OUR PORTRAIT GALLERY. - NO. XXVI.
SIR WILLIAM R. HAMILTON,
Professor of Astronomy in the University of Dublin,
Astronomer Royal for Ireland,
President of the Royal Irish Academy, &c. &c.

[Robert Perceval Graves]
[Dublin University Magazine, vol. 19 (1842), pp. 94-110.]

The name of an English Sir William Hamilton, the ambassador at the court of Naples, is still unforgotten as holding a distinguished place among the virtuosos of his time; and Scotland boasts at present of another Sir William Hamilton, who fills the chair of logic in her metropolitan university, and whose reputation as a champion of his national school of logic and metaphysics is eminent throughout Europe; we Irishmen have also our Sir William Hamilton - SIR WILLIAM ROWAN HAMILTON: with peculiar gratification we this month suspend his portrait in our gallery; and, as we do so, we risk nothing in predicting, that to him, his achievements of science, and his fame, Ireland will in years far distant jealously vindicate her title, as among the intellectual possessions of which she has most reason to be proud.

Sir William Hamilton, we are happy to think, is still a young man, being now in the thirty-seventh year of his age. He was born on the 4th of August 1805, in the house of his father, Mr. Archibald Hamilton, in Dominick-street, Dublin. His father was by profession a solicitor, and is still remembered by many in this city as a gentleman possessing character and abilities which gave him a high place in general estimation. The branch to which he belongs of the respectable family of Hamilton, settled, we are informed, in the north of Ireland, in the reign of James the First; its leading representative being subsequently a baronet of some local distinction, Sir James Hamilton, to whose title, it has been thought by members of the family, that the legitimate succession was vested in the uncle of the subject of our memoir, although investigations, at one time entered upon with a view to substantiating the claim, were rendered fruitless by a defect in some country parish register.

At the very earliest age indications were perceived of W. R. H.'s possession of extraordinary intellectual powers, in consequence of which, his father, unable from professional occupation to superintend their development himself, and recognising with a laudable promptitude their extent and value, consigned him when less than three years old to the care of the Rev. James Hamilton, the uncle of the young genius. To this affectionate relative and estimable man, who was then, and is still, curate of Trim, in the county of Meath, and whose own collegiate course had been distinguished both in science and classics,¹ belongs to the honour of being the chief, we believe we might almost say, the sole early instructor of his nephew, whose home continued to be with him at Trim until he became an undergraduate at the university.

In consequence of Mr. A. Hamilton, the father, having some friends among the body who then held the patronage of India, he originally destined his son to a life in the east, and accordingly directed that the mind of the child should be early employed in the acquisition of the oriental languages. Happily the subsequent development of his scientific powers frustrated this plan, but its immediate results were too remarkable in themselves, and for the proof they give of the activity and versatility of his faculties, to allow us to pass them unnoticed. At the age of four he had made some progress in Hebrew: in the two succeeding years he had acquired the elements of Greek and Latin; and when thirteen years old was in different degrees acquainted with thirteen languages, besides the vernacular - Syriac, Persian, Arabic, Sanscrit, Hindoostanee, Malay, French, Italian, Spanish and German; and we are not sure that this list is a complete one. We well remember to have heard, long before we ever saw our friend, of Dr. Meredith, formerly fellow of Trinity College, and a man of great learning and ability, reporting with expressions of astonishment, that he had examined in the country a child of six or seven, who read and translated and understood Hebrew better than many candidates for fellowship; this child was young Hamilton: we know also that he not unfrequently wrote letters in Persian; and we think the anecdote should not be lost, that one which he sent in that language as a greeting to the Persian Ambassador, Mirza Abou Hassan Khan, when on a visit to Dublin in 1819, drew from the ambassador the exclamation, that he did not think there was a man in these countries who could have indited such a letter. We believe Sir William has not found it possible or thought it worth his while to keep up his knowledge of all the languages which we have mentioned as occupying his attention in childhood, and that he scarcely ever makes an allusion to these early acquisitions: they constitute, however, an essential part of his intellectual history, and as such claim a record even in the present sketch. It is pleasant to be able to add, and, considering the advancement made by him in both departments, the fact is wonderful, that early as he was trained to the acquirement of languages and the pursuit of science, this training does not appear to have been a mere hotbed-forcing of the intellect, but to have allowed free play and proportionate encouragement to the physical, and imaginative, and moral energies of the human being. We believe that there was not, in his childhood, the want of any element natural and appropriate to that stage of his existence, and that he was then equally a boy, as he is now, in the fullest sense of the word, a man.

