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

CONTINUANTS (GUNTHER, 1874)

415

a way calling for no special note are those of Hattendorf (1872),
Diekmann (1875), Guldberg (1876), Baraniecki (1878), and Mansion
(1878).
GUNTHER, S. (1875).
[Das independente Bildungsgesetz der Kettenbriiche. Denkschr. d.
k. Akad. d. Wiss. in Wien: Math.-Nat. Cl., xxxvi. pp. 187-194.]
Of this paper the portion which is not introductory and semihistorical concerns the development of
X -(l
al.X - a2.a* 2..X.......or say,........ X -an-1..... - n-1 X
in a series arranged according to powers of x.
The result obtained is, as might have been expected, that to
which he would have been led by the use of the combinatorial
'rule' more than once already referred to, and found fully enunciated by Stern in 1833 (Crelle's Journal, x. p. 6).
HELMLING, P. (1876).
[Anwendung der Determinanten zur Darstellung transcendenter
Funktionen. (Title also in Latin.) Dissert. 43 pp. Dorpat.]
The subject here is the evaluation of certain definite-integrals
by establishing for each a trinomial or quadrinomial recurrenceformula after the manner of Euler* (1777), and then making use of
continuants or the analogous special determinants noted by Sylvester
in 1853 as arising in this way (Hist., ii. p. 416). No new property
is brought to light.
SALMON, G. (1876).
[.... MODERN HIGHER ALGEBRA. Third Edition.
xx+318 pp. Dublin.]
In this edition the sketch of the theory of determinants with
which the book opens is extended to fifty pages, and half a page* Acta Petrop., i. p. 3.