n6 The Rev. Thos. P. Kirkman on 



Two of the integral 5 -partitions of 5 are 00005 an d 

 1 1 1 1 1, in dictionary order. We write them for our use thus : 



afiyde afiyce 



00005 IIII I 



In Fig. 1, afiyd are vacant, and $6 = e. is split to receive 

 the whole belt 3Bi 



In the Plate, Fig. 1 shows two dark lines in A, by- 

 mistake, instead of the single one 56. 



In Fig. 2, the first place a is split to receive the first unit 

 A of 3Bi ; the second, j3, to receive B ; the third, y, to receive 

 Ci ; the places Se to receive D x and D 2 , all of 3Bi. 



In both figures, the primes stand in their order and in 

 their postures, under their marginal triangles, as they stood 

 in the belt 3Bi. 



The dotted edges are the shifted halves of the dark 

 diagonals. These two partitions have guided us to two 

 distributions of 3Bi. 



Two of the M permutations of the 5 -partitions of 5 are 

 05000 and 201 1 1, not in dictionary order. We write them 

 for use thus 



ajjyde apyde 



05000 20111 



In Fig. 3, /3= 13 is split to receive the whole belt 3Bi. 



In Fig. 4 the first place is filled with AB ; the second, 

 (3= 13 is vacant ; the three last places in order are split to 

 receive GDiD 2 . Thus these two permutations have guided 

 us to two correct distributions of^Bi. All the primes in 

 both, read in the order of the places aflySe, stand as they 

 stood in the belt. Of Fig. 5 we shall speak later. 



The figures 1, 2, 3, 4 are not very like partitioned 

 R-gons ; but if the numbered summits (Art. 6) be 62 

 successive points on a circle, the diagonals be drawn, and 

 the marginal triangles be completed, there will be seen an 

 inscribed partitioned polygon of 62 summits. 



