1904-5.] Dr Muir on the Theory of Continuants. 
679 
Scott, R. F. (1880, Feb.). 
Mansion, P. (1880, March). 
[A Treatise on the Theory of Determinants, and their applica- 
tions in analysis and geometry. xii + 251 pp. Cambridge.] 
[Elements de la theorie des determinants, avec de nombreux 
exercices. 3 e edition. 64 pp. Mons.]. 
The title of one of Scott’s chapters (chap. xiii. pp. 169-179) 
is “Applications to the theory of continued fractions,” and it is 
accurately descriptive of the contents. As in Gunther’s text-book, 
both ascending and descending continued fractions are dealt with 
by means of determinants, the numerator of the last convergent 
to 
+ b 2 4 - . . . + b n 
$2 ^71 
viz., the determinant 
h 
-1 
a 2 
-1 
h 
a 5 
. . . 
K 
. a n 
being actually spoken of as “ the continuant for an ascending 
fraction.” FTo new property of continuants is given. 
The continuant exercises in Mansion’s third edition occur on 
pp. 13, 21. 
LIST OF AUTHORS 
whose writings are herein dealt with. 
1854. 
Smith . 
PAGE 
. 648 
1875. 
Diekmann . 
page 
. 673 
1872. 
Studni&ka . 
. 649 
1876. 
Guldberg 
. 673 
1872. 
Hattendorff 
. 650 
1876. 
Salmon 
. 673 
1872. 
Casorati 
. 650 
1877. 
Muir . 
. 673 
1872. 
Bauer . 
. 652 
1877. 
Muir . 
. 674 
1872. 
Nachreiner 
. 658 
1877. 
Gunther 
. 677 
1873. 
Gunther 
. 660 
1878. 
Baraniecki . 
. 677 
1873. 
Gunther 
. 663 
1878. 
Mansion 
. 677 
1873. 
Gunther 
. 666 
1878. 
Muir . 
. 677 
1874. 
Muir . 
. 667 
1878. 
Scott . 
. 678 
1874. 
Muir . 
. 670 
1879. 
Sylvester . 
. 678 
1874. 
Wo LSTEN HOLME . 
. 670 
1880. 
Scott . 
. 679 
1874. 
Gunther 
. 671 
1880. 
Mansion 
. 679 
1875. 
Gunther 
. 671 
( Issued separately May 17, 1905.) 
