TRANSACTIONS OF SECTION A. 501 



to show themselves. Dr. Graves has given us a letter from his mother in which 

 she writes to her sister of the marvellous precocity of her little four-year-old boy, 

 telling how ' he reads Latin, Greek, and Hebrew.' 



His mental development did not belie these early indications, for at the age of 

 thirteen, thanks to the teaching and care of his uncle, who was a most extra- 

 ordinary linguist, he had not only acquired a considerable knowledge of the classics 

 and the modern European languages, but also attained some proficiency in Arabic, 

 Sanscrit, and I'ersian. His mathematical studies, on the other hand, appear to 

 have been carried on without help from anyone, and it is noteworthy that he does 

 not seem to have used common text-books, but to have gone direct to the great 

 origuial authors ; e.g., he read his algebra iu Newton's ' Arithmetica Universalis': 

 while at the age of fifteen he set himself to read the ' Principia,' and two years 

 later began a systematic study of Laplace's ' Mecanique Celeste.' His own esti- 

 mate of his powers may be gathered from a characteristic letter to his sister 

 written just after he had entered Trinity College: — 



' One thing only have 1 to regret in the direction of my studies, that they 

 should be diverted— or rather rudely forced— by the College course from their 

 natural bent and favourite channel. That bent, you know, is science— science in 

 its most exalted heights, in its most secret recesses. It has so captivated me, 

 so seized on, I may say, my affections that my attention to classical studies is an 

 etlbrt and an irksome one ; and I own that, before I entered College, I did not 

 hope that in them I would rise above mediocrity. My success surprised me, but 

 it has also given me a spur by holding out a prospect that even in the less agreeable 

 part of my business I may hope still to succeed.' 



This letter is interesting as indicating on Hamilton's part a consciousness 

 wherein lay his real strength and vocation. Not that his interest in litera- 

 ture ever abated. To the last he loved to try his hand at poetical compositioUj 

 frequently inserting in his letters to his friends sonnets of his own. 



He knew Wordsworth intimately, and the poet to whom he sent some of his 

 productions gives him the following candid advice : — 



' It would be insincere not to say that something of a style more terse and 

 a harmony more accurately balanced must be acquired before the bodily form of 

 your verses will be quite worthy of their living souls. You are peifectly aware 

 of this, though perhaps not in an equal degree with myself; nor is it desirable you 

 should be, for it might tempt you to labour which would divert you from subjects 

 of infinitely greater importance.' 



Hamilton was first in his College classes in every subject and at every examina- 

 tion, and it was fully expected that he would carry oft" both the medals in 

 Mathematics and Classics at his Degree when the following circumstances 

 suddenly changed all his plans. Dr. Brinkley, the Professor of Astronomy in 

 the University, was appointed to a Bishopric, and Hamilton, though still an 

 undergraduate, was invited to ofier himself for the vacant Chair. Sir George 

 Airy and more than one of the Fellows of Trinity were also candidates, but 

 Hamilton was unanimously elected. 



His career as an original author dates from this time, for immediately after 

 his appointment he communicated to the Royal Irish Academy the first of three 

 remarkable papers on ' Systems of Rays.' 



Two striking features may be observed in these papers, as indeed in all his 

 scientific memoirs : the generality and comprehensiveness with which lie states 

 his object at the outset and the confidence with which he follows the bold and 

 original lines of treatment which he lays down for himself, and closely connected 

 with this, the determination not to be baffled by any laboriousness of calculations 

 which the application of his method may involve him in. In his first paner he 

 begins by examining what happens to a system of rays of light emanating from a 

 point and subjected to any number of reflections at curved surfaces. He 

 establishes the theorem that such a system will be cut orthogonally by a system 

 of surfaces, the length of the path measured from the original source to any of 



