PROFESSOR TAIT ON KNOTS. 157 
one form fromeach of 82 groups of seven, and 5 unique forms. Here they 
are— 
CDEFGAB 30. CEBGDAF 59. CAF GBED 
= 

2 CDEGABF 31. CEBAGDF | 60. CAFGDBE 
3 CDEAGBFEF 32. CE GABDE |.61. CAFBGED 
4* CDEBGAF 33.° CF GADBE | 62.,CAGBDEF 
&. CDEBGAE 34.%>* CF GABED | 63.* CABGDEF 
6 CDFEFGBAE 35. CEGBAED |.64. DEFGABC 
aac DE AG BE 36.. CE GBADE |}.65. DEGABCFE 
wee DG E ABE 37. CF. GBDAE | 6. DEGACBFEF 
§ CDGFBAE 38° CF AGBDE | 67.* DEGBACE 
10. CDGABEF 39° CF AGDBE | 68. DEGCABFE 
ie CDGBRAE SF 40* CE AGBED | 69. DEAGBCF 
12, CDAGBEF AL CEFABGODE|.70. DEAGCBE 
mC DABG EF 42 OE AB GED!) 71% DE.G ABC E 
14* CDBAGEF 43, 1C BB GA DE |i 724 DE GA CBE 
-15* CDBGAEF 44. CF BGDAE| 73. DFGBACE 
fo -CHRFGABD | 4 CEFBGAED | 7:DFAGCBE 
im CEEGBAD | 4. CFBAGED |.~7%. DGABCEF 
18. CEFGADB 47. CF BAGDE 746 DGACBEF 
19 CEFAGBD | 48. CGEBADF vw DGBACERER 
290.* CEGFBAD | 49. CGEBDAF 78: 0G B.C A EP 
2 CE GE DAB 50. CGFABDE 72 DAGBCEF 
22* CEGABDF 5 © GLE A BED). 80:--DA’'G.C B EF 
23. CEGADBFEF be (CG Py Ave) | <8. EG. AvB. Cp 
2* CEGBADF San OG BAP EF 82. EGABCDF 
ae CE GBD AF 4. CGEFBAED | 83% EGABDCF 
por Cin AG BDF ab: O1G As By DBE 84. EGACBDF 
tae CEAGDBFE 56. CGABDEF 8.* EGBADCFE 
ms CEABG DF 57. CGBADEF 86. FGABCDE 
29. CEBGADF 58. CAFGBDE 87. GABCDEF 


On testing these by the rules of § 5, I found that 22 only, viz., those marked 
with an asterisk, correspond to real knots. 
§ 10. When we study these groups by the method of § 5, we find that more 
than one of them correspond to different readings of the scheme of one and 
the same knot.. Of course that knot will be the least symmetrical which has 
the greatest number of essentially different schemes. The following grouping 
has thus been arrived at (the notation is that of § 5 above) :— 
VOL. XXVIII. PART I. 258 
