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Hamilton

William Rowan Hamilton was born at midnight between the 3rd and 4th of August, 1805, at Dublin, in the house which was then 29, but subsequently 36, Dominick Street. His father, Archibald Hamilton, was a solicitor, and William was the fourth of a family of nine. With reference to his descent, it may be sufficient to notice that his ancestors appear to have been chiefly of gentle Irish families, but that his maternal grandmother was of Scottish birth. When he was about a year old, his father and mother decided to hand over the education of the child to his uncle, James Hamilton, a clergyman of Trim, in County Meath. James Hamilton's sister, Sydney, resided with him, and it was in their home that the days of William's childhood were passed.

In Mr. Graves' "Life of Sir William Rowan Hamilton" a series of letters will be found, in which Aunt Sydney details the progress of the boy to his mother in Dublin. Probably there is no record of an infant prodigy more extraordinary than that which these letters contain. At three years old his aunt assured the mother that William is "a hopeful blade," but at that time it was his physical vigour to which she apparently referred; for the proofs of his capacity, which she adduces, related to his prowess in making boys older than himself fly before him. In the second letter, a month later, we hear that William is brought in to read the Bible for the purpose of putting to shame other boys double his age who could not read nearly so well. Uncle James appears to have taken much pains with William's schooling, but his aunt said that "how he picks up everything is astonishing, for he never stops playing and jumping about." When he was four years and three months old, we hear that he went out to dine at the vicar's, and amused the company by reading for them equally well whether the book was turned upside down or held in any other fashion. His aunt assures the mother that " Willie is a most sensible little creature, but at the same time has a great deal of roguery." At four years and five months old he came up to pay his mother a visit in town, and she writes to her sister a description of the boy;-

"His reciting is astonishing, and his clear and accurate knowledge of geography is beyond belief; he even draws the countries with a pencil on paper, and will cut them out, though not perfectly accurate, yet so well that a anybody knowing the countries could not mistake them; but, you will think this nothing when I tell you that he reads Latin, Greek, and Hebrew."

Aunt Sydney recorded that the moment Willie got back to Trim he was desirous of at once resuming his former pursuits. He would not eat his breakfast till his uncle had heard him his Hebrew, and he comments on the importance of proper pronunciation. At five he was taken to see a friend, to whom he repeated long passages from Dryden. A gentleman present, who was not unnaturally sceptical about Willie's attainments, desired to test him in Greek, and took down a copy of Homer which happened to have the contracted type, and to his amazement Willie went on with the greatest ease. At six years and nine months he was translating Homer and Virgil; a year later his uncle tells us that William finds so little difficulty in learning French and Italian, that he wishes to read Homer in French. He is enraptured with the Iliad, and carries it about with him, repeating from it whatever particularly pleases him. At eight years and one month the boy was one of a party who visited the Scalp in the Dublin mountains, and he was so delighted with the scenery that he forthwith delivered an oration in Latin. At nine years and six months he is not satisfied until he learns Sanscrit; three months later his thirst for the Oriental languages is unabated, and at ten years and four months he is studying Arabic and Persian. When nearly twelve he prepared a manuscript ready for publication. It was a "Syriac Grammar," in Syriac letters and characters compiled from that of Buxtorf, by William Hamilton, Esq., of Dublin and Trim. When he was fourteen, the Persian ambassador, Mirza Abul Hassan Khan, paid a visit to Dublin, and, as a practical exercise in his Oriental languages, the young scholar addressed to his Excellency a letter in Persian; a translation of which production is given by Mr. Graves. When William was fourteen he had the misfortune to lose his father; and he had lost his mother two years previously. The boy and his three sisters were kindly provided for by different members of the family on both sides.

It was when William was about fifteen that his attention began to be turned towards scientific subjects. These were at first regarded rather as a relaxation from the linguistic studies with which he had been so largely occupied. On November 22nd, 1820, he notes in his journal that he had begun Newton's "Principia": he commenced also the study of astronomy by observing eclipses, occultations, and similar phenomena. When he was sixteen we learn that he had read conic sections, and that he was engaged in the study of pendulums. After an attack of illness, he was moved for change to Dublin, and in May, 1822, we find him reading the differential calculus and Laplace's "Mecanique Celeste." He criticises an important part of Laplace's work relative to the demonstration of the parallelogram of forces. In this same year appeared the first gushes of those poems which afterwards flowed in torrents.

