312 



or r-gon ; so that the present memoir may be considered as a com- 

 pletion, or rather an extension and completion, of the investigations 

 in his former memoir. The number of distinctions to be made in the 

 problem of the present memoir is very great ; thus, a partition of the 

 polygon may be either reversible or irreversible ; and if reversible, 

 then the axis of reversion may be either agonal, monogonal, or dia- 

 gonal, that is, it may pass through no angle, one angle only, or two 

 angles of the polygon ; and in the last case it may be either drawn or 

 undrawn. Again, there may be a single axis or a greater number of 

 axes of reversion : in the case of m such axes, the partition is said to 

 be m-ly reversible ; and in like manner an irreversible partition may 

 consist of a single irreversible sequence of configurations, or it may 

 contain such sequence m times repeated; it is then said to be m-ly 

 irreversible. In consequence of this multiplicity of distinctions, the 

 author's final results are necessarily very complicated, and cannot be 

 exhibited in an abstract ; they appear, however, to contain a com- 

 plete solution of the problem, i. e. to afford the means of finding, 

 without anything tentative, the number of the ^-partitions of an 

 r-gon when k and r are given numbers. 



December 18, 1856. 



The LORD WROTTESLEY, President, in the Chair. 

 The following communications were read : , 



I. "On the Scelidothere (Scelidotherium leptocephalum, Owen), 

 a large extinct Terrestrial Sloth." By Professor R. OWEN, 

 F.R.S. Received October 30, 1856. 



(Abstract.) 



The extinct species of large terrestrial Sloth, indicated by the 

 above name, was first made known by portions of its fossil skeleton 

 having been discovered by Charles Darwin, Esq., F.R.S., at Punta 

 Alta, Northern Patagonia. These portions were described by the 



