194 



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 Rowan Hamilton, for his "Researches re- 

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

 Transactions of the Academy. 



2. To the Rev. Samuel Haughton, F. T. C. D., for his Memoir 

 " On the Equilibrium and Motion of solid and fluid Bodies," pub- 

 lished 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 vo • 

 lume. And 



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

 actions of the Irish Archaeological Society, his Irish Grammar, and 

 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, — theactual 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. 



It is now twenty years since the Rev. Mr. Warren of Cambridge* 



* Since the delivery of this Address the attention of the writer has been 

 directed by Sir William Hamilton to the earlier steps of the inquiry. The 

 first appears to have been made by M. Buee, in a Paper published in 

 the Philosophical Transactions for 1806, in which he lays down the prin- 



