11 
Ordinary Meeting, November 17th, 1857. 
W. Fairbairn, F.R.S., &c., President, in the Chair. 
A paper was read by the Rev. Thos. P. Kirkman, M.A., 
F.R.S., “On the triedral partitions of the ic-ace, and the 
triangular partitions of the a;-gon.” On introducing it, the 
author gave a brief statement of the problem of the Polyedra, 
with which the present subject was connected. He showed 
that the theory of these solids, which has so long been a sealed 
secret, has been in part laid open in four memoirs of his own, 
printed in the Philosophical Transactions of 1856 and 1857, 
copies of which are in the library of the society. The first 
step is the important theorem, that every p-edral ^'-acron can 
be reduced, by the vanishing of a single edge, either to a 
(/)— l)-edral g'-acron, or to a p-edral {q — l)-acron. The 
next is the reduction of the whole problem to this; — How 
many a:-edra are r-gonous, i.e. can be reduced thus to the 
pyramid on an r-gonal base? The present memoir gives 
analytical and explicit expressions of the number of one great 
class of r-gonous ic-edra. But much yet remains to be 
effected in this very intricate theory. 
In the course of conversation on the library, and the sum 
required for the binding and preservation of the books, espe- 
cially the transactions of learned societies at home and from 
abroad, a regret was expressed, that its scientific treasures 
are so seldom inspected and turned to profit. This elicited 
the remark, that it was highly improbable that cultivator||Of 
the more abstruse sciences would arise, until more substantial 
rewards were placed within reach of students ; and an opinion 
was expressed, that if it were not for the fellowships and 
other preferments in the gift of our great universities, there 
would be a lower standard of learning and fewer cultivators 
of it, in this country than at present. To this it was replied, 
that there are already scholarships offered at Owens College 
Proceedings No. 4. 
