362 
Proceedings of the Royal Society 
and therefore from the theory of continuants, 
2a + 6 (a + 6) 2 0 0 
1 2a + 36 (a + 2 6) 2 0 
0 1 2 a + 5b (a + 3b) 2 
0 0 1 2a + 76 .... 
0 0 0 1 
s w = J.. _ 
a a? 0 
1 2a + b (a + 6) 2 
0 1 2a + 3b 
0 0 1 
0 0 0 
• • • * i • > • « 
where the denominator is of the n ih order and the numerator of the 
( n - l) th , being formed from the denominator by the omission of 
the first row and first column. 
There is, however, another such expression for S« of more interest 
and less likely to occur to one, viz., 
0 .... 
0 
(■ a + 2b ) 2 .... 
2 a + 5b .... 
1 
1 -b - b - b - b - b 
1 na -2b -3b - 46 — (n - 1)6 
1 [n — 1 )a a — 26 - 36 — (n — 1)6 
1 (n - 2 )a a a - 26 — (n — 1)6 
1 (n - 3 )a a a a — (n - 1)6 
1 2 a a a a a 
a(a + b)(a + 26) |<3! + (n — 1)6} 
This is easily verified for the cases where n — 2 and n- 3 . When 
n = 4 we have 
1 -6-6 - 6 
1 -b - b 2b 
1 4a -26 -36 
1 4a — 2b 0 
1 3 a a — 36 
o 
e 
e 
CO 
rH 
12 a a a 
, 
1 2a a a + 36 
a(a + b)(a + 26)(a + 36)S 4 = 
