1903 - 4 .] Dr Muir on the Theory of Continuants. 
159 
and finally 
= a k,k+\ a k+l,Tt+‘i. 
— a k,k+i a k+l,k+2 
. . a, 
m,m+ 1 
K (m + 1 , m) K(m + 2, m) 
K (m + 1 ,n) K(m + 2 ,n) 
• a m,m+ 1 * + 2,w) • 
(P) 
Further, by using this to make a substitution in the previous result 
(a) there is obtained 
K (h,m) 
K (h,n) 
K (7c, m) 
K (h,ri) 
— a k-l,k a k,Jc+l 
’ K (/ i,k - 2)K(m + 2,n) , (y) 
which on putting k = h + 1 and m = M - 1 becomes 
K(7i,«- 1) K(A+ 1,»- 1) 
K(A,m) K(A+1,») 
— a h,h+i a h+l,h+‘2 • • • • a n-l,n > 
— a result which may be compared with one of Schlafli’s and 
Worpitzky’s, but which is more general in that the main diagonal 
of each “ K-Determinant ” does not consist of units. 
LIST OF AUTHORS 
1853. 
1853. 
1853. 
1853. 
1854. Sylvester 
1855. Schlafli 
1856. Ramus .... 142 
dealt with. 
PAGE 
1857. Cayley. . . .144 
1858. Painvin . . .147 
1858. Heine .... 149 
1858. Schlafli . .151 
1865. Worpitzky . . . 153 
1869. Thiele .... 157 
1870. Thiele .... 157 
whose 
Sylvester . 
Spottiswoode 
Sylvester . 
Sylvester . 
ritings are herein 
page 
. 130 
. 134 
. 135 
. 138 
141 
141 
( Issued separately, February 26, ] 904. ) 
