573 



XXIV. " Supplementary Researches on the Partition of Num- 

 bers." By ARTHUR CAYLEY, Esq., F.R.S. Received 

 March 19, 1857. 



(Abstract.) 



The paper is supplementary to the author's memoir, "Researches 

 on the Partition of Numbers," which comprises the two papers 

 abstracts of which appear in the ' Proceedings' of the Meeting of the 

 3rd of May, 1855. It contains some additional developments in 

 relation to the theorem referred to at the conclusion of the former 

 memoir, and an application to the determination of the expression 

 forP(l, 2,3,4, 5, 6,) 9. 



XXV. " On the Anatomy and Physiology of the Spongiadte" 

 By J. S. BOWERBANK, F.R.S., F.L.S., &c. Received June 



17, 1857. 



(Abstract.) 



The arrangement of the Spongiadce by Lamarck, based entirely on 

 external form, is wholly inadequate for the discrimination of species. 

 The classification adopted by Drs. Fleming, Grant, and Johnston, 

 dependent more especially on the chemical constituents of those 

 bodies, is far too limited to be applied in generic characters. The 

 author has, therefore, for this purpose rejected both systems, and has 

 retained the latter one for forming primary divisions only, and he 

 purposes founding the generic characters principally on the organic 

 structure and mode of arrangement of the skeleton, in accordance 

 with the practice so generally adopted by naturalists with regard to 

 many of the higher classes of animals. Tethea, Geodia, Dysidea and 

 a few others are the only well-defined genera that have yet been 

 established ; while others, such as Halichondria, even in the narrow 

 circle of the list of British species, contain at least ten distinct 

 modes of arrangement of the skeleton, each of which is constant and 

 well-defined in its character. 



It is not intended to propose the rejection of any of the well-esta- 

 blished genera of preceding authorities, but to confine each genus 

 strictly within the bounds indicated by the peculiar mode of struc- 

 ture of the skeleton which exists in that species of sponge which is 



2x2 



