77 



rubbing of the entire Cross, giving the elaborate patterns on 

 both sides, and the curious inscription along its edge, which 

 he translated ; and he then concluded by expressing his con- 

 viction, that notwithstanding that during the five days he 

 remained at lona he was unceasingly occupied, he had, never- 

 theless, left much unnoticed, with regard to the numerous 

 group of buildings in the vicinity of the cathedral, as well as 

 of many interesting localities in the interior of the island, 

 connected with the history of the celebrated St. Columbkille 

 and the Culdees. 



May 12, 1845. 



CAPTAIN LARCOM, R. E., Vice-President, in the 

 Chair. 



Charles Bournes, Esq., W. C. Dobbs, Esq., Wm. Henn, 

 Esq., D. B. Starkey, Esq., and Benjamin Wilme, Esq., were 

 elected Members of the Academy. 



Mr. William Roberts, F. T. C. D., read a paper on some 

 Geometrical Theorems relative to Elliptic Functions. 



It is well known that the arc of a spherical ellipse is ex- 

 pressed by an elliptic function of the third order, with a circu- 

 lar parameter : and it has been also proved (see M. Liouvllle's 

 Journal of Pure and Applied Mathematics, vol. ix.) that the 

 arc of the intersection of a sphere with a cone of the second 

 degree, one of whose external principal axes is a diameter, and 

 whose vertex is situated on the surface, may be made to sup- 

 ply a general representation of the three elliptic transcendants ; 

 at least with the aid of the modular transformations, which 

 have been given by Lagrange and M. Jacobi. The object of 

 the present communication is to shew that these results are 

 but particular cases of the general theorem, that the arc 