We now turn from this record of the literary pursuits of his youth to trace cursorily the history of his scientific powers and investigations,- that department of his history, which, as more identified with his public character, will, perhaps, excite a peculiar interest. For the whole of what, for want of a proper word, we have called, by way of distinction, his literary education, he owns himself indebted, we know, to his uncle: in science he was more self-taught. At the age of ten, having accidently fallen-in with a Latin copy of Euclid, he became rapidly and deeply immersed in the study of geometry; and a little before this he had acquired a liking for arithmetical calculation, and was beginning to take an interest in the elements of algebra, a taste which had become fully confirmed when he had reached the age of twelve. In testimony of this we may introduce the anecdote that it was at this time that Zerah Colburn, the American boy was exhibited in Dublin, as an arithmetical prodigy, and that opportunities occurred for trials of skill between him and Hamilton, in which, rather in play than otherwise, they exchanged questions and fought arithmetical duels; but we have heard Sir William declare, that in these encounters his competitor was usually the more expert of the two combatants. Between the ages of twelve and fifteen he had explored and made himself familiarly acquainted with what may be called the public domain of arithmetic, trigonometry, astronomy, optics, and mechanics, using not only the popular treatises, but also the works of the highest name and authority on these subjects. For instance, at the earliest of the ages we have mentioned, when first interested in arithmetic, he passed almost at once to the study of Newton's ``Arithmetica Universalis.'' Of the mode of his study of science in these early years we are able to communicate a fact, which appears to us of considerable value. We have heard from himself that he attributes much of his subsequent progress in science to his habit of never grudging any labour towards fixing clearly theorems in his mind, by applying them to the solution of problems; and that accordingly ``the questions for exercise,'' of various sorts, which he used thus to resolve, while learning the elements of mathematics, were very numerous indeed. As an example of this, we remember his stating, that after being both astonished and delighted by the demonstration of the existence of incommensurability, he was led often to meditate upon it, and to engage for pleasure, in long numerical, and usually, unwritten processes of approximation to the values of surd roots; and this was before he was thirteen years of age. Neither, with reference to his future lot, is the fact without interest, that the possession of a telescope of his own enabled him at this period, to be somewhat of a practical astronomer, and that the same manuscript books which bear testimony to his early travails in the oriental languages contain also records of some of his boyish observations of eclipses of the moon, and of Jupiter's satellites, and of other astronomical phenomena. From fifteen to seventeen, Newton's ``Principia,'' the application of algebra to geometry - the differential, and in part, the integral calculus, together with such original investigations as the study of these subjects naturally suggested to such a mind as his, occupied most of the time which he could spare to science from the collegiate entrance-course, which necessarily made classical literature engage then a large share of his attention. These studies, to which that of Laplace's Méchanique Celeste, in the following year, is to be added, may be said to have brought to a close that stage of his scientific progress in which he is to be considered as predominantly a learner.

Soon after this occurred an event which doubtless exercised an encouraging influence on the young aspirant in science: we allude to his introduction to Brinkley, his illustrious predecessor in the chair of astronomy. This introduction was marked by circumstances equally honourable to both individuals, and which we cannot deny ourselves the pleasure of relating. In the summer of 1822 W. R. H. was engaged, as we have mentioned, in reading the Méchanique Celeste of Laplace; an objection to a demonstration occurred to him, and a friend (Mr. George Kiernan) induced him to write down his remarks on the subject, and then soon afterwards showed them to Dr. Brinkley. The perusal of these led to the expression of a wish on the part of Dr. Brinkley, that Mr. K. would on the next opportunity introduce to him their author: this kind intention was conveyed to W. R. H. at that time staying with his uncle at Trim, in the autumn of the above-mentioned year, and he determined to take advantage of it at the approaching Christmas, which he was to spend in Dublin. In the mean time he prepared a paper on ``Contact between Algebraic Curves and Surfaces,'' (containing among other things an investigation of the parabola osculating to a curve of double curvature,) and with this in his hand, additionally to prove himself sensible of the honour to which he was invited, and not unworthy of it, he came up to visit the Observatory, and the celebrated mathematician who presided over it, or, as he must then have felt, to approach an established throne of science, and to receive audience of one whose name shed lustre on that mighty seat of dignity, and whose word of approbation could confer rank in the scientific world, as well as stamp the value of part exertions, and encourage to continued efforts. The result was what might have been anticipated by all who knew the character and abilities of both. Dr. Brinkley, we need not say, received the young Hamilton with kindness; he read and approved his paper, and showed the interest he took in it by asking to see some of the investigations in a more developed form: this request was complied with by Hamilton, who in the following month laid before him a longer paper on the same subject, entitled ``Developments.'' We have ascertained that both papers still exist: they ought some day to see the light. From that time forward for several years Hamilton was admitted to a personal intimacy with the eminent man, to whom he was afterwards by so many titles to be the worthy successor. How fully and gratefully this privilege - a testimony equally to his personal as to his scientific character - was estimated by the younger of the two is evinced in a manner honourable to both parties, by a sentence at the close of the second part of his paper on Caustics. This paper, which was the product of the succeeding year, and the germ of that ``Theory of Systems of Rays,'' which first gave general distinction to Sir W. Hamilton's name, was presented in the year 1824 by Dr. Brinkley, as its sponsor, to the Royal Irish Academy, of which he was then president; it is thus concluded:-

``But whatever may be the opinions of others as to their value, I have the pleasure to think that my paper is inscribed to the one who will best be able to perceive and appreciate what is original;- whose kindness has encouraged, whose advice has strengthened me;- to whose approbation I have ever looked as a reward sufficient to repay me for industry however laborious, for exertion however arduous.''

And, on the other hand, as manifesting the complete and generous recognition by the elder savan, of the powers and attainments of his youthful friend, we can record, from our distinct remembrance of the fact being communicated to us by a mutual relative at a period certainly anterior to the date last named, that Brinkley, speaking of Hamilton, emphatically declared, ``This young man, I do not say will be, but is, the first mathematician of his age.'' They who know how eminently qualified to judge, and how habitually sober and truthful in speech, was Dr. Brinkley, will know the amount of value to be attached to this expression of his opinion on such a point, even though it be only reported as his conversational dictum. Our pen would fain linger to depict with fuller illustration the mutually reflected honour and regard of these two lights in the hemisphere of science; but we must hasten on; suffice it to say, that the receding star rejoiced to behold and to attest the culminating lustre of his successor, and that, when in due time, he sank beneath the horizon of the grave, a fitting close was put to the high intercourse which had been theirs during life in an éloge pronounced by that successor at the Royal Irish Academy, upon the intellect, the labours, and the virtues of the illustrious departed.²

