CONSTRUCTION OF KNOTS OF FEWER THAN TEN CROSSINGS. 309 



made on eighteen of our thirty inferior knots. The remaining twelve, viz. — 



6 J , 8 T , g W , s Ag , 8 Ap , s Ag , C 9 , 9 I , 9 Bw , 9 ~Dl , 9 &d , 9 lt , 



are found to be no bases. 



In 10 A above, 4 4 means 4444, and the circles are in parentheses. 



No non-prime solid knot has fewer than sixteen crossings. The simplest is 

 4 10 3 8 , 4 zo. monch., in which two opposite 4-gons are each covertical with four 

 triangles, the triangles being four pairs of collaterals. 



In order that a prime solid knot P may be a base, it must have not more 

 than three summits A3B3, which must be so placed that, by drawing a lowest 

 triangle of the non-prime Q to be formed, every pair of covertical triangles 

 shall disappear. 



All non-primes can be easily constructed by our simple rule without 

 omission or repetition when the primes of more than twelve crossings are 

 before us. 



This may suffice on solid knots until their value in electricity and magnetism 

 is so enhanced as to call for a formal treatise on the whole subject. 



VOL. XXXII. PART II. 3 E 