His somewhat discursive studies had, however, now to give place to a more definite course of reading in preparation for entrance to the University of Dublin. The tutor under whom he entered, Charles Boyton, was himself a distinguished man, but he frankly told the young William that he could be of little use to him as a tutor, for his pupil was quite as fit to be his tutor. Eliza Hamilton, by whom this is recorded, adds, "But there is one thing which Boyton would promise to be to him, and that was a FRIEND; and that one proof he would give of this should be that, if ever he saw William beginning to be UPSET by the sensation he would excite, and the notice he would attract, he would tell him of it." At the beginning of his college career he distanced all his competitors in every intellectual pursuit. At his first term examination in the University he was first in Classics and first in Mathematics, while he received the Chancellor's prize for a poem on the Ionian Islands, and another for his poem on Eustace de St. Pierre.

There is abundant testimony that Hamilton had "a heart for friendship formed." Among the warmest of the friends whom he made in these early days was the gifted Maria Edgeworth, who writes to her sister about "young Mr. Hamilton, an admirable Crichton of eighteen, a real prodigy of talents, who Dr. Brinkley says may be a second Newton, quiet, gentle, and simple." His sister Eliza, to whom he was affectionately attached, writes to him in 1824:--

"I had been drawing pictures of you in my mind in your study at Cumberland Street with 'Xenophon,' &c., on the table, and you, with your most awfully sublime face of thought, now sitting down, and now walking about, at times rubbing your hands with an air of satisfaction, and at times bursting forth into some very heroical strain of poetry in an unknown language, and in your own internal solemn ventriloquist-like voice, when you address yourself to the silence and solitude of your own room, and indeed, at times, even when your mysterious poetical addresses are not quite unheard."

This letter is quoted because it refers to a circumstance which all who ever met with Hamilton, even in his latest years, will remember. He was endowed with two distinct voices, one a high treble, the other a deep bass, and he alternately employed these voices not only in ordinary conversation, but when he was delivering an address on the profundities of Quaternions to the Royal Irish Academy, or on similar occasions. His friends had long grown so familiar with this peculiarity that they were sometimes rather surprised to find how ludicrous it appeared to strangers.

Hamilton was fortunate in finding, while still at a very early age, a career open before him which was worthy of his talents. He had not ceased to be an undergraduate before he was called to fill an illustrious chair in his university. The circumstances are briefly as follows.

We have already mentioned that, in 1826, Brinkley was appointed Bishop of Cloyne, and the professorship of astronomy thereupon became vacant. Such was Hamilton's conspicuous eminence that, notwithstanding he was still an undergraduate, and had only just completed his twenty-first year, he was immediately thought of as a suitable successor to the chair. Indeed, so remarkable were his talents in almost every direction that had the vacancy been in the professorship of classics or of mathematics, of English literature or of metaphysics, of modern or of Oriental languages, it seems difficult to suppose that he would not have occurred to every one as a possible successor. The chief ground, however, on which the friends of Hamilton urged his appointment was the earnest of original power which he had already shown in a research on the theory of Systems of Rays. This profound work created a new branch of optics, and led a few years later to a superb discovery, by which the fame of its author became world-wide.

At first Hamilton thought it would be presumption for him to apply for so exalted a position; he accordingly retired to the country, and resumed his studies for his degree. Other eminent candidates came forward, among them some from Cambridge, and a few of the Fellows from Trinity College, Dublin, also sent in their claims. It was not until Hamilton received an urgent letter from his tutor Boyton, in which he was assured of the favourable disposition of the Board towards his candidature, that he consented to come forward, and on June 16th, 1827, he was unanimously chosen to succeed the Bishop of Cloyne as Professor of Astronomy in the University. The appointment met with almost universal approval. It should, however, be noted that Brinkley, whom Hamilton succeeded, did not concur in the general sentiment. No one could have formed a higher opinion than he had done of Hamilton's transcendent powers; indeed, it was on that very ground that he seemed to view the appointment with disapprobation. He considered that it would have been wiser for Hamilton to have obtained a Fellowship, in which capacity he would have been able to exercise a greater freedom in his choice of intellectual pursuits. The bishop seems to have thought, and not without reason, that Hamilton's genius would rather recoil from much of the routine work of an astronomical establishment. Now that Hamilton's whole life is before us, it is easy to see that the bishop was entirely wrong. It is quite true that Hamilton never became a skilled astronomical observer; but the seclusion of the observatory was eminently favourable to those gigantic labours to which his life was devoted, and which have shed so much lustre, not only on Hamilton himself, but also on his University and his country.

