1904-5.] Dr Muir on the Theory of Continuants. 677 
Gunther, S. (1877, June). 
Baraniecki, M. A. (1878, Nov.). 
Mansion, P. (1878, June). 
[Lehrbuch der Determinantentheorie fur Studirende. 2 te 
durchaus umgearbeitete .... Auflage. xii + 209 pp. 
Erlangen.] 
[Teorya Wyznacznikow (Determinantow) ; Kurs Universytecki. 
xxiv + 600 pp. Paris.] 
[Elemente der Theorie der Determinanten, mit vielen Uebungs- 
aufgaben. vi + 50 pp. Leipzig.*] 
Although continued-fraction determinants are dealt with in all 
of these text-books, there is nothing noteworthy in them to detain 
us. Gunther’s new matter refers more directly to the subject of 
the fractions than to the related determinants. Baraniecki gives 
six pages (pp. 447-453) of exposition, confining himself to what 
we have called “ simple ” continuants, and assigning them the 
first place (§ 108) in his chapter on skew determinants. Mansion, 
quite appropriately in view of the scope of his booklet, introduces 
(p. 18) two or three properties merely as exercises for the 
student. 
Muir, Th. (1878, Sept.). 
[On the word “ Continuant.” American Journ. of Math., i. 
pp. 344.] 
Sylvester having, without knowledge of the circumstances, 
complained of the introduction of the word “ continuant,” the 
introducer had to explain that the word had been proposed in 
ignorance of Sylvester’s papers of 1853, and that, as soon as this 
ignorance was removed, he had drawn pointed attention to those 
papers, persistently adhering, however, to the use of the new word 
for four reasons, which are shortly stated. 
In a note, Sylvester agrees that the second and third of the 
reasons afford “quite a sufficient justification for the use of the 
word in question.” 
* This the author reckoned as the second edition of his “Elements” 
published at Mons in 1875. 
