142] NUMERICAL TABLES SUPPLEMENTARY TO SECOND MEMOIR ON QUANTICS. 281
at-TABLE.
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
1
5
13
33
73
151
289
526
910
1514
-0
1
4
12
31
71
147
285
519
902
1502
-1
1
4
12
31
70
146
282
515
894
1492
-2
1
3
11
28
66
139
272
499
873
1460
-3
3
10
27
63
134
263
486
851
1430
-4
2
8
23
57
123
247
461
816
1379
-5
2
7
21
52
116
233
440
783
1331
-6
5
17
45
103
214
409
738
1265
-7
4
15
40
94
197
383
696
1214
-8
3
11
33
81
176
348
645
1127
-9
9
28
71
158
319
597
1057
-10
6
22
59
137
284
543
974
-11
5
18
51
120
255
495
900
-12
13
40
101
221
441
816
-13
10
33
86
194
394
742
-14
7
25
70
164
345
662
-15
20
58
141
302
593
-16
14
45
116
258
519
-17
11
36
97
222
457
-18
27
77
185
393
-19
21
63
156
340
-20
15
48
127
286
-21
38
104
243
-22
28
82
200
-23
22
66
167
-24
50
134
-25
39
109
-26
29
85
-27
68
-28
51
-29
40
-30
The numbers of each table are connected in several ways with those of the
preceding tables. One of these connexions, which is of some importance, is best ex
plained by an example: in the «/-table, 8-20, the number of terms of degree 8 and
weight 20 is 73 ; and we have 73 = 1 + 6 + 16 + 23 -1- 27, viz. (see p. 288) these
are the numbers of the terms in a 4 , a 3 , a 2 , a 1 , a 0 respectively : the complementary
factors, (for example) of a 3 are be/ 3 , &c. terms in b, c, d, e, f of the degree 5 and
weight 20, and (replacing therein each letter by that which immediately precedes it)
these are in number equal to the terms in a, b, c, d, e of the degree 5 and weight
20 — 5, = 15 ; thus the number 6 of the terms in question is that for the deg-weight
5- 15 of the ae-table : and so 1, 6, 16, 23, 27 are the numbers in the ae-table for
the deg-weights 4-16, 5-15, 6-14, 7-13 and 8-12 respectively, or (making a change rendered
necessary by the abbreviated form of the tables) say for the deg-weights 4-0, 5-10,
6- 14, 7-13 and 8-12.
C. II.
36
