1904 - 5 .] Signed Primary Minors of a Determinant. 
375 
and consequently that the sum of the signed primary minors of a 
continuant of the n ih - order can he got when the corresponding 
sums for the cases of the (n - 1 ) th and (n - 2 ) th order are known. 
(5) By repeated application of the preceding result we obtain 
ultimately an expression involving only the continuants 
. and their co- 
efficients. The following is the general theorem thus reached : — 
If the cofactors of a n , a n a n _ 1 , a n a n _ 1 a n _ 2 , . . .in the continuant 
/ \ ... \ 
l a 15 a 2 , . . . , a n 1 he denoted by K n _j , K n _ 2 , K n _ 3 , . . . , and 
\ Ci . . . / 
the cofactors of a x , a x a 2 , a^ag , . . .be denoted by H n _j , H n _ 2 , 
H n _ 3 , . . . , the sum of the signed primary minors of the con- 
tinuant K n is 
K„_, + K„_ 2 (l , + <v_! § Hj , - 1 ) (VI) 
"h K w _g(l ) b n _2 + c n _ 2 , b n _f ) n _ 2 + c n _^c n _ 2 $ H2 ) — Hi , 1) 
”1“ 4( 1 ) b n — 3 c n _ g , b n _ 2 b n _ g + c n _ 2 c n _ g . b n _ f) n _ 2 b n _£ 
+ c n _^c n _ 2 c n _^ $ Hg , — H 2 , Hj - 1) 
+ 
+ (1 , &1 + Cj , & 2 &1 + C 2 Ci , • • . • $ H n _i , — H n _ 2 
Bor example, the sum of the signed primary minors of the con- 
tinuant Kg, 
b i 
a i a 2 J + KX 1 > b 2 + C 2$ a 3’ ~ !) 
i.e. 
i.e. 
+ (1 > b \ + G 1 , b f\ + C 2 C 1 $ a 2 a S b 2 C 2 ' > 1) > 
a x a 2 - b Y c x + «i(a 3 - b 2 - c 2 ) 
+ ¥3 ~ b 2 c 2 - a s( b l + C l) + ( b 2 b l + C 2 C l) > 
a Y a 2 + a 2 a^ + a^ - a 1 (b 2 + c 2 ) - afb-^ + cf) 
— b-x^ — b 2 c 2 + bf> 2 -f c x c 2 . 
