PROFESSOR C. N. LITTLE ON ALTERNATE KNOTS OF ORDER ELEVEN. 255 



5. The manner of using these plates to identify a given elevenfold knot can 

 be seen from the following example. Having drawn at 

 random the figure in the margin, it is to be noticed that it is a 

 reduced, non-composite form of eleven crossings. Mark the 

 parts of the leading partition, and write down Listing's type 



symbol — 



f 6 2 3 2 2 2 

 1 54 2 32 3 



As the leading partition has six parts, the knot belongs to Class VI. Write now 

 a graph of the leading partition showing how the parts are arranged : — 



/2-3x X 



6 -2- 6 



\3/ 



The two 6-gons have six connections, a 3-gon and 2-gon, a 2-gon, a 3-gon, and two 

 single crossings, which may be represented, in order, by a, b, c, d, d, and these letters 

 have six circular arrangements as follows : — 



abcdd bcdad 

 acbdd acdbd 

 cabdd abdcd 



But for each of these arrangements a may have three forms since c is asymmetrical, as 

 follows : — 



-2-3 = 



-3 = 3- 



= 3-2- 



There are, therefore, eighteen distinct forms of this knot. A glance at Plate II. 

 shows that it is the last of the six eighteen-form knots there given — No. 353. 



