1904 - 5 . ] Dr Muir on the Theory of Continuants. 
673 
s p _ r _ 2 = n- 2 p + 2r + 3 + 2 (p - r - 3) t = n 
Ya 
c j5-r-3 °p-r-2 jLmJ ' 
Z 2 ^2 
“^2 
a: 
Sp_ r _ 2 = K+2r + 3 + 2(p-r 
verstanden.” 
3) t = s p _ r _ 2 + 2 
As an example of the effectiveness of this formula, the case 
where n = 1 6, p = 7 is fully worked out. 
Diekmann, J. (1875). 
Guldberg, A. S. (1876, June). 
[Einleitung in die Lehre von den Determinanten und ihre 
Anwendung . . . viii + 88 pp. Essen.] 
[Determinanternes Teori. viii 4- 112 pp. Kristiania.] 
Of these two text-books, the first devotes a page and a half 
(pp. 23-24) to the relation between determinants and continued 
fractions ; the second indirectly touches on the subject by occupying 
a page (pp. 62-63) in showing that 
x V\ • 
-IIP* • 
. - 1 x p 3 
.-11 
x + p 1 p 1 
p 2 x + p 2 + Pz . 
Salmon, G. (1876, Sept.). 
[Lessons introductory to the Modern H-igher 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 — 
a model of compact exposition — is assigned to the special form we 
are now considering. The name “ continuant ” is adopted. 
Muir, Th. (1877, Jan.). 
[A theorem in continuants. Philos. Magazine , (5), iii. pp. 
137-138. 
The theorem in question is 
co + ape , o> + ape , 
)= 
co + ape , co + ape , 
+ a? 
> ’ * * 
. aj Vq 
) 
. . a n + xj. 
PROC. ROY. SOC. ED1N. — VOL. XXV. 43 
