332 



PROFESSOR TAIT ON KNOTS. 



of a knot, do not alter the partitions. But it is also to be remembered that 

 identity of partitions, alone, does not necessarily secure identity of form. 

 The 3, 4, 5, and 6-folds may be disposed of in a single line. 



33 

 222 



71=4 



332 



w=5 



442 55 



3322 , 22222 



n=6 



4332 



543 

 33222 



552 

 33222 



Here the bar indicates not only that the right and left-handed partitions 

 are alike in number and value, but also that they are similarly connected, i.e., 

 that the knot is amphicheiral. 



I. 



5333 4433 

 43322 or 43322 



For the Sevenfolds, we have 



II. 



5432 

 43322 



or 



5432 

 33332 



III. 



5432 



44222 



or 



4433 

 44222 



IV. 



644 

 332222 



5522 

 44222 



VI. 



VII. 



662 



77 



332222 



2222222 



For the Eightfolds, 



I. 





II. 





III. 









54322 54322 

 53332 or 44332 



54322 

 or 43333 



53332 

 44422 ' 



44332 



44332 



3r 44422 



IV. 



V. 





VI. 





VII. 



5443 



54322 

 44332 





6532 

 32 333322 



6532 

 or 433222 





333322 



0r 54322 0r 443 



43333 



VIII. 





IX. 



X. 



XI. 





6433 

 433222 



5443 

 or 433222 



5542 

 433222 



54322 54322 

 44332 or 54322 



55222 

 44332 



55222 

 or 54322 



XII. 



XIII. 



XIV. XV. 



XVI. 



XVII. XVIII. 





6532 

 433222 



655 763 754 

 3322222 3322222 3322222 





772 



54322 



55222 



3322222 



I. 



4 I in:; 

 133332 



Finally, for the Ninefolds, the list is 



II 



I. 



63333 63333 54333 54333 44433 44433 



533322 or 443322 or 533322 or 443322 or 533322 or 443322 



