has somewhat impeded the applications of which it is susceptible.  The exigencies of examinations are partly responsible for the fact that the method has not become more familiar to students of the higher mathematics.  An eminent professor has complained that Hamilton’s essay on dynamics was of such an extremely abstract character, that he found himself unable to extract from it problems suitable for his examination papers.

The following extract is from a letter of Professor Sylvester to Hamilton, dated 20th of September, 1841.  It will show how his works were appreciated by so consummate a mathematician as the writer:—­

“Believe me, sir, it is not the least of my regrets in quitting this empire to feel that I forego the casual occasion of meeting those masters of my art, yourself chief amongst the number, whose acquaintance, whose conversation, or even notice, have in themselves the power to inspire, and almost to impart fresh vigour to the understanding, and the courage and faith without which the efforts of invention are in vain.  The golden moments I enjoyed under your hospitable roof at Dunsink, or moments such as they were, may probably never again fall to my lot.

“At a vast distance, and in an humble eminence, I still promise myself the calm satisfaction of observing your blazing course in the elevated regions of discovery.  Such national honour as you are able to confer on your country is, perhaps, the only species of that luxury for the rich (I mean what is termed one’s glory) which is not bought at the expense of the comforts of the million.”

The study of metaphysics was always a favourite recreation when Hamilton sought for a change from the pursuit of mathematics.  In the year 1834 we find him a diligent student of Kant; and, to show the views of the author of Quaternions and of Algebra as the Science of Pure Time on the “Critique of the Pure Reason,” we quote the following letter, dated 18th of July, 1834, from Hamilton to Viscount Adare:—­

“I have read a large part of the ‘Critique of the Pure Reason,’ and find it wonderfully clear, and generally quite convincing.  Notwithstanding some previous preparation from Berkeley, and from my own thoughts, I seem to have learned much from Kant’s own statement of his views of ‘Space and Time.’  Yet, on the whole, a large part of my pleasure consists in recognising through Kant’s works, opinions, or rather views, which have been long familiar to myself, although far more clearly and systematically expressed and combined by him. . . .  Kant is, I think, much more indebted than he owns, or, perhaps knows, to Berkeley, whom he calls by a sneer, `GUTEM Berkeley’. . . as it were, `good soul, well meaning man,’ who was able for all that to shake to its centre the world of human thought, and to effect a revolution among the early consequences of which was the growth of Kant himself.”