1887 .] 
Dr T. Muir on Simple Alternants. 
441 
the duad 0, y + 1 along with the triads ] 
f 0, l,/? + y + 2 
0, 2, f3 + y + 1 
0 3 9. ~ + + 
for a(0, 2, g, r - 1) by considering 
the duad 0, y + 1 along with the triads ] 
(0, 2, /? + y + 1 
and the triads ] 
^0, 2-1, /3 + y- 2 + 4 
f 1? 2, fi + y 
1, 3, /3 + y- 1 
[ 1, 2-1, /3 + y~2 + 3; 
and for a(l, 2, y, r — 2) by considering 
the duad 0, y + 1 along with the triads < 
1, 2, (3 + y 
1 > 3, /3 + y - 1 
[ 1, 2 ~ 1> /? + y “2 + 3 . 
Hence, as before, the number of dovetailings is x\ (x' ) + y\ 
y ; and, therefore, the coefficient required is 
x' - {(«'- 1 ) + y'} + y f 
i.e. 1. 
Lastly, the coefficient of '2 t a (t bPcyd s is determined for a(0, 1, q, r) by 
considering 
f 0, y + 8 + 1 
[0, 1, /3 + y + 8+2 
. . . . ll,y + 8 along with each 0, 2, /? + y + 8+l 
each of the duads < 
.... ot the triads < 
IS, y+1 
for a(0, 2, y, r - 1) by considering 
f 0, y + 8 + 1 
[0, 2-1, £ + y + S-2 + 4; 
i 
each of the duads -< 
1, y + 8 
along with each 
of the triads 
0, 2, /3 + y + 8+ l 
| 0, 2 - 1 » /3 + y + 8~2 + 4 
8, y + 1 [ 
/ 1, 2, /? -h y + 8 
and along with each ) 
of the triads ) . n , Q 
l 1, 2-1, p + y + 8-2 + 3; 