In his early years at Dunsink, Hamilton did make some attempts at a practical use of the telescopes, but he possessed no natural aptitude for such work, while exposure which it involved seems to have acted injuriously on his health. He, therefore, gradually allowed his attention to be devoted to those mathematical researches in which he had already given such promise of distinction. Although it was in pure mathematics that he ultimately won his greatest fame, yet he always maintained and maintained with justice, that he had ample claims to the title of an astronomer. In his later years he set forth this position himself in a rather striking manner. De Morgan had written commending to Hamilton's notice Grant's "History of Physical Astronomy." After becoming acquainted with the book, Hamilton writes to his friend as follows:--

"The book is very valuable, and very creditable to its composer. But your humble servant may be pardoned if he finds himself somewhat amused at the title, `History of Physical Astronomy from the Earliest Ages to the Middle of the Nineteenth Century,' when he fails to observe any notice of the discoveries of Sir W. R. Hamilton in the theory of the 'Dynamics of the Heavens.'"

The intimacy between the two correspondents will account for the tone of this letter; and, indeed, Hamilton supplies in the lines which follow ample grounds for his complaint. He tells how Jacobi spoke of him in Manchester in 1842 as "le Lagrange de votre pays," and how Donkin had said that, "The Analytical Theory of Dynamics as it exists at present is due mainly to the labours of La Grange Poisson, Sir W. R. Hamilton, and Jacobi, whose researches on this subject present a series of discoveries hardly paralleled for their elegance and importance in any other branch of mathematics." In the same letter Hamilton also alludes to the success which had attended the applications of his methods in other hands than his own to the elucidation of the difficult subject of Planetary Perturbations. Even had his contributions to science amounted to no more than these discoveries, his tenure of the chair would have been an illustrious one. It happens, however, that in the gigantic mass of his intellectual work these researches, though intrinsically of such importance, assume what might almost be described as a relative insignificance.

The most famous achievement of Hamilton's earlier years at the observatory was the discovery of conical refraction. This was one of those rare events in the history of science, in which a sagacious calculation has predicted a result of an almost startling character, subsequently confirmed by observation. At once this conferred on the young professor a world-wide renown. Indeed, though he was still only twenty-seven, he had already lived through an amount of intellectual activity which would have been remarkable for a man of threescore and ten.

Simultaneously with his growth in fame came the growth of his several friendships. There were, in the first place, his scientific friendships with Herschel, Robinson, and many others with whom he had copious correspondence. In the excellent biography to which I have referred, Hamilton's correspondence with Coleridge may be read, as can also the letters to his lady correspondents, among them being Maria Edgeworth, Lady Dunraven, and Lady Campbell. Many of these sheets relate to literary matters, but they are largely intermingled With genial pleasantry, and serve at all events to show the affection and esteem with which he was regarded by all who had the privilege of knowing him. There are also the letters to the sisters whom he adored, letters brimming over with such exalted sentiment, that most ordinary sisters would be tempted to receive them with a smile in the excessively improbable event of their still more ordinary brothers attempting to pen such effusions. There are also indications of letters to and from other young ladies who from time to time were the objects of Hamilton's tender admiration. We use the plural advisedly, for, as Mr. Graves has set forth, Hamilton's love affairs pursued a rather troubled course. The attention which he lavished on one or two fair ones was not reciprocated, and even the intense charms of mathematical discovery could not assuage the pangs which the disappointed lover experienced. At last he reached the haven of matrimony in 1833, when he was married to Miss Bayly. Of his married life Hamilton said, many years later to De Morgan, that it was as happy as he expected, and happier than he deserved. He had two sons, William and Archibald, and one daughter, Helen, who became the wife of Archdeacon O'Regan.

The most remarkable of Hamilton's friendships in his early years was unquestionably that with Wordsworth. It commenced with Hamilton's visit to Keswick; and on the first evening, when the poet met the young mathematician, an incident occurred which showed the mutual interest that was aroused. Hamilton thus describes it in a letter to his sister Eliza:--

"He (Wordsworth) walked back with our party as far as their lodge, and then, on our bidding Mrs. Harrison good-night, I offered to walk back with him while my party proceeded to the hotel. This offer he accepted, and our conversation had become so interesting that when we had arrived at his home, a distance of about a mile, he proposed to walk back with me on my way to Ambleside, a proposal which you may be sure I did not reject; so far from it that when he came to turn once more towards his home I also turned once more along with him. It was very late when I reached the hotel after all this walking."

Hamilton also submitted to Wordsworth an original poem, entitled "It Haunts me Yet." The reply of Wordsworth is worth repeating:--

"With a safe conscience I can assure you that, in my judgment, your verses are animated with the poetic spirit, as they are evidently the product of strong feeling. The sixth and seventh stanzas affected me much, even to the dimming of my eyes and faltering of my voice while I was reading them aloud. Having said this, I have said enough. Now for the per contra. You will not, I am sure, be hurt when I tell you that the workmanship (what else could be expected from so young a writer?) is not what it ought to be. . .

