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

CONTINUANTS (FURSTENAU, 18712)39

397

The points of connection of this paper of Flirstenau's with the
~opening part of Jacobi's of 1850 (?), should be carefully noted.
Sylvester's anticipation (1853) of such determinant forms as those
for iD,...should also be recalled (Hist., ii. p. 418).
STUDNICKA, F. J. (1872).
[Ueber eine besondere Art von symmetralen Determinanten und
deren Verwendung in der Theorie der Kettenbrilehe. Sitzungsb.. bdhm. Ges. d. Wiss. (Prag), Jahrg. 1872, pp. 74-78.1
The determinant referred to in the title is
a. -1I
1 a2 -
1 a3....
and the fact of its skewness leads Studnic~ka, unfortunately, to
follow Cayley's method of 1847 in finding the ordinary expansion
of it.
There is then formulated the familiar 'rule' referred to by
Sylvester in his first paper of 1853.
CASORATI, F. (1872).
[Le proprieta' cardinali degli strumenti otti6i anche non centrati,...Rendiconti del Reale Istituto Lombardo, v., fasc. iv. 13 pp.]
In the-course of his investigation Casorati has to deal with a
series of quantities /3,, /35 3 /..32.., each of which, after the
second, is dependent on the two preceding it in the manner indicated by the set of equations
/A = 'a1/31 + /30,3= u2/32 + /3l + 77 -14= u3/33 + /32
35=U4/34 + /33 + 7T-3
/36 =U5/33+ /34
/3r U6/36 + /35 + 77-5
38= u7/37+ /36