71 
If we suppose, now, that the two points approximate inde- 
finitely, we sce, as a particular case of the more general theo- 
rem just stated, that Mor two consecutive elements of a shortest 
line traced upon the surface, the product of the perpendicular let 
fall from the centre upon the tangent plane, and the semi-diameter 
parallel to the element of the curve, remains the same. 
Of this celebrated theorem it would, perhaps, be hard to 
discover a more elementary demonstration.— May 25, 1850. 
Sir W. R. Hamilton added some remarks on a very simple 
proof of the celebrated Theorem of Joachimsthal, derived from 
the Calculus of Quaternions. 
Mr. Mallet exhibited a specimen of Gadolinite from the 
____trap-rock in the vicinity of Galway, at the west side of Lough 
Corrib, discovered recently by himself, and identified by Mr. 
William Mallet. 
Fesruary 10, 1851. 
HUMPHREY LLOYD, D.D., Presivent, 
im the Chair. 
Wrut1am Otiver Barker, M. D., was elected a Member of 
the Academy. 
The Rev. Dr. Todd exhibited an original letter dated Ar- 
— magh, October 19, 1680, from George Codan,* a Franciscan 
_ Friar, addressed to the Duke of Ormond, the then Lord Lieu- 
_ tenant of Ireland, praying protection and deliverance from 
i imprisonment, and asserting his innocence of the charge of 
3 disaffection to the Government, followed by a panegyric of the 
Duke in Trish verse. The letter is as follows: 
* The name subscribed to the letter is not very easily read. It seems to 
be either Codan or Cudan. 