"My household desire to be remembered to you in no formal way. Seldom have I parted--never, I was going to say--with one whom after so short an acquaintance I lost sight of with more regret. I trust we shall meet again."

The further affectionate intercourse between Hamilton and Wordsworth is fully set forth, and to Hamilton's latest years a recollection of his "Rydal hours" was carefully treasured and frequently referred to. Wordsworth visited Hamilton at the observatory, where a beautiful shady path in the garden is to the present day spoken of as "Wordsworth's Walk."

It was the practice of Hamilton to produce a sonnet on almost every occasion which admitted of poetical treatment, and it was his delight to communicate his verses to his friends all round. When Whewell was producing his "Bridgewater Treatises," he writes to Hamilton in 1833:--

"Your sonnet which you showed me expressed much better than I could express it the feeling with which I tried to write this book, and I once intended to ask your permission to prefix the sonnet to my book, but my friends persuaded me that I ought to tell my story in my own prose, however much better your verse might be."

The first epoch-marking contribution to Theoretical Dynamics after the time of Newton was undoubtedly made by Lagrange, in his discovery of the general equations of Motion. The next great step in the same direction was that taken by Hamilton in his discovery of a still more comprehensive method. Of this contribution Hamilton writes to Whewell, March 31st, 1834:--

"As to my late paper, a day or two ago sent off to London, it is merely mathematical and deductive. I ventured, indeed, to call it the 'Mecanique Analytique' of Lagrange, 'a scientific poem'; and spoke of Dynamics, or the Science of Force, as treating of 'Power acting by Law in Space and Time.' In other respects it is as unpoetical and unmetaphysical as my gravest friends could desire."

It may well be doubted whether there is a more beautiful chapter in the whole of mathematical philosophy than that which contains Hamilton's dynamical theory. It is disfigured by no tedious complexity of symbols; it condescends not to any particular problems; it is an all embracing theory, which gives an intellectual grasp of the most appropriate method for discovering the result of the application of force to matter. It is the very generality of this doctrine which 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."

At several meetings of the British Association Hamilton was a very conspicuous figure. Especially was this the case in 1835, when the Association met in Dublin, and when Hamilton, though then but thirty years old, had attained such celebrity that even among a very brilliant gathering his name was perhaps the most renowned. A banquet was given at Trinity College in honour of the meeting. The distinguished visitors assembled in the Library of the University. The Earl of Mulgrave, then Lord Lieutenant of Ireland, made this the opportunity of conferring on Hamilton the honour of knighthood, gracefully adding, as he did so: "I but set the royal, and therefore the national mark, on a distinction already acquired by your genius and labours."

The banquet followed, writes Mr. Graves. "It was no little addition to the honour Hamilton had already received that, when Professor Whewell returned thanks for the toast of the University of Cambridge, he thought it appropriate to add the words, 'There was one point which strongly pressed upon him at that moment: it was now one hundred and thirty years since a great man in another Trinity College knelt down before his sovereign, and rose up Sir Isaac Newton.' The compliment was welcomed by immense applause."

A more substantial recognition of the labours of Hamilton took place subsequently. He thus describes it in a letter to Mr. Graves of 14th of November, 1843:--

"The Queen has been pleased--and you will not doubt that it was entirely unsolicited, and even unexpected, on my part--'to express her entire approbation of the grant of a pension of two hundred pounds per annum from the Civil List' to me for scientific services. The letters from Sir Robert Peel and from the Lord Lieutenant of Ireland in which this grant has been communicated or referred to have been really more gratifying to my feelings than the addition to my income, however useful, and almost necessary, that may have been."

The circumstances we have mentioned might lead to the supposition that Hamilton was then at the zenith of his fame but this was not so. It might more truly be said, that his achievements up to this point were rather the preliminary exercises which fitted him for the gigantic task of his life. The name of Hamilton is now chiefly associated with his memorable invention of the calculus of Quaternions. It was to the creation of this branch of mathematics that the maturer powers of his life were devoted; in fact he gives us himself an illustration of how completely habituated he became to the new modes of thought which Quaternions originated. In one of his later years he happened to take up a copy of his famous paper on Dynamics, a paper which at the time created such a sensation among mathematicians, and which is at this moment regarded as one of the classics of dynamical literature. He read, he tells us, his paper with considerable interest, and expressed his feelings of gratification that he found himself still able to follow its reasoning without undue effort. But it seemed to him all the time as a work belonging to an age of analysis now entirely superseded.

