308 



which was the germ of that "Theory of Systems of Kays," the publi- 

 cation of which first rendered Hamilton's name celebrated amongst 

 mathematicians. Brinkley encouraged the youthful author by his kind- 

 ness, and guided him by his counsel. He communicated the paper on 

 Caustics to the Academy, before which it was read in December, 1824, 

 and referred to a Committee, consisting of Dr. Mac Donnell, Mr. Harte, 

 and Dr. Lardner. Their report bore testimony to the novelty and 

 value of the results, and the analytic skill displayed in the conduct of 

 the investigations ; but recommended the author to give a fuller deve- 

 lopment to the processes and reasonings by which his formulee and con- 

 clusions were arrived at. Acting on this advice, he employed himself 

 in the intervals of collegiate study in recasting and enlarging his paper, 

 which was anew presented to the Academy, under the title of " Theory 

 of Systems of Kays," on the 23rd of April, 1827. This memoir was in 

 itself of the highest interest and value ; so comprehensive in its method 

 as to extend unlimitedly, and with universal success, over the whole 

 field of optics. It also contained the germs of thought which developed 

 themselves in works which afterwards gained for Hamilton the highest 

 distinction. Its table of contents announced an intention of publishing 

 in the third part of the essay an application to dynamics of the same 

 general principle, of which the application to optics was thus in part 

 made public ; and its third supplement contains the announcement of 

 Hamilton's remarkable discovery of Conical Kefraction. 



The Professorship of Astronomy in Trinity College became vacant 

 in the year 1827, on the promotion of Dr. Brinkley to the Bishopric 

 of Cloyne. Perhaps there was no incident in the life of Hamilton 

 more remarkable than his selection at that time to fill Brinkley 's place. 

 An undergraduate of one -and- twenty, he was preferred to rival candi- 

 dates of high qualifications and influence, and the decision of the Uni- 

 versity authorities in making the appointment was ratified by the 

 j adgment of the public. It seemed to be self-evident that a man who had 

 given such proofs of the possession of a transcendant poAver in dealing 

 with the most abstract questions in mathematical physics must be the 

 worthy and rightful successor of Brinkley. As Professor of Astronomy, 

 two spheres of exertion belonged to him — that of lecturer upon the 

 science, and that connected with the practical working of the Observa- 

 tory. Those who, have attended his lectures can bear witness to their 

 merit. They were full of practical teaching, and calculated by their 

 eloquence to excite in their hearers an enthusiasm for the study which 

 they were intended to illustrate. For the business of the Observatory, 

 it must be admitted that Hamilton was not equally well fitted. The 

 bias of his genius was undoubtedly to pure mathematics; but, if we 

 estimate the total amount and value of the work which he has done — 

 the impulse which he has given to the whole of mathematical science 

 — we shall see little reason to find fault with that decision by which he 

 was placed in the professorial chair, and sustained in the possession 

 of it. 



It was in 1834 that Hamilton received the Cunningham Medal of 

 this Academy, and the .Royal Medal of the Koyal Society, as the reward 



