250 



the surface made by the diametral planes parallel to these 

 elements. The reduction of these integrals to the normal 

 form of elliptic functions may be effected in a variety of ways ; 

 the simplest, probably, is that given by M. Jacobi, for the 

 rationalization of such integrals, in the tenth volume of 

 Crelle's Journal. 



" The combination, 821 S2i+i + Saj 22i'+i, of the perimeters 

 of the curves derived from conjugate hyperbolae, which, as we 

 have seen, admits of being put under such a remarkable geo- 

 metrical form, has also a very curious signification in mathe- 

 matical physics. This remark I owe to my distinguished 

 friend, M. Liouville, who mentioned it to me in conversation 

 a short time since." 



December Uth, 1848. 



REV. HUMPHREY LLOYD, D. D., President, 

 in the Chair. 



A COLLECTION of stone, bronze, and iron antiquities, with 

 some casts of specimens in the Museum at Copenhagen, were 

 presented by the Royal Society of Northern Antiquities. 



The Rev. Dr. Todd (Secretary) directed the attention of 

 the meeting to a highly interesting group of antique relics, 

 which had been presented to the Academy by the Royal So- 

 ciety of Northern Antiquities at Copenhagen. He observed that 

 those specimens were, some of them, analogous to antique re- 

 mains of a similar character which had been found in Ireland, 

 several of which were in the possession of the Academy. The 

 existence of such an analogy between the weapons and instru- 

 ments used in ancient times, by the inhabitants of this and 

 more northern countries, was known to the Academy, and a 

 small collection of antiques of this nature, found in Ireland, 

 had been selected and transmitted by the Academy to the 

 Northern Society, along with a large collection of drawings 