We now return to the year 1823,- when Hamilton was in his eighteenth year. It is an important era in the life of our subject, for it was at this time that he began to employ himself in applying algebraic geometry to optics; an application which he then supposed had not been previously attempted by any other person. In this and the succeeding year, pursuing, at the intervals of his studies for the university examinations, the train of research we have indicated, he arrived at numerous results of the highest interest; most of them altogether new, though in some, as he afterwards found, he had been partly anticipated by Malus; but in connection with which the great feature was, that the method invented, and employed by him was so comprehensive as to extend unlimitedly and with universal success over the whole field of optics; ``dominant,'' to use the expression, in reference to it, of the elegant historian of geometry M. Chasles, ``toute cette vaste theorie.'' These investigations, presented in a general and abstract point of view, were embodied in the manuscript essay on ``Caustics,'' to which we have before made allusion, and which, after its communication to the Academy by Dr. Brinkley, in December, 1824, was immediately referred by them to a committee, consisting of Dr. MacDonnell, Mr. Harte, and Dr. Lardner. This committee returned, in June, 1825, a report - our limits prevent us giving more than its substance - which bore testimony to the novelty and value of the results, and the analytic skill displayed in the conduct of the investigations; but which recommended to the author, as necessary to fit his memoir for publication, a fuller development of the processes and reasonings by which his formulæ and conclusions were arrived at. Acting on this advice of the committee he employed himself at the intervals of collegiate study in recasting and enlarging his paper, which was now anew presented to the Academy under the title of ``Theory of Systems of Rays,'' on the 23rd of April, 1827, and was published in 1828 as a paper in the fifteenth volume of the Transactions of the Royal Irish Academy. The 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. The second and third parts of the above-mentioned theory, in the form in which they were presented to the Academy in 1827, remain as yet unpublished; but many of the theorems which they contain, along with many others, have been embodied in the three ``Supplements'' which have appeared in subsequent volumes of the Irish Transactions, and in the two essays, ``On a General Method in Dynamics,'' published by the Royal Society of London.

Having been brought, in order of time, to its source, we have thought it better thus summarily to present to the prospective glance of our readers the whole history of the progress of this great work, by which Sir William Hamilton has, in the opinion of those most competent to judge, revolutionized mathematical optics, and established the means of conquest to a similar extent over other territories of science; but we must now revert to his personal history, of which our sketch must be the more rapid, as we hope to find room for a popular view of the contents of his works.

We cannot allow his collegiate career to pass by in an allusion. It was in the summer of 1823, the year already named by us as dating the commencement of his optical researches, that he entered college,- a year later than had been intended, but illness had kept him back. We well remember the rumour of the intellectual prowess of ``Hamilton the prodigy,'' which preceded him to the courts of the university, and appalled the courage of his future class-fellows. And, sooth to say, never were expectations more fully realized, or rivals' fears better justified. He began by gaining the first place at entrance, upon a first mark in every book, and the first premium at the subsequent examination in Hebrew. This commencement was only the earnest of what followed. In a class which contained many competitors of more than ordinary distinction, and in a division which usually concentrated the best of them, he never once was beaten, but uniformly, at every quarterly examination, obtained the chief honour in both science and classics: on two occasions the honour was enhanced by an optime, once for his answering in Greek, and afterwards at the examination in Physics. To those who are unacquainted with the conduct of examinations at Dublin, it may be necessary to state that an optime is a judgment conferred there, only when the examiner considers his answerer to have absolutely mastered the subject of examination. We need scarcely add that the total number of occasions on which this judgment has been awarded is very small, and we believe it is a fact, that Sir Wm. Hamilton is the only individual upon collegiate record who ever obtained two of them. To this list of honours in the main courses of academic study, are to be added similar successes at Hebrew and Catechetical Examinations, and the acquisition of two Vice-Chancellor's prizes for English poems, of which the subjects were ``The Ionian Islands,'' and ``Eustace St. Pierre.'' This uninterrupted, universal, and distinguished success produced, as may be imagined, an excitement of admiration amongst his compeers, of which we dare to say the glow has not yet altogether subsided in the breasts of many. And in justice to both them and him we must attest, that never were academic honours borne more meekly,- never had an academic victor a richer addition to his crown from

``Generous rival's sympathy.''

During his passage through the university, William R. Hamilton resided in Dublin, at the house of his cousin, Mr. Arthur Hamilton, the barrister, a relative amply endowed with the pleasantest and best qualities of a companion and friend, and whose faithful affection supplied the loss which the subject of our sketch and his sisters had sustained at an early age of both their parents. In the beginning, however, of the summer of 1827, he retired to the country - to the haunt of his childhood, at Trim - in order to study for the two gold medals which then crowned the honours of the undergraduate course at Dublin,- (these honours, indeed, had never both been won by a single aspirant, in competition with the main body, or pensioner division, of the class; but in his case the double triumph was looked forward to as not only likely, but certain,) - and to lay in store to meet the subsequent requisition of the Fellowship Examination. But his immediate plans and his ulterior destiny were suddenly changed by a great and unexpected distinction; we allude to his appointment at this time to the high and responsible situation of Andrews' Professor of Astronomy to the University of Dublin and Royal Astronomer of Ireland: an appointment truly extraordinary - perhaps without parallel, when considered as bestowed upon an undergraduate of one-and-twenty,- but in this particular case, we think, equally conferring honour upon the university authorities from whom it emanated, as upon the individual whom it justly signalised. The post in question had become vacant some months before by the resignation of Dr. Brinkley, on his nomination to the Bishopric of Cloyne. To place in the chair of such a man a successor worthy of him, was an object which naturally demanded the anxious care of those in whom the appointment was vested: and their impartiality and public spirit were tested by the decision which was called for from them upon many rival pretensions of no mean order. Among their own body were fellows of high qualifications and influence, desirous of the appointment; and from Cambridge appeared as a candidate, with a reputation almost as high as he now enjoys, George Biddel Airy, the present Astronomer Royal of England. However, when the period approached at which the final determination must be declared, what had been the expressed wish of so many in conversation, the idea which the peculiar eminencies of the individual naturally suggested, but which the circumstances of his youth and standing as naturally prevented being quickly put forward as a proposal, became a subject of serious deliberation with the board. That deliberation proved of so favourable a character, that his friend and tutor, Dr. Boyton, to whom this circumstance became known, immediately wrote to communicate the fact, and to advise him at once to come up to town and propose himself as a candidate for the appointment: a step which, before receiving this encouragement, his modesty had withheld him from taking; although he must have often heard himself mentioned by friends and admirers in connexion with the vacant situation, as the individual who would most appropriately fill it, an was therefore abundantly entitled to look for it. He now felt that it was his duty to act upon Dr. Boyton's letter, which was seconded by the advice of his relatives, and in the course of a week from its receipt the honour became his, with all its attendant pleasure and congratulations, of being the successor of Brinkley in the Professorship of Astronomy.

