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

DETERMIINANTS IN GENERAL (GUNTHER, 1875)

55

determinants; this, however, in the second edition he was well
advised in relegating to a less prominent position. A third noteworthy characteristic is the assigning of a whole chapter (vi.) of
thirty pages to Kettenbruchdeterminanten. The geometrical applications extend to only twelve pages. And, lastly, we may mention
that, there being no footnotes, the bibliographical references are
collected at the end of each chapter, where they form rather
formidable-looking lists.
So far as general determinants are concerned, there is nothing
fresh to note.
MANSION, P. (1874, 1875, 1876).
[Principes de la theorie des determinants, d'apres Baltzer et Salmon.
Nouv. Corresp. Math., i. pp. 114-128, 170-178, 206-222.]
[ELEMENTS DE LA THIORIE DES DETERMINANTS, d'apres Baltzer et
Salmon. 44 pp. Mons.]
[INTRODUCTION A LA THEORIE DES DETERMINANTS. A l usage des
etablissements d'instruction moyenne. 24 pp. Gand.]
The second of these is a separate publication of the first; it
is a singularly clear though short exposition with a sufficiency of
worked and unworked examples to make it very suitable for use in
schools. Nothing so good for beginners had as yet appeared in
French. The third, as may be guessed, is still more elementary,
having its origin in notelets contributed to the Revue de Vl'nstruction
Publique en Belgique (1875, 1876).
GUNTHER, S. (1875).
[Didaktische Bemerkungen zur Determinantentheorie. Zeitschrift
f. math. u. naturw. Unterricht, vi. pp. 138-150.]
The remarks concern (1) the cofactor of a single element, or of
the product of two or more elements, (2) special cases arising in
the solution of simultaneous linear equations, (3) zero-axial skew
determinants of even order. Under the last head the attempted
proof of Cayley's property is based on a surprisingly questionable
lemma.