304 REV. T. P. KIRKMAN ON THE ENUMERATION, DESCRIPTION, AND 



58. We demand next the number of the imsolid 9-fold knots, and first, 

 of those which have no concurrence. 



To construct these we are to lay 2 upon 7, 3 upon 6, 4 and 2 2 upon 5, and 

 32 upon 3. 



For 2 upon 7 (art. 34) imposing 4 Ajfc, we get 



On 7 A , 9 B» ; 



„ 7 B , 9 Bp and 9 B£ ; 



„ 7 C , 9 Br; 



„ 7 1) , 9 os ; 



„ 7 E , 9 B£ , 9 B% , 9 Bv : 



„ 7 F , 9 Bw , 9 Baj ; 



„ 7 tx , 9 by ; 



j) 7 tl > gt)2! , g^<^ j 



On 7 I , 9 C5 , 9 Cc ; 

 „ 7 K. , 9 La , 9 Le ; 

 „ 7 L , 9 C/ ; 

 „ r M, 9 C^; 

 „ 7 JN , gL/i/ ; 



„ 7 R , qLj . 



On 7 J we do nothing, because we cannot cover both its least marginal 

 charges ; and nothing on 7 P, because we cannot both spoil the concurrence and 

 cover the least marginal charge. 



59. For 3 upon 6, the charge must be 5 Affc (art. 26) or 3 Af, or 3 A/e, 



5 Affc on 6 A gives 9 C& and d Cl ; 



C B „ 9 Cm , d Cn , 9 Cp ; 



» 0^ » 9^2 • 



On 6 D we cannot cover both marginals 4 A/c . 

 On 6 E we cannot cover both. 



On 6 F, 5 Afc imposed to spoil the concurrence would be 5 A1fc on 3 A 

 wrongly constructed by one charge 6 Affc only. 



On 6 G we cannot both spoil the concurrence and cover the least marginal. 

 On 6 H it requires two charges to spoil the two concurrences. 

 Next, for 3 upon 6 again, 



3 A/ on C A gives 9 Cr; 



3 A/e on 6 A „ 9 Cs , 9 Ct , 9 Cw , 9 Cv , 9 Cw ; 



for the e charged on A (art. 41) is in turn every different edge, a,£,c,6?,0. 



s Aff on 6 B gives 9 Ca; , 9 Ct/ ; 

 s Afe on C B „• 9 Cz , 9 Da ; 



3 A/on 6 C 



,D6: 



3 A/e on C „ S)c : 



3 A/on c F „ 9 T>d; 

 3 Afe on fl J „ 9 De . 