From that time the residence of Sir William Hamilton has been at the Observatory, near Dublin. Here we have had the pleasure of seeing him carrying on his life of high and abstract labour, and of sharing occasionally the means of intellectual improvement, of elevation and enjoyment, which his society lavishly supplies to all who come within its influence. At first his new abode was made a home to him by the presence of his sisters, whose cultivated intellects and kindred tastes added to the uniting bond of nature many strong and delightful links of sympathy. Of this sisterhood it is impossible here to resist the temptation of mentioning that one - E. M. H. - has been no unfrequent contributor to the pages of the Dublin University Magazine, where, we doubt not, many of our readers remember poems discriminated by that signature, and remarkable for depth and earnestness of thought and feeling, elevation of principle, and force and vividness of expression; and from our pages we may refer to the distinct volume which Miss Hamilton has given to the world. During the Viceroyalty of Lord Anglesey, the Observatory was additionally enlivened by the presence of two youthful sons of the Marquess, who were for a short period pupils of Sir William Hamilton, an advantage subsequently enjoyed for a longer time, and with an ample result of intellectual profit to himself, and honouring attachment towards his instructor by the Viscount Adare, to whose name upon the roll of her nobility Ireland may refer with pride, as that of one whose accomplishments and principles add lustre to his rank. Upon the 9th of April, 1833, Sir William Hamilton married Miss Helen Maria Baily, daughter of the Rev. H. Baily, Rector of Nenagh, in the county of Tipperary, and his home has since been enriched by the birth of three children. For the whole of this period that home has been a centre to which his high and various endowments of its occupant have attracted, not only the scientific stranger, but numbers from a wide circle, whose moral and intellectual tendencies have been of a congenial nature; and consequently few scenes have been oftener brightened by the mutual kindlings of genius, by the rich interchange of thought, of imagination, and of wit, than the Observatory at Dunsink. These social enjoyments are, however, speaking strictly, of course occasional only; for, usually, laborious study hold there its reign, and displays its insignia.

The works which we shall afterwards mention, as proceeding from his pen, will show how hard and how successfully Sir William Hamilton has been working in his retirement, as a scientific Author. As Professor of Astronomy two spheres of exertion belong to him: that of Lecturer upon the Science, in College, and that connected with the practical working of the Observatory. Upon his duties as Lecturer Sir William Hamilton entered with zeal, and has bestowed most strenuous and persevering pains,- pains which we cannot but trust have been rewarded by the propagation throughout the students of our university of high and true views of the philosophy of science. In these lectures he has exerted himself to present before his hearers, not merely such information as a teacher of the ``use of the globes,'' or a university text-book might afford them, but, together with the necessary illustrations of astronomy, such views of its connexion with the other branches of science, and of its relations to the human reason and imagination, as would enable them to possess a comprehensive survey of their subject, and in the light of that survey to pursue its study. Often have we been delighted to attend his introductory lectures, full as they always have been of close logic, of sound metaphysic, of truth united to poetry, and of a high moral consecrating the whole, and all these elements fitted, by the eloquence in which they were couched, to produce in his youthful audience an ardent, and at the same time a wise enthusiasm for the studies thus recommended.³ We can scarcely imagine a book that, to a particular class of intellectual inquirers, would be more delightful or more serviceable, than one formed by a collection of these introductory addresses: and we cannot but entertain the hope, that Sir William Hamilton will one day make this present to the young and generous aspirers after truth among his countrymen.

To the practical working of the Observatory Sir William Hamilton, the bias of whose genius is undoubtedly to pure mathematics, is not naturally so adapted as to the other departments of scientific labour. Here, however, he has, we know, diligently kept up the regular course of observations and reductions; and in justice to him we feel bound to protest against its being thought that the astronomer who presides over it is singly responsible if the Dublin Observatory should not hold a very high rank for the completeness and relative value of its observations: for, besides the disadvantage of our climate, an inadequate staff of assistants - at present there is only one - renders the Observatory totally incapable of answering the requirements, within the last ten years greatly multiplied, of the present state of astronomical science. We have no doubt but that with a sufficient body of assistants, the directing head of Sir William Hamilton would soon raise this department to nearly as high a standing as it is possible for it to attain.

