A. (1861, 1865).
[Zur Theorie der bestimmten Integrale. Zeitschrift f. Math. u.
Phys., vi. pp. 289-310.]
[Ueber eine Determinante bestimmter Integrale. Zeitschrift f.
Math. u. Phys., xi. pp. 69-77.]
Of the five notes composing the first of these two papers the second
(pp. 294-300) concerns Catalan's first determinant of 1839. This
Enneper improves in neatness by reducing to the order n —1, the
result now being
Ia,,-l a.- -2
' aI u __u
J~n-i
Rn B. R * *- R2
0 an- a2
r^-^ pzn —1 p2l
S Rjl - -a-...... j a]
(^_ pn-a,,_2 a,
Rn j Rn-1 R- n
where
a >a2>a... > a,_2,
R = (a 2- )..... (a2 U2) (u-a2)... ( U-a2_ p<n,
and R,, = ^ /(a-u2-u2)... (<^_L- u).
In the third note of the same paper he makes an equal improvement on Tissot's determinant of 1852; of Catalan's second
determinant of 1839 he says nothing.
His paper of 1865, however, is devoted to showing that Catalan's
two results are not essentially different, the first being deducible
from the second,-a not unnatural conclusion since the two are
viewable as generalizations of the expressions for the surface and
volume of an ellipsoid.