376 
Proceedings of Royal Society of Edinburgh. 
SESS. 
(6) For the case of a ‘simple’ continuant, i.e. when each of 
the b’s is 1 and each of the c’s is -1, the expression (VI 
becomes 
(<h a 2 ’ * 
• «») 
"I - (a^a 2 . . 
• a n-\) * a n 
+ (a 1 a 2 , . 
. a n _ 2 ) . {(a w _ 1 a n ) + 2| 
+ (u 4 # 2 . . 
. a n _ 3 ) • {(® w -2 W n-i®7t) + 
+ (a^a 2 . . 
• a„- 4 ) • B to -3a„- 2 a»-ia») + 2(a B . 
+ 
and therefore, like the continuant itself, has all its terms 
positive. (VII) 
For example, the sum of the signed primary minors of the 
continuant ( a Y , a 2 , a 3 , a 4 ) is 
i.e. 
(a x a 2 a^) + (a^) • a x 
+ a l ■ {( ffl :A) 
+ {( < W*4 ) + 2« 4 } 
+ a Y + a 3 + {a x a 2 + l)a 4 + afa 3 a^ + 3) 
+ a 2 a 3 a 4 + a. 2 + 3a 4 , 
i.e. 
a{d 2 a 3 + a 4 a 2 a 4 + a Y a z a^ + a 2 a 3 a 4 
+ 4a^ + a 2 4 - a 3 + 4a ^ . 
(7 ) If the expression (VI) in § 5 be arranged in the order of the 
H’s and their cofactors, it becomes 
H m _ 4 + H n _ 2 (l , + Cj $ K 4 , - 1) (VIII) 
+ H n _ 3 (l , b 2 + c 2 , bf 2 + c 4 c 2 jj K 2 , - K 4 , 1) 
+ ..... 
which according to (VI) is the sum of the signed primary minors 