Sir William Hamilton has been before the public eye as an active and influential member of the British Association of Science. He joined it so early as in 1832, when it assembled for its second meeting at Oxford; and there, having been called upon, he laid before its members a concise view of his optical method, and in behalf of the Royal Irish Academy returned thanks, in a speech gracefully evincing a combined pride of nationality, as an Irishman, and of compatriotism, as a Briton. At Cambridge, the next year, his discovery of conical refraction (which had been made in the interval, and of which we shall give an account hereafter) was a principal feature of discussion, and he received upon the occasion, from that university, the honour of admission, in company with some other eminent men, to an ad eundem degree of A. B. He took an active part, also, at the meetings subsequently held at Edinburgh, Dublin, Bristol, Liverpool, and Newcastle; but we can now only refer to that which passed with such distinguished eclat in our own metropolis. Amongst its conductors Sir William Hamilton held the prominent post of secretary, in which capacity he delivered the Annual Address, afterwards published in their Report, and to which (since our limits forbid us to extract) we refer, as exhibiting a good specimen of his characteristic eloquence and ability, in the development which it contains of the power of the social sympathy as an impulse to science. It was during this meeting that Lord Normanby, then Lord Lieutenant, seized, with a happy tact, the opportunity of paying a most handsome compliment both to Professor Hamilton and to Ireland, by conferring upon the foremost representative of our nation's science, and in the face of the assembled Association the honour of knighthood. The appropriate scene was the library of our university. It was no slight addition to the honour that Professor Whewell, in his speech at the banquet which followed, should suggest, as a parallel remembrance, the fact that, a hundred and thirty years before, a great man in another Trinity College knelt down before his sovereign, and rose up Sir Isaac Newton.

Another distinction has since been conferred upon Sir William Hamilton. We refer to his election, in the year 1837, to the Presidentship of the Royal Irish Academy. This post was for many years filled by Dr. Brinkley, both when Professor of Astronomy, and afterwards when Bishop of Cloyne. Upon his death, in 1835, Sir William Hamilton paid to the late Provost, Dr. Lloyd, the tribute of his personal respect, by coming forward in the Academy and proposing that the vacant seat of honour should be filled by a man, whose combined pretensions, founded upon his personal character and attainments, and his long-continued services to the science of his country, called for such a rewarding recognition from the national Academy. This eminent and excellent man too soon followed his predecessor to the grave, again leaving vacant the presidential chair; and it was upon this occasion that Sir William Hamilton successfully aspired to the distinction; although he had to encounter the competing claims of the Archbishop of Dublin and Professor Lloyd, who were at the same time put in nomination. To the honour we speak of Sir William Hamilton, besides his high scientific reputation, had some peculiar titles. Long connected with the Academy - as an author, from his boyhood - he had for many years taken a zealous interest in its welfare; had enriched its Transactions with his valuable papers; had been the means, as we happen to know, of inducing several of its most distinguished members to join the body, and, perhaps may with truth be said, to have been mainly instrumental in raising the institution from a state of comparative neglect and inaction to that which it at present enjoys of activity and repute. We may add, that for discharging efficiently the duties of President he possesses eminently the qualifications of wide and accurate knowledge, of a well-tempered impartiality, and (we name an attribute especially valuable in the leader of such a society) a generous aptitude to acknowledge and to give the fullest meed of applause to the talents and services of his fellow-labourers in literature and science: we have been struck by the evidence of these merits exhibited in the published volume of the Academy's Proceedings, containing addresses delivered by him on presenting medals to Mr. Petrie, Dr. Apjohn, and Professor M`Cullagh.

We shall now essay the execution of that part of our undertaking, of which we have already given notice, and to which some of our readers may be looking forward as to matter more interesting than the biographical portion of our sketch: we mean the presenting a concise statement of the substance of the principal works of Sir William Hamilton: in doing which, we shall endeavour in popular language to give a true - though necessarily very general - answer to the inquiry which has been often made of us in society - namely, what are the nature and extent of those scientific labours and discoveries which have gained for Sir William Hamilton the high reputation he enjoys?

In fulfilment of this part of our task, we shall first attempt to give a slight and rapid outline of the researches which have been published by Sir William Hamilton in his Essay on the Theory of Systems of Rays, and in his Supplements to that essay, contained in the fifteenth and following volumes of the Transactions of the Royal Irish Academy.

These researches may be said, upon the whole, to relate to mathematical optics; and especially to contain a fundamental conception, and general method and formula for the application of Algebra (including the differential calculus) to the most varied problems of that science. It is true, that before their publication, many problems of this class, perhaps all that are required for the most important practical applications, had been already resolved: many valuable and elegant treatises upon the subject had been published; and a tendency had shown itself, of late years, to assume the algebraical form, and to adopt more or less the Cartesian method of co-ordinates, which may be employed in all applications of algebra to geometry. But with the exception of the profound Traité d'Optique of Malus (the well-known discoverer of the polarization of light by ordinary reflexion) this method of calculation, introduced into algebraic geometry by Des Cartes, does not appear to have been extensively and systematically applied to the solution of optical problems, especially so as to take account of the three dimensions of space. And the calculations of Malus, although symmetric, were so extremely complex, that they not only conducted to true results with difficulty, but even in some cases led (through a pardonable, because scarcely evitable, inadvertency) into important error. In a word, it appears that no appropriate general method had been discovered for the treatment of optical problems. Either there were special contrivances employed for the solution of particular (though practically important) cases, which could not easily be extended to new and more general questions: or when the universally applicable method of co-ordinates was used, and the three dimensions of space all kept in view, no adequate advantage was taken of anything peculiar to the laws of light, but common to all those laws, so as to combine, with the degree of generality aimed at, all such facility and elegance as the nature of the subject might allow. A method was to be found, or formed, which should effect for the science of algebraical optics, what the method of Des Cartes had done for algebraical geometry, or that of Lagrange for algebraical mechanics.

