17 
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 Iona 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 are 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. Liouville’s 
z Journal of Pure and Applied Mathematics, vol. ix.) that the 
_ are 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- 
| 4 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 are 
