1913-14.] Some Factorable Continuants, 
and perform the operations 
225 
Cj + C 3 + C 5 + c 7 , 
C 2 + C 4 + C 6 + C 8 , 
E 8 + 9E 6 - 5E 4 - 5R 2 , 
R r + E 5 -|E 3 -4E 1 , 
C 3 + f c 5 + fC 7 , C 5 -C 7 , 
C 4 + |C 6 -C S , C 6 - 9C 8 , 
-^G _ f-^4 - > -^4 “ -^2 ’ 
R 5 - f R 3 + tRj. » R 3 -Ri, 
and we have 
a f3 
(3 a 108 + 1) 
0 a f(/3 + 2) 
!(£ + 2)' a 4(0+3) 
0 a M±l) 
-K/8 + 4) a 
0 a 
- 5 
- 5(/3 + 6) a 
= (a 2 - /3 2 )(a 2 - 0 + 2 2 )(a 2 ~/3 + 4 2 )(a 2 - /3 + 6 2 ) 
= (<2 + + (3 + 2)(a + (3 + 4)(a + (3 + 6) 
(a-0)(a-0-2)(a-0-4)(a-0-6). 
5. Other and more general types of continuants than T tt given in art. 2, 
whose quadratic factors are brought out by the same set of line-multipliers, 
are the following : 
(2 n-W 
2 n - 1 
a + (2n — 2)y b ( 2»-2)(q + y ) 
3-2 n 2n - 3 
2{^+ (2w - 3)8} a (2w - 3)( 0 + 28) 
5-2 n 2n- 5 
(2n-2XP+_S) fi + ( 2n-2)S 
2n - 3 3-2 n 
(2n — l)a 
274-1 
2w 
= {a&-a0}{a5-(a + 2y)(0 + 2S)} . . . - (a + 2» - 2. y)(fi + 2n - 2 . 8)}, 
VOL. XXXIV. 15 
