326 



which touches the surface at the first corner of the quadri- 

 lateral." 



More generally the theorem here referred to shews that 

 for the inscribed quadrilateral we may substitute a gauche 

 polygon with any even number, 2ra, of sides ; and for the no- 

 nagon, another gauche polygon, with ini- I sides, connected 

 with that polygon of 2n sides, by the same law of construction 

 as that which had connected the nonagon with the quadrila- 

 teral ; and that then the tangent plane to the surface at the 

 first corner of the polygon of 2n sides, will be parallel to the 

 plane through the first, middle, and last corners (1, 2ra+ 1 

 4n + \) of the polygon of 4ra + 1 sides. 



The Secretary presented, from the Rev. W. C. Armstrong, 

 an earthen sepulchral urn, found on the 17th of March last, 

 in a field, part of Moydow glebe, county Longford ; together 

 with the jaw bone of a man whose skeleton was found near 

 the urn. He also presented, from Mr. R. Hitchcock, a large 

 stone-hammer, used by miners, and found near Killarney. 



Several donations of books were also made to the Library, 

 which will be found noticed in the Appendix. 



Thanks were returned to the several donors. 



April 23rd, 1849. 



SIR WILLIAM BETHAM in the Chair. 



Dr. Harvey made a communication respecting the nature of 

 the Fructification of the Rhodospermatous Algai. 



" In the Rhodospermatous Algae, or Floridese, the fructifi- 

 cation presents itself under two forms. Two sorts of reproduc- 

 tive bodies are produced by each species of these algse, both 

 sorts equally capable of germinating into a new plant, both, 

 therefore, performing the functions of a seed. These repro- 