In order to realise the magnitude of the revolution which Hamilton has wrought in the application of symbols to mathematical investigation, it is necessary to think of what Hamilton did beside the mighty advance made by Descartes. To describe the character of the quaternion calculus would be unsuited to the pages of this work, but we may quote an interesting letter, written by Hamilton from his deathbed, twenty-two years later, to his son Archibald, in which he has recorded the circumstances of the discovery:--

Indeed, I happen to be able to put the finger of memory upon the year and month--October, 1843--when having recently returned from visits to Cork and Parsonstown, connected with a meeting of the British Association, the desire to discover the laws of multiplication referred to, regained with me a certain strength and earnestness which had for years been dormant, but was then on the point of being gratified, and was occasionally talked of with you. Every morning in the early part of the above- cited month, on my coming down to breakfast, your (then) little brother William Edwin, and yourself, used to ask me, 'Well papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: 'No, I can only ADD and subtract them,'

But on the 16th day of the same month--which happened to be Monday, and a Council day of the Royal Irish Academy--I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an UNDERCURRENT of thought was going on in my mind which gave at last a RESULT, whereof it is not too much to say that I felt AT ONCE the importance. An ELECTRIC circuit seemed to CLOSE; and a spark flashed forth the herald (as I FORESAW IMMEDIATELY) of many long years to come of definitely directed thought and work by MYSELF, if spared, and, at all events, on the part of OTHERS if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse--unphilosophical as it may have been--to cut with a knife on a stone of Brougham Bridge as we passed it, the fundamental formula which contains the SOLUTION of the PROBLEM, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on 'Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following."

Writing to Professor Tait, Hamilton gives further particulars of the same event. And again in a letter to the Rev. J. W. Stubbs:--

"To-morrow will be the fifteenth birthday of the Quaternions. They started into life full-grown on the 16th October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge--which my boys have since called Quaternion Bridge. I pulled out a pocketbook which still exists, and made entry, on which at the very moment I felt that it might be worth my while to expend the labour of at least ten or fifteen years to come. But then it is fair to say that this was because I felt a problem to have been at that moment solved, an intellectual want relieved which had haunted me for at least fifteen years before.

But did the thought of establishing such a system, in which geometrically opposite facts--namely, two lines (or areas) which are opposite IN SPACE give ALWAYS a positive product--ever come into anybody's head till I was led to it in October, 1843, by trying to extend my old theory of algebraic couples, and of algebra as the science of pure time? As to my regarding geometrical addition of lines as equivalent to composition of motions (and as performed by the same rules), that is indeed essential in my theory but not peculiar to it; on the contrary, I am only one of many who have been led to this view of addition."

Pilgrims in future ages will doubtless visit the spot commemorated by the invention of Quaternions. Perhaps as they look at that by no means graceful structure Quaternion Bridge, they will regret that the hand of some Old Mortality had not been occasionally employed in cutting the memorable inscription afresh. It is now irrecoverably lost.

It was ten years after the discovery that the great volume appeared under the title of "Lectures on Quaternions," Dublin, 1853. The reception of this work by the scientific world was such as might have been expected from the extraordinary reputation of its author, and the novelty and importance of the new calculus. His valued friend, Sir John Herschel, writes to him in that style of which he was a master:--

"Now, most heartily let me congratulate you on getting out your book--on having found utterance, ore rotundo, for all that labouring and seething mass of thought which has been from time to time sending out sparks, and gleams, and smokes, and shaking the soil about you; but now breaks into a good honest eruption, with a lava stream and a shower of fertilizing ashes.

Metaphor and simile apart, there is work for a twelve-month to any man to read such a book, and for half a lifetime to digest it, and I am glad to see it brought to a conclusion."

We may also record Hamilton's own opinion expressed to Humphrey Lloyd:--

"In general, although in one sense I hope that I am actually growing modest about the quaternions, from my seeing so many peeps and vistas into future expansions of their principles, I still must assert that this discovery appears to me to be as important for the middle of the nineteenth century as the discovery of fluxions was for the close of the seventeenth."

Bartholomew Lloyd died in 1837. He had been the Provost of Trinity College, and the President of the Royal Irish Academy. Three candidates were put forward by their respective friends for the vacant Presidency. One was Humphrey Lloyd, the son of the late Provost, and the two others were Hamilton and Archbishop Whately. Lloyd from the first urged strongly the claims of Hamilton, and deprecated the putting forward of his own name. Hamilton in like manner desired to withdraw in favour of Lloyd. The wish was strongly felt by many of the Fellows of the College that Lloyd should be elected, in consequence of his having a more intimate association with collegiate life than Hamilton; while his scientific eminence was world-wide. The election ultimately gave Hamilton a considerable majority over Lloyd, behind whom the Archbishop followed at a considerable distance. All concluded happily, for both Lloyd and the Archbishop expressed, and no doubt felt, the pre-eminent claims of Hamilton, and both of them cordially accepted the office of a Vice-President, to which, according to the constitution of the Academy, it is the privilege of the incoming President to nominate.

