40 
In lower orders Professor Tait has found: 
Orders. Forms. 
3 1 
4 1 
5 2 
6 3 
7 10 
8 27 
9 100 
Knots. 
82 
] 
4 
C. N. Little—Knots, with a Census for Order Ten. 
The fourth column contains the numbers as they are given by Tait, 
the perversions of knots not being counted. 
In so long a labor as is involved in making such a census the 
opportunities for error are many. 
Any errors or omissions that 
may be found in the census are to be attributed to the writer rather 
than to the method, which is simple and direct. 
TABLE I.—Partitions of 20. 
| 
Crass II. Cu. IV.—Contin’d|Cu. V.--Contin’d.| Crass VI. |cz. VIL-Conti’d 
a IX. 992 (8623 IE 1025 642° 
Cuass III. 8732 | 85322 II. 9324 11.4 63224 
{ 1082 IX. 8642 II. 4 8472? II 8424 5295 
I eis 863° 84322 a 83223 54324 
* \ 1064 8572 834 ( (524 53393 
l 105? 8543 ; 7293 II. . 74322 4394 
922 xe 848 76322 73592 423298 
983 7242 75492 xX. 6224 43492 
974 axe 232 75329 65328 359 
965 7652 74239 X. 64723 
VIII. 8%4 1643 1498 643222 Crass VIIL 
875 IX, 1573 624.22 6342 5 
VIII. 86? 754? 62329 52423 ee 
7°6 IX. 622 65222 523292 i i a 
6°53 542322 
Scoala IX. 6°42 te 54332 432° 
9 3424 
10532 65°4 6432 535 
10 10422 xan 54 64232 Xe 42° CLass XI. 
1043? CLaAss V. 5332 423°2 
( 972? ll { 1042° 52429 4°34 106 oo 
9632 > | 10322? 52432 . 3°2 
II.-2 9542 9528 5433 Crass VII, (ieee 
9532 IL ) 2832 45 Il. 828 aie 
| 9423 9332 I. 7325 "210 
y TABLE II.— Clutches for p=3. 
re We A! a oh i a) eee ee 
Partition. =} o 3 Partition. =) 23 Partition, 228 
929 811 Aa 974 631 Ac 875 532 Ad 
983 ea o} 965 5 41 Ae 7°26 43 3 Af 
= 
ee 