A method of this kind has, we may assert, been invented by Sir W. H., and has been by him embodied in a new and fundamental formula, for the study of optical systems. It seems to have occurred to him,⁴ on abstract philosophical grounds, that in order to set out hopefully in any general deduction of the consequences of the laws of the propagation of light by rays, it was desirable to start from an equally general induction respecting those laws themselves; from the highest axiom (in the Baconian sense of the word) which had yet been discovered respecting them. Now, such an axiom is supplied by that celebrated and general result, which is called by some the law of least action, and by others the law of the quickest propagation of light. From this result of induction, admitted to be valid, at least as such, by the adherents of the two rival theories, by those who suppose light to consist of particles emitted, and by those who hold it to be communicated by transmitted vibrations, Sir W. H. accordingly sets out. And as it expresses that a certain quantity (which in one theory is the action, and in the other theory is the time expended by light in its propagation along any bent or curved path, from one point to another), is, under certain conditions, invariable - namely, when the two extreme points are fixed; so he inquires how the same quantity varies under certain other conditions - namely, when the extreme points are changed. And the expression which he obtains for the law of such new variation, becomes his fundamental formula, his ``equation of the characteristic function;'' deduced, indeed, as has been stated, from the most general known law respecting the successive directions of any one path of light, but reciprocally including that law, and adapted rather to the study of optical systems, than to that of any single ray.

It would be impossible to enter here into any further details respecting the precise nature of this very general and abstract conception. But we may be permitted to illustrate its bearing by a single elementary example. It has long been known that when light, setting out from any given luminous point, is reflected at any second point upon a given plane mirror, and reaches, after this reflection, any third point; then, first, the reflected ray proceeds as if from a given image of the first point, situated behind the mirror; and, secondly, the whole bent path traversed by the light, is equal to the distance of the last point of that path from the image of the first point. Now, the general method of Sir W. H., when applied to this simple case, connects these two old theorems together, and shows that the former might have been deduced as a consequence from the latter. In other words, the knowledge of the law of the length of the bent path, in this and other cases of reflexion of light, conducts, according to his general method, to the knowledge of the laws of the directions of the extreme parts of that path. And analogous connexions are established by him for refraction, ordinary or extraordinary.

Among the results of this general view or method may be mentioned, the facility with which it conducts to a proof of the existence and determination of the properties of a certain series of surfaces, which cut perpendicularly the rays of any ordinary system, reflected or refracted any number of time by any combination of mirrors, lenses, and atmospheres. It is true that the theorem of the general existence of such surfaces had been distinctly perceived by Huyghens, and had even formed an essential element in his theory of light; since those surfaces were, in fact, the waves, which in that theory were considered as each marking out, for some one moment of time, the boundary of the spaces traversed by the light in all the several rays of the system. Indeed, in this now celebrated, though for a long time forgotten theory of Huyghens, the rays were derived from the perpendicular wave-surfaces, rather than the latter from the former. But the mathematical deduction of the theorem of the general existence of such perpendicular surfaces, from the consideration of the rays as mathematical lines, and from the purely mathematical laws of reflexion and refraction (abstraction being made of every physical hypothesis), would seem to have been not exempt from difficulty, in a recent state of optical science; since Malus, in the important Treatise above referred to, was led to deny the fact of such existence, even for the very simple case of two successive reflexions. And although Dupin had confirmed the theory of Huyghens, before the publication of Sir W. H.'s first essay, yet Plana, one of the most eminent Italian analysts, in a letter published in the Correspondence⁵ of Professor Quetelet, of Brussels, later by several years than the researches of Dupin, avowed himself unable to trace the error of Malus to its source, or to point out the mode of refuting it. Sir W. H.'s answer, published in the same Correspondence,⁶ met, and removed this difficulty on its own ground; but really, to any one who had caught the spirit of his method, and had understood his fundamental formula (which was not then known in Italy), the mathematical difficulty could not have arisen, nor could the mathematical existence of the surfaces in question have possibly eluded notice. As a matter of personal, though it cannot claim to be of historical interest, we may be permitted to mention what our acquaintance with the subject of the present sketch enables us to do, that the controverted theorem above referred to, was arrived at in his own investigations, during his first collegiate years, and before he had any knowledge of the researches of Huyghens, Malus, or Dupin.

But the published results which Sir W. Hamilton has deduced from his general method, are by no means limited to new proofs of previously known theorems, original or interesting as such proofs may sometimes be; they are, so far as we have been able to ascertain, for the most part entirely new. Our limits compel us to give here a selection, or sample, rather than a catalogue. But we cannot avoid alluding to the theorems respecting osculating focal reflectors and refractors, ordinary and extraordinary, concerning which our author has established a series of new theorems, analogous in part to the known theorems respecting spheres osculating to other surfaces: the discovery of the principal foci, and principal rays, or axes, of a reflected or refracted system generally, including, as infinitely particular cases, those foci and axes of the same kind which alone had previously been treated of; the consequent general theory of optical images and aberrations, with its application to instruments of revolution, of which last application, indeed, only an outline has as yet been published (in the Transactions of the Mathematical Section of the British Association, at the Cambridge meeting), and the prediction of conical refraction. This last result may, perhaps, properly receive a somewhat fuller notice here, because it has attracted more interest than the rest in England and elsewhere.

The law of the reflexion of light at ordinary mirrors, appears to have been known to Euclid; that of ordinary refraction at a surface or water, glass, or other uncrystallised medium was discovered in a much later age by Snellius: Huyghens discovered, and Malus confirmed, the law of the extraordinary refraction produced by one-axed crystals, such as Iceland spar; and finally, the law of the extraordinary double refraction at the faces of biaxal crystals, such as topaz or arragonite, was found in our own time by Fresnel. But even in these cases of extraordinary or crystalline refraction, no more than two refracted rays had every been observed, or even suspected to exist, if we except a theory of Cauchy, that there might possibly be a third ray, though probably imperceptible to our senses. Sir W. H., however, in investigating by his general method the consequences of the law of Fresnel, was led to conclude that there ought to be, in certain cases, which he assigned, not merely two, nor three, nor any finite number, but an infinite number, or a cone of refracted rays within a biaxal crystal, corresponding to and resulting from a single incident ray; and that, in certain other cases, a single ray within such a crystal should give rise to an infinite number of emergent rays, arranged in a certain other cone. He was led, therefore, to anticipate from theory two new laws of light, to which he gave the names of INTERNAL AND EXTERNAL CONICAL REFRACTION. This anticipation he announced to a general meeting of the Royal Irish Academy, on the occasion of presenting to that body the Third Supplement to his Theory of Systems of Rays, in which he had embodied his reasonings upon the subject, on the 22nd of October, 1832. On the following day he requested his friend, Professor Lloyd, to undertake an experimental investigation, with a view to effect the actual exhibition of the new phenomena thus predicted. It was difficult, for some time, to procure crystals of the requisite size and purity; but these, and other difficulties, were surmounted in perfectly establishing, by experiment, what Sir W. H. had predicted from theory.

