218 



average), and contained 41*8 grs. of nitrogen daily. It was largest 

 on the Sunday, and the faeces then contained an increase of nitrogen 

 equal to the quantity lost by the urine on that day. Hence the assi- 

 milation was defective, but it was increased by labour. 



The author then showed the relations of urea and carbonic acid, 

 and their dependence upon food, season, and period of the day, and 

 discussed the relation of urea to exertion and nutrition, showing that 

 unless there be continued waste of the nitrogenous tissue, there 

 cannot be any important increase of urea from exertion. 



The paper was accompanied by numerous explanatory tables and 

 curves. 



The following communication was read : 



<*0n the Theory of the Polyedra." By the Rev. T. P. 

 KIRKMAN, M.A., F.R.S., and Hon. Member of the Lite- 

 rary and Philosophical Society of Manchester. Received 

 May 10, 1861. 



(Abstract.) 



The complete resolution of the problem of the polyedra embraces 

 the construction of all P-edra Q-acra, with an account of the symmetry 

 of the solids when symmetrical. Such construction being impracti- 

 cable from the magnitude of the task, it is desirable that a method 

 should be found of classifying and enumerating the P-edra Q-acra, so 

 that from this knowledge of the inferior polyedra, the same can be 

 obtained concerning the higher, without any constructions, and with- 

 out any tentative process. 



I have found that all attempts to enumerate a separate and well- 

 defined family of the P-edra Q-acra, beyond that I have called * The 

 partitions of the R-pyramid' (Phil. Trans. 1858), have been fruitless, 

 and that the simplest method of solving the problem is to solve it 

 entirely. 



It is necessary first to have an accurate classification of polyedra as 

 to symmetry. This is 



1. Zoned symmetry; 



2. Zoneless axial symmetry ; 



3. Mixed symmetry, both 1 and 2 ; 



4. Neuter symmetry, neither 1 nor 2 ; 



5. Asymmetrical. 



