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fessor Mac Cullagh. I have seen him sit for hours with his paper 

 before him, and all the outline of an elaborate investigation placed 

 upon it. All the while he never took up his pen to execute the work 

 which he had planned. He continued to brood over his task, and 

 scanned it on every side, in the hope of being able to avoid the neces- 

 sity of going through some " sea of trouble," in the shape of length- 

 ened analytical computations. His taste in mathematics was refined — 

 almost fastidious ; and he could not bring himself to look with approval 

 upon any demonstration which appeared wanting in symmetry and ele- 

 gance. I must not be understood as in the least depreciating Mac Cul- 

 lagh's power and skill in calculation. His researches in physical 

 optics prove that he possessed these qualities in the highest degree. 

 I only state the fact, that he sometimes was tempted to subject 

 his faculty of mathematical insight to a painful and dangerous strain, 

 in order to avoid the irksomeness of labour that was little more than 

 mechanical. 



In the case of Hamilton, it is, moreover, deserving of notice, that he 

 evinced a readiness to grapple with the difficulties of calculation, even 

 where there was no prospect of his labour being rewarded by any dis- 

 covery. He engaged in exercises of this kind sometimes from a wish 

 to strengthen his intellectual hold of general propositions by scrutiniz- 

 ing the results obtained, by applying them in a number of particular 

 instances ; and sometimes, perhaps, from a wish to mature and keep in 

 exercise those powers of calculation upon the exactitude and prompt 

 operation of which so much depends in the conduct of difficult mathema- 

 tical investigations. I have known him spend hours, or even days, in 

 working numerical examples of some theorem in pure or applied ma- 

 thematics, or in testing the accuracy of some formula of approximation. 

 Occasionally he engaged in tasks of this nature, in the kindly endea- 

 vour to convince some half-crazed squarer of the circle that his pro- 

 posed construction was inaccurate. Finding almost always that it was 

 hopeless to convince the mathematical fanatic of the unsoundness of any 

 of his premises, he would take pains to show him that the results he ob- 

 tained were false in particular instances. 



And this leads me to notice a feature in his character which deserves 

 to be recorded. From the lofty height of his genius and learning he 

 was accustomed to stoop with the utmost readiness to hold intellectual 

 converse with inferior minds. Many of his visitors at the Observatory, 

 and the members of the class who attended his lectures in Trinity 

 College, can recall instances of his patience and good nature in 

 answering their questions, and clearing up the difficulties which beset 

 them in their elementary studies of mathematics and natural phi- 

 losophy. 



It is remarkable that, while he possessed such powers of calculation, 

 and was almost prodigal in the exercise of them, he was to the last 

 degree solicitous about the metaphysics of every subject on which he 

 undertook to write. We have seen a decisive instance of this tendency 

 of his mind in his treatment of algebra considered as the science of pure 



