567 



and perhaps their combination would have cost no serious 

 trouble to any experienced geometer who had chosen to attack 

 the problem. But to his own mind the whole foregoing in- 

 vestigation presents itself as being (what in fact in his case it 

 was) a mere translation of the quaternion analysis into ordi- 

 nary geometrical language, on this particular subject. And 

 he will not complicate the present Abstract by giving, on this 

 occasion, any account of those other theorems respecting po- 

 lygons in surfaces, to which the Calculus of Quaternions has 

 conducted him, but of which he has not yet seen how to 

 translate the proofs (for it is easy to translate the results) into 

 the usual language oi geometry. 



Sir William Rowan Hamilton gave also an account of 

 some general researches, respecting curvatures of surfaces, 

 and geodetic triangles thereon, conducted by the method of 

 quaternions ; but desires that the publication of the Abstract 

 of this communication may be postponed to another occasion. 



I 



May 27th, 1850. 

 THE REV. HUMPHREY LLOYD, D.D., President, 



in the Chair. 

 Dr. Todd exhibited to the Academy two small quarto paper 

 MSS. in the Irish language and character, the property of the 

 Royal Burgundian Library at Brussels. 



He stated that his attention was first called to these MSS. 

 by the communication made to the Academy on the 24th of 

 May, 1847, by Mr. Bindon, relative to the Irish MSS. pre- 

 served in that library. Soon afterwards Mr. Graves, the Se- 

 cretary of Council, having had occasion to visit Brussels, was 

 kind enough to send him (Dr. Todd) a very detailed account 

 of these and one or two other MSS., which seemed to be of 

 peculiar interest to'dio student of Irish history. This induced 