The result excited at the time a very considerable sensation among scientific men in England and on the Continent; it was thought a happy boldness to have thus seized and brought into view, by dint of reasoning, a new class of phenomena, to which nothing similar had been before observed, and which even seemed, in the words used by an eminent English philosopher, to be ``in the teeth of all analogy.'' At the Cambridge meeting of the British Association, in 1833, the attention of the mathematical and physical section was largely given to the subject: and Herschel, Airy, and others, spoke warmly in praise of the discovery. In the introductory discourse with which the proceedings of that meeting were opened, Professor Whewell made it a topic, and expressed himself in the following words - ``In the way of such prophecies, few things have been more remarkable than the prediction, that under particular circumstances, a ray of light must be refracted into a conical pencil, deduced from the theory by Professor Hamilton, and afterwards verified experimentally by Professor Lloyd.''⁷ Previously, in the same year, Professor Airy had publicly recorded his impression upon the subject as follows - ``Perhaps the most remarkable prediction that has ever been made, is that lately made by Professor Hamilton.''<sup>8</sup> More lately, Professor Plücker, of Bonn, in an article on the general form of luminous waves, published in the nineteenth volume of Crelle's Journal, has used these words - ``Aucune experience de physique a fait tant d'impression sur mon esprit, que celle de la refraction conique. Un rayon de lumiere unique entrant dans un crystal et en sortant sous l'aspect d'un cone⁹ lumineux: c'etait une chose inouie et sans aucune analogie. Mr. Hamilton l'annonça, en partant de la forme de l'onde, qui avoit été deduite par les longs calculs d'une theorie abstraite. J'avoue que j'aurois désesperé de voir confirmé par l'experience un resultat si extraordinaire, predit par la seule theorie que la genie de Fresnel avait nouvellement créé. Mais Mr. Lloyd ayant démontré que les experiences etaient en parfaite concordance avec les predictions de Mr. Hamilton, tout préjugé contre une theorie si merveilleusement soutenue, a dû disparaitre.'' And it seems to be in part to this subject that reference is made in a passage of the article, attributed to Sir John Herschel, on the inductive sciences, in the last June number (page 233) of the Quarterly Review, where mention is made of a sound induction enabling us to predict, bearing not only stress, but torture: of theory actually remanding back experiment to read her lesson anew; informing here of facts so strange, as to appear to her impossible, and showing here all the singularities she would observe in critical cases, he never dreamed of trying.

Be that as it may, it is our pleasing duty as Irishmen to acknowledge the cordiality of the reception which the intellectual exertions of the subject of this sketch has met with in Great Britain, and in foreign countries. Herschel led the way, by giving, as the concluding sentence of his Treatise on Light, in the ``Encyclopædia Metropolitana,'' a most handsome notice of the Theory of Systems of Rays, then only passing through the press of our academy, but known by private circulation. Airy, at the Cambridge meeting, spoke of our friend as having rendered optics a new science. Whewell, in his History of the Inductive Sciences, and Babbage, in his Ninth Bridgewater Treatise, have assigned no unimportant place to the prediction of the conical refractions. An appreciation of what had been done in this matter was marked, not only here, by the award to Sir W. Hamilton from the Royal Irish Academy, of their Cunninghame Gold Medal, but also by his receiving, from the Royal Society of London, one of the Royal Gold Medals entrusted to their disposal by King William the Fourth. Besides being a member of many scientific societies in England and Scotland, and welcomed to personal intimacy with the most eminent men of science there, he has received many diplomas, and other marks of attention and respect from abroad. He is a member of the American Academy of Arts and Sciences; of the Academies of Berlin, Turin, and St. Petersburgh; and we believe of others, which we shall not now try to recollect. But the mention of the Imperial Academy of St. Petersburgh reminds us of his labours in another direction, of which the diploma from the Russian Society was more especially designed to attest their view of the importance.

Sir W. H., though from motives, we believe, of private convenience, he has not hitherto allowed himself to be proposed as a member of the Royal Society of London, has taken occasion to express his high respect and cordial goodwill towards that society, not only in his inaugural address to our academy, on being elected its president, but also by contributing, in imitation of his predecessor, Dr. Brinkley, some papers to the Philosophical Transactions. The papers thus published by him in London, are entitled, ``On a General Method in Dynamics;'' and they contain a system of complete and rigorous integrals of the celebrated differential equations of motion of a system of bodies, which had for so long a time tormented the scientific world of Europe: these integrals having been discovered by the application to this important question, of the same general algebraical method which he had already applied to optics. Indeed, as we have before recorded, a notice of the applicability of the method to dynamics, was very early and distinctly given in his first contribution to the Transactions of the Royal Irish Academy; but the subject seems to have passed from his thoughts, till after he had completed the investigations respecting conical refraction. He then returned to it, and the papers above mentioned were drawn up. They have, we know, been thought important upon the Continent: and we believe that we are safe in saying, that the great German mathematician, Jacobi (author of the Nova Fundamenta Functionum Ellipticarum Theoriæ), has considered it worth his while to translate largely from them, and to accompany his translations with copious comments, though we cannot at present procure the work in which his remarks are contained. And it was for these particular contributions to science that Sir W. Hamilton received the honour, rare in these countries, of being elected a corresponding member of the St. Petersburgh Academy; the diploma assigning as the reason, in Latin words which we forget, ``that he had deserved extremely well of science, with respect to the accomplishment of the integration of the general equations in dynamics.''