In another chapter I have mentioned as a memorable episode in astronomical history, that Sir J. Herschel went for a prolonged sojourn to the Cape of Good Hope, for the purpose of submitting the southern skies to the same scrutiny with the great telescope that his father had given to the northern skies. The occasion of Herschel's return after the brilliant success of his enterprise, was celebrated by a banquet. On June 15th, 1838, Hamilton was assigned the high honour of proposing the health of Herschel. This banquet is otherwise memorable in Hamilton's career as being one of the two occasions in which he was in the company of his intimate friend De Morgan.

In the year 1838 a scheme was adopted by the Royal Irish Academy for the award of medals to the authors of papers which appeared to possess exceptionally high merit. At the institution of the medal two papers were named in competition for the prize. One was Hamilton's "Memoir on Algebra, as the Science of Pure Time." The other was Macullagh's paper on the "Laws of Crystalline Reflection and Refraction." Hamilton expresses his gratification that, mainly in consequence of his own exertions, he succeeded in having the medal awarded to Macullagh rather than to himself. Indeed, it would almost appear as if Hamilton had procured a letter from Sir J. Herschel, which indicated the importance of Macullagh's memoir in such a way as to decide the issue. It then became Hamilton's duty to award the medal from the chair, and to deliver an address in which he expressed his own sense of the excellence of Macullagh's scientific work. It is the more necessary to allude to these points, because in the whole of his scientific career it would seem that Macullagh was the only man with whom Hamilton had ever even an approach to a dispute about priority. The incident referred to took place in connection with the discovery of conical refraction, the fame of which Macullagh made a preposterous attempt to wrest from Hamilton. This is evidently alluded to in Hamilton's letter to the Marquis of Northampton, dated June 28th, 1838, in which we read:--

And though some former circumstances prevented me from applying to the person thus distinguished the sacred name of FRIEND, I had the pleasure of doing justice...to his high intellectual merits...I believe he was not only gratified but touched, and may, perhaps, regard me in future with feelings more like those which I long to entertain towards him."

Hamilton was in the habit, from time to time, of commencing the keeping of a journal, but it does not appear to have been systematically conducted. Whatever difficulties the biographer may have experienced from its imperfections and irregularities, seem to be amply compensated for by the practice which Hamilton had of preserving copies of his letters, and even of comparatively insignificant memoranda. In fact, the minuteness with which apparently trivial matters were often noted down appears almost whimsical. He frequently made a memorandum of the name of the person who carried a letter to the post, and of the hour in which it was despatched. On the other hand, the letters which he received were also carefully preserved in a mighty mass of manuscripts, with which his study was encumbered, and with which many other parts of the house were not unfrequently invaded. If a letter was laid aside for a few hours, it would become lost to view amid the seething mass of papers, though occasionally, to use his own expression, it might be seen "eddying" to the surface in some later disturbance.

The great volume of "Lectures on Quaternions" had been issued, and the author had received the honours which the completion of such a task would rightfully bring him. The publication of an immortal work does not, however, necessarily provide the means for paying the printer's bill. The printing of so robust a volume was necessarily costly; and even if all the copies could be sold, which at the time did not seem very likely, they would hardly have met the inevitable expenses. The provision of the necessary funds was, therefore, a matter for consideration. The Board of Trinity College had already contributed 200 pounds to the printing, but yet another hundred was required. Even the discoverer of Quaternions found this a source of much anxiety. However, the board, urged by the representation of Humphrey Lloyd, now one of its members, and, as we have already seen, one of Hamilton's staunchest friends, relieved him of all liability. We may here note that, notwithstanding the pension which Hamilton enjoyed in addition to the salary of his chair, he seems always to have been in some what straitened circumstances, or, to use his own words in one of his letters to De Morgan, "Though not an embarrassed man, I am anything rather than a rich one." It appears that, notwithstanding the world-wide fame of Hamilton's discoveries, the only profit in a pecuniary sense that he ever obtained from any of his works was by the sale of what he called his Icosian Game. Some enterprising publisher, on the urgent representations of one of Hamilton's friends in London, bought the copyright of the Icosian Game for 25 pounds. Even this little speculation proved unfortunate for the purchaser, as the public could not be induced to take the necessary interest in the matter.

