4 



" The problem of the enumeration of the polyhedra is one 

 of extreme difficulty, and I am not aware that it has been dis- 

 cussed elsewhere than in Mr. Kirkman's valuable series of 

 papers on this subject in the Memoirs of this Society, and in 

 the Philosophical Transactions. A case of the general problem 

 is that of the enumeration of the polyhedra with trihedral 

 summits ; and Mr. Kirkman, in the earliest of his papers, viz., 

 that ' On the Representation and Enumeration of Polyhedra' 

 (Mem. Vol. XII., pp. 47, 70, 1855), has in fact, by an 

 examination of the particular case, accomplished the enumera- 

 tion of the octahedra with trihedral summits. 



" It is intended, in the present paper, to give a method for 

 the derivation of the triangular-faced polyacrons of a given 

 number of summits from those of the next inferior number of 

 summits, and to exemplify it by finding, in an orderly manner, 

 the triangular-faced polyacrons up to the octacrons ; thus, as 

 regards the examples, stopping at the same point as Mr. 

 Kirkman ; for although perfectly practicable, it would be very 

 tedious, and there would be no commensurate advantage to 

 carry them further." 



At this, the first Meeting of the Session, a large number 

 of books, chiefly Transactions of learned Societies abroad, 

 were laid on the table. The Chairman congratulated the 

 Society on the rapid increase of its Library, which was mainly 

 owing to the great ability and zeal of Mr. Ekman, the 

 Honorary Librarian. 