Many other investigations on scientific subjects have been published by Sir W. H., either fully or in outline, in the Transactions and Proceedings of the Royal Irish Academy, in the Transactions of the British Association, in the London and Edinburgh (now entitled also Dublin) Philosophical Magazine, and perhaps through other channels of publication. Thus, at the Bristol meeting of the Association, he gave an account (very brief, it is true) of a certain ``Calculus of Principal Relations,''<sup>10</sup> already announced by him in a still briefer manner before,<sup>11</sup> which includes as particular cases what he had done in optics and dynamics, and has for its object to integrate the differential equations to which the calculus of variations conducts, by combining, in a peculiar way, the principles of the latter calculus with those of the calculus of partial differentials. At the same meeting he presented, by invitation, a Report (since published by the Association) on the Researches of Mr. Jerrard,<sup>12</sup> respecting Equations of the Fifth Degree, in which, while he acknowledged the great ingenuity of those researches, he maintained that they had not succeeded in effecting their chief object - namely, the solution of equations of degrees higher than the fourth. Sir W. H. has since published, in the Transactions of the Royal Irish Academy,<sup>13</sup> an elaborate Essay on Equations of the Fifth Degree, in which he confirms, by reasoning of his own, the argument, or at least the conclusion, of Abel (an analyst of Norway, whose early death has often been regarded as one of the greatest losses sustained by science in recent times) - namely, that a general solution of such equations, by any combination of radicals and rational functions, is impossible. Of this essay, we know that it has been considered by a very high scientific authority, as definitely settling the long-vexed and interesting question upon which it treats; a result which the doubtful expressions used in Professor Peacock's Report<sup>14</sup> prove not to have been attained by Abel's ``Demonstration;'' and although this Essay of our friend bears the modest title, ``On the argument of Abel,'' we believe no one of his works displays more fully his great powers of original investigation, and his familiarity with the principles of the most abstract analysis. To give even the titles of all his shorter papers would exceed our limits, on which we have already trespassed; and we shall therefore conclude this part of our sketch by saying a word or two upon a treatise of a peculiar and semi-metaphysical kind, which he has published in the Transactions of the Academy, on ``Algebra Considered as the Science of Pure Time.''¹⁵

Sir William Hamilton, with his strong propensity to generalize, to take of every subject the most central view, and to look not only in physical but even in mathematical science, for somewhat which may interest the imagination, and be of kin to poetry, has not escaped the temptation to indulge in metaphysical reading and speculation, more than is very common, or perhaps quite approved of among mathematicians. Though a firm believer in the Christian revelation, and an attached member of the Church of England, he has allowed himself to be charmed, not only by Berkeley and Coleridge, but by Kant. And though we suppose that he would disclaim the implicit adoption of the teaching of any of the three, who indeed differ widely among themselves, yet we regard him as having made a decidedly Kantian movement, when he conceived and published that view of algebraic science, including the various calculi, to which we have just now referred. Kant's pure intuitions of space and time, now made familiar to the English reader by ``Whewell's Philosophy of the Inductive Sciences,'' had enjoyed very unequal fortunes as compared with one another. The intuition of space was easily admitted by all whose leanings were in this direction, to be the subject-matter of geometry as a science. But the intuition of time was not (we believe) claimed by Kant, or by his followers<sup>16</sup> as being, in any similar way the ground of any pure mathematical science; except so far as the doctrine of motion<sup>17</sup> may be such, which however seems to involve other elements. The pendant to the Kantian view of geometry appears to have been supplied by Sir William Hamilton's conception of algebra; which, as a science, rests according to him, essentially on the pure intuition of time. It must be observed, to guard against misapprehension, that he seems to regard this pure intuition, or original mental form, as ``closely connected, and in some part coincident with the notion of continuous progression;'' and that he is careful to distinguish his science of pure time ``on the one hand from all actual outward chronology, or collections of recorded events and phenomenal marks and measures, and on the other hand from all dynamical science, or reasonings and results from the notion of cause and effect.'' Unless some such view be adopted, and the conception of time (thus generalised and guarded) be admitted as a fundamental element of algebra, it will indeed by hard, as he has shown, to maintain that algebra is a Science at all; and we shall be almost driven to concede what is contended for by some eminent men, that algebra is rather to be accounted an Art or a Language; or at least that its theorems are nothing else than either, on the one hand, practical rules, or on the other hand, laws of symbolism. We do not feel competent to offer an opinion of our own upon the subject, and doubt whether the question raised by our countryman will ever be entirely decided. It seems to be connected with some of those deep and subtle strifes of intellect, which divide speculative minds at this day, as much, if not as warmly, as in the oldest times.

The train of circumstances which led to the publication of his view we may mention as evincing the friendly spirit by which he has always been actuated towards his fellow-labourers in the field of science. His old college-companion and competitor, John T. Graves Esq. (now of the Inner Temple, London) had published, in the Philosophical Transactions for 1829, a paper upon imaginary logarithms, in which conclusions were contained not easily reconcilable with generally received principles, and which met at the time with a good deal of opposition from eminent quarters. Sir William Hamilton records, that ``in reflecting on the important symbolic results of Mr. Graves, and in attempting to explain to himself those remarkable symbolisms, he was conducted to his theory ``of Conjugate Functions, or Algebraic Couples,'' which he then gave to the world, in confirmation of the conclusions of his friend