71 



If we suppose, now, that the two points approximate inde- 

 finitely, we see, as a particular case of the more general theo- 

 rem just stated, that For two consecutive elements of a shortest 

 line traced upon the surface, the product of th'e 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 Gal way, at the west side of Lough 

 Corrib, discovered recently by himself, and identified by Mr. 

 William Mallet. 



February 10, 1851. 



HUMPHREY LLOYD, D. D., President, 

 in the Chair. 



William Oliver 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 

 imprisonment, and asserting his innocence of the charge of 

 disaffection to the Government, followed by a panegyric of the 

 Duke in Irish 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. 



