U)5 



mits of several varieties, according to the nature of the sec- 

 tions of the cone parallel to its principal planes, and the 

 position of its internal axis. This curve may be made to 

 furnish, by means of its arc, a geometrical representation of 

 the three species of elliptic trancendents, including the two 

 cases of the third. 



In the course of the investigations alluded to, Mr. Roberts 

 was also led to consider two species of the curve called the 

 spherical conic, which appear to possess many remarkable 

 analogies to the properties of the equilateral hyperbola. 

 These cases occur when the axis minor is a quadrant, and 

 when the semi-axes a and b are connected by the relation 



sin a z=. tan b. 



The following extract of a letter from Andrew Dur- 

 ham, Esq., to the Marquess of Downshire, was read to the 

 Academy by Sir William Betham, with his Lordship's per- 

 mission : 



" Belvedere, Lisburn, 



" 29th December, 1841. 

 " My Lord, 



" As your Lordship and party were prevented from at 

 tending the interesting search at Drumboe Tower, I beg 

 to inform your Lordship that about seven feet below where 

 we commenced excavating, we found a skeleton, in situ, lying 

 by compass N.W. by W., wanting both legs and feet from 

 the knees, and also the right arm. The earth we removed 

 was of a blackish colour, as if composed of decomposed vege- 

 table matter, full of stones, many of which, from the mortar 

 on them, must have fallen from the top and the entrance, 

 which is about five feet from the external level ; and on the 

 eastern side, it also abounded in bones of different animals, 

 and a few bones seemingly of black cattle. Under this earth 

 we came to a surface of mortar; this induced us to proceed 

 still more cautiously; and immediately under this mortar we 



