Or 
PROFESSOR TAIT ON KNOTS. 15 
and ADBECADBEC\|A 
one of the two forms of which is the pentacle or Solomon’s seal 
§ 8. The case of six intersections gives the following choice : — 
Cee) Ey vit) AB 
DE, EAS Bee 
EARLE eAy Bie 
I ages Gy 01D 
I found, by trial, that there are 80 possible arrangements included in this form ; 
and that the following 20 alone are distinct. I have appended to each the number 
of apparently different forms in which it occurs among the 80 arrangements -— 

1.CDEFAB Unique 11. EF ABCD Unique 
2,CDFBA E Six forms 12. DF ABCE Six forms 
3. CD FAB E Six forms 13. CF ABDE Six forms 
4 CDAFBE Six forms - 14. DF ACBE Six forms 
5. CD BF AE Three forms 15. DF B ACE Three forms 
6. CE F BAD Six forms 16. CF BADE Six forms 
7. CE FABD Six forms 17. CAF BDE Six forms 
8. CE AF BD Three forms 18. CABF DE Three forms 
9. DE F ABC Unique 19. DAFC BE Two forms 
10. CF E BAD Two forms 20. F ABC DE Unique 
Of these, all but (5), (6), (7), (8), (12), (14), (15), (18), violate the conditions 
of § 5, and therefore do not correspond to real knots. Of those excepted the 
schemes agree in pairs when the branch first taken from the starting-point is 
changed. 
Hence there are only four forms of 6-fold knottiness. These are as follows :-— 
(a). (5) and (18) agree in giving the scheme 
ACBACBDFEDFE|A 
of which one form is the following :— 
This form consists of two separate trefoil knots. 
