ADDRESS DELIVERED BEFORE THE ROYAL IRISH ACADEMY. 469 



sent occasion to remind you, that the principal alteration in the 

 rules respecting the award of medals under the Cunningham be- 

 quest has been to extend the limit within which the Council are 

 enabled to bestow such rewards, and to confine them only to 

 memoirs or works printed and published in Ireland, or relating to 

 Irish subjects. 



A considerable interval having elapsed since the last award of 

 these prizes, the Council for the present year, on coming into office, 

 referred the matter to the three Committees of which that body is 

 composed. Upon the recommendation of these Committees, in 

 their several departments, the Council have adjudicated Medals to 

 the following gentlemen : 



1. To Sir William Eowan Hamilton, for his " Eesearches re- 

 specting Uuarternions," published in the twenty-first volume of 

 the Transactions of the Academy. 



2. To the Eev. Samuel Haughton, Fellow of Trinity CoUege, 

 Dublin, for his Memoir " On the Equilibrium and Motion of 

 Solid and Fiuid Bodies," published in the same volume. 



3. To the Rev. Edward Hincks, D. D., for his various papers 

 on Egyptian and Persepolitan Writing, also published in the same 

 volume. 



4. To John O'Donovan, Esq., for his contributions to the 

 Transactions of the Irish Archaeological Society, for his Irish Gram- 

 mar, and for his edition of the Annals of the Four Masters.- 



In attempting to lay before the Academy a concise account of 

 the origin of the new Calculus invented by Sir William Hamilton, 

 and of the principles upon which it is based, I shall avail myself of 

 the elucidations and applications of the theory which its gifted 

 author has, from time to time, communicated to the Academy, and 

 of which abstracts have appeared in our Proceedings as also of the 

 series of papers published by him in the Philosophical Magazine 

 upon the same subject. Of the latter, the author's letter to John 

 T. Graves, Esq., written immediately after the discovery, possesses 

 a high value, not only as a fragment of scientific history, but still 

 more, as laying bare in a new instance that most interesting and 

 instructive of all the mental phenomena, the actual train of 

 thought which takes place in the creative mind, from the first dawn 

 of truth within it to its full and noon-tide effulgence. 