After the completion of his great book, Hamilton appeared for awhile to permit himself a greater indulgence than usual in literary relaxations. He had copious correspondence with his intimate friend, Aubrey de Vere, and there were multitudes of letters from those troops of friends whom it was Hamilton's privilege to possess. He had been greatly affected by the death of his beloved sister Eliza, a poetess of much taste and feeling. She left to him her many papers to preserve or to destroy, but he said it was only after the expiration of four years of mourning that he took courage to open her pet box of letters.

The religious side of Hamilton's character is frequently illustrated in these letters; especially is this brought out in the correspondence with De Vere, who had seceded to the Church of Rome. Hamilton writes, August 4, 1855:--

"If, then, it be painfully evident to both, that under such circumstances there CANNOT (whatever we may both DESIRE) be NOW in the nature of things, or of minds, the same degree of INTIMACY between us as of old; since we could no longer TALK with the same degree of unreserve on every subject which happened to present itself, but MUST, from the simplest instincts of courtesy, be each on his guard not to say what might be offensive, or, at least, painful to the other; yet WE were ONCE so intimate, an retain still, and, as I trust, shall always retain, so much of regard and esteem and appreciation for each other, made tender by so many associations of my early youth and your boyhood, which can never be forgotten by either of us, that (as times go) TWO OR THREE VERY RESPECTABLE FRIENDSHIPS might easily be carved out from the fragments of our former and ever-to-be-remembered INTIMACY. It would be no exaggeration to quote the words: 'Heu! quanto minus est cum reliquis versari, quam tui meminisse!'"

In 1858 a correspondence on the subject of Quaternions; commenced between Professor Tait and Sir William Hamilton. It was particularly gratifying to the discoverer that so competent a mathematician as Professor Tait should have made himself acquainted with the new calculus. It is, of course, well known that Professor Tait subsequently brought out a most valuable elementary treatise on Quaternions, to which those who are anxious to become acquainted with the subject will often turn in preference to the tremendous work of Hamilton.

In the year 1861 gratifying information came to hand of the progress which the study of Quaternions was making abroad. Especially did the subject attract the attention of that accomplished mathematician, Moebius, who had already in his "Barycentrische Calculus" been led to conceptions which bore more affinity to Quaternions than could be found in the writings of any other mathematician. Such notices of his work were always pleasing to Hamilton, and they served, perhaps, as incentives to that still closer and more engrossing labour by which he became more and more absorbed. During the last few years of his life he was observed to be even more of a recluse than he had hitherto been. His powers of long and continuous study seemed to grow with advancing years, and his intervals of relaxation, such as they were, became more brief and more infrequent.

It was not unusual for him to work for twelve hours at a stretch. The dawn would frequently surprise him as he looked up to snuff his candles after a night of fascinating labour at original research. Regularity in habits was impossible to a student who had prolonged fits of what he called his mathematical trances. Hours for rest and hours for meals could only be snatched in the occasional the lucid intervals between one attack of Quaternions and the next. When hungry, he would go to see whether any thing could be found on the sideboard; when thirsty, he would visit the locker, and the one blemish in the man's personal character is that these latter visits were sometimes paid too often.

As an example of one of Hamilton's rare diversions from the all- absorbing pursuit of Quaternions, we find that he was seized with curiosity to calculate back to the date of the Hegira, which he found on the 15th July, 622. He speaks of the satisfaction with which he ascertained subsequently that Herschel had assigned precisely the same date. Metaphysics remained also, as it had ever been, a favourite subject of Hamilton's readings and meditations and of correspondence with his friends. He wrote a very long letter to Dr. Ingleby on the subject of his "Introduction to Metaphysics." In it Hamilton alludes, as he has done also in other places, to a peculiarity of his own vision. It was habitual to him, by some defect in the correlation of his eyes, to see always a distinct image with each; in fact, he speaks of the remarkable effect which the use of a good stereoscope had on his sensations of vision. It was then, for the first time, that he realised how the two images which he had always seen hitherto would, under normal circumstances, be blended into one. He cites this fact as bearing on the phenomena of binocular vision, and he draws from it the inference that the necessity of binocular vision for the correct appreciation of distance is unfounded. "I am quite sure," he says, "that I SEE DISTANCE with EACH EYE SEPARATELY."

