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

434 HISTORY OF THE THEORY OF DETERMINANTS
each factor being less than the preceding by 2a- 1, and the whole
a function of a(a-1).
The special case is noted where a= -, and where therefore all
the n~+l resulting factors are alike. This Painvin writes in
the form
1
2,;,a 2
2 n 2
— 1 3
rv* 2
— 2.. -+2 p-3..... = (-i '+
~2t~ ~- n...p-2 2......-n+... p-4 1 -
— n p - n2 2.......* —1+2 p- 6.... = (p- -)+.... p-2+2 n
-1 p-2n
HEINE, E. (1858, Sept.).
[Auszug eines Schreibens tiber die Lameschen Functionen an
den Herausgeber. Einige Eigenschaften der Laindschen
Functionen. Crelle's Journ., lvi. pp. 79-86, 87-99.]
In the case of Heine the functions afterwards known as
"continuants" made their appearance under totally different
circumstances, namely, while he was engaged in transforming a
special homogeneous function of the second degree by means
of an orthogonal transformation. It will be remembered that
if the quadric