142] NUMERICAL TABLES SUPPLEMENTARY TO SECOND MEMOIR ON QUANTICS. 277 
of bottom terms of each of the preceding columns: thus in the af- or quintic table 
the complete column for degree 3 would be 
D 3 
W 8-7 
-0 6 
-1 6 
-2 5 
-3 4 
-4 3 
-5 ~2~ 
-6 1 
-7 1 
where the concluding terms 2, 1, 1 are the bottom terms of the three preceding 
columns respectively. And the meaning is that for degree 3, and weight 8, or 7, the 
number of terms is = 6; for weight 7 — 1, =6, the number of terms is = 6 ; and 
similarly for weights 5, 4, 3, 2, 1, 0 the numbers are 5, 4, 3, 2, 1, 1; the numbers are 
those of the terms 
w. 
0 
l 
2 
3 
4 
5 
6 
7 
8 
a 3 
a?b 
a 2 c 
aH 
a 2 e 
«*/ 
abf 
acf 
adf 
air 
abc 
abd 
abe 
ace 
ade 
ae 2 
b 3 
ac 1 
acd 
ad 2 
by 
bef 
b 2 c 
Wd 
We 
Wee 
bde 
be 2 
bed 
bd 2 
c 3 e 
c 3 
chi 
cd 2 
No. 
l 
l 
2 
3 
4 
5 
6 
6 
6 
The like remarks and explanations apply to the other tables. 
ad-TABLE. 
D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 
0 2-1 3 
5-4 
6 
8-7 
9 
11-10 
12 
14-13 15 
17-16 
18 
20-19 
21 
23-22 
24 
26-25 
27 
1 1 2 
3 
5 
6 
8 
10 
13 
15 
18 
21 
25 
28 
32 
36 
41 
45 
50 
-0 
—“L1_ 
3 
4 
6 
8 
10 
12 
15 
18 
21 
24 
28 
32 
36 
40 
45 
50 
-1 
1 
4 
5 
7 
9 
12 
14 
17 
20 
24 
27 
31 
35 
40 
44 
49 
- 2 
1 
7 
8 
11 
13 
17 
19 
23 
26 
31 
34 
39 
43 
49 
- 3 
| 
10 
12 
15 
18 
22 
25 
29 
33 
38 
42 
47 
-4 
1 14 
16 
20 
23 
28 
31 
36 
40 
46 
-5 
1 
19 
21 
26 
29 
35 
38 
44 
-6 
L 
24 
27 
32 
36 
42 
-7 
■| 30 33 39 -8 
| 37 1 -»