The commencement of 1865, the last year of his life saw Hamilton as diligent as ever, and corresponding with Salmon and Cayley. On April 26th he writes to a friend to say, that his health has not been good for years past, and that so much work has injured his constitution; and he adds, that it is not conducive to good spirits to find that he is accumulating another heavy bill with the printer for the publication of the "Elements." This was, indeed, up to the day of his death, a cause for serious anxiety. It may, however, be mentioned that the whole cost, which amounted to nearly 500 pounds, was, like that of the previous volume, ultimately borne by the College. Contrary to anticipation, the enterprise, even in a pecuniary sense, cannot have been a very unprofitable one. The whole edition has long been out of print, and as much as 5 pounds has since been paid for a single copy.

It was on the 9th of May, 1865, that Hamilton was in Dublin for the last time. A few days later he had a violent attack of gout, and on the 4th of June he became alarmingly ill, and on the next day had an attack of epileptic convulsions. However, he slightly rallied, so that before the end of the month he was again at work at the "Elements." A gratifying incident brightened some of the last days of his life. The National Academy of Science in America had then been just formed. A list of foreign Associates had to be chosen from the whole world, and a discussion took place as to what name should be placed first on the list. Hamilton was informed by private communication that this great distinction was awarded to him by a majority of two-thirds.

In August he was still at work on the table of contents of the "Elements," and one of his very latest efforts was his letter to Mr. Gould, in America, communicating his acknowledgements of the honour which had been just conferred upon him by the National Academy. On the 2nd of September Mr. Graves went to the observatory, in response to a summons, and the great mathematician at once admitted to his friend that he felt the end was approaching. He mentioned that he had found in the 145th Psalm a wonderfully suitable expression of his thoughts and feelings, and he wished to testify his faith and thankfulness as a Christian by partaking of the Lord's Supper. He died at half-past two on the afternoon of the 2nd of September, 1865, aged sixty years and one month. He was buried in Mount Jerome Cemetery on the 7th of September.

Many were the letters and other more public manifestations of the feelings awakened by Hamilton's death. Sir John Herschel wrote to the widow:--

"Permit me only to add that among the many scientific friends whom time has deprived me of, there has been none whom I more deeply lament, not only for his splendid talents, but for the excellence of his disposition and the perfect simplicity of his manners--so great, and yet devoid of pretensions."

De Morgan, his old mathematical crony, as Hamilton affectionately styled him, also wrote to Lady Hamilton:--

"I have called him one of my dearest friends, and most truly; for I know not how much longer than twenty-five years we have been in intimate correspondence, of most friendly agreement or disagreement, of most cordial interest in each other. And yet we did not know each other's faces. I met him about 1830 at Babbage's breakfast table, and there for the only time in our lives we conversed. I saw him, a long way off, at the dinner given to Herschel (about 1838) on his return from the Cape and there we were not near enough, nor on that crowded day could we get near enough, to exchange a word. And this is all I ever saw, and, so it has pleased God, all I shall see in this world of a man whose friendly communications were among my greatest social enjoyments, and greatest intellectual treats."

There is a very interesting memoir of Hamilton written by De Morgan, in the "Gentleman's Magazine" for 1866, in which he produces an excellent sketch of his friend, illustrated by personal reminiscences and anecdotes. He alludes, among other things, to the picturesque confusion of the papers in his study. There was some sort of order in the mass, discernible however, by Hamilton alone, and any invasion of the domestics, with a view to tidying up, would throw the mathematician as we are informed, into "a good honest thundering passion."

Hardly any two men, who were both powerful mathematicians, could have been more dissimilar in every other respect than were Hamilton and De Morgan. The highly poetical temperament of Hamilton was remarkably contrasted with the practical realism of De Morgan. Hamilton sends sonnets to his friend, who replies by giving the poet advice about making his will. The metaphysical subtleties, with which Hamilton often filled his sheets, did not seem to have the same attraction for De Morgan that he found in battles about the quantification of the Predicate. De Morgan was exquisitely witty, and though his jokes were always appreciated by his correspondent, yet Hamilton seldom ventured on anything of the same kind in reply; indeed his rare attempts at humour only produced results of the most ponderous description. But never were two scientific correspondents more perfectly in sympathy with each other. Hamilton's work on Quaternions, his labours in Dynamics, his literary tastes, his metaphysics, and his poetry, were all heartily welcomed by his friend, whose letters in reply invariably evince the kindliest interest in all Hamilton's concerns. In a similar way De Morgan's letters to Hamilton always met with a heartfelt response.

Alike for the memory of Hamilton, for the credit of his University, and for the benefit of science, let us hope that a collected edition of his works will ere long appear--a collection which shall show those early achievements in splendid optical theory, those achievements of his more mature powers which made him the Lagrange of his country, and finally those creations of the Quaternion Calculus by which new capabilities have been bestowed on the human intellect.

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