387 



by him into analysis in 1843, involving the three new imagi- 

 naries i, j, k, for which the fundamental formula, 

 ^2 = j2 = h? = ijk = - 1 , 



holds good. (See the Proceedings of November 13th, 1843). 

 And Sir W. R. Hamilton thinks that the name " Biqua- 

 TERNioN," which he has been for a considerable time accus- 

 tomed to apply, in his own researches, to an expression of 

 this form q + V (- 1) q', is a designation more appropriate to 

 such expressions than to the entirely diflferent (but very inte- 

 resting) octonomials of Messrs. J. T. Graves- and Arthur 

 Cayley, to which Octaves the Rev. Mr. Kirkman, in his paper 

 on Pluquaternions, has suggested (though with all courtesy 

 towards the present author), that the name of hiqiiaternion 

 might be applied. 



Dr. Todd presented, on behalf of Mr. Caulfield of Cork, 

 the rubbing of a grave-stone found in the ancient church of 

 Keel, East Carbery, County Cork. 



The stone from which the rubbing was taken is flat, and 

 the exact size and shape of the paper; and is a species of 

 granite, of a kind, as Mr. Caulfield thinks, quite different 

 from any found in the neighbourhood. The back of the stone 

 is somewhat concave, and, as Mr. Caulfield thinks, made so 

 by art. 



Mr. Caulfield stated, in a letter to Dr. Todd, that he had 

 opened in the same district three forts, in one of which, called 

 Aghalusky, he found Ogham inscriptions on the flags of the 

 ceiling. " Near one of the forts, called Tullymurrihy," Mr. 

 Caulfield says, " my attention was attracted by a rise in the 

 ground, which I determined to have opened, and was rewarded 

 by the appearance of loose stone masonry ; and after getting 

 larger stones removed, to the depth of seven feet, I came to an 

 earthen floor, on one end of which were enormous quantities 

 of bones, teeth, charcoal, and large heaps of the bones of 



VOL. IV. 2 G 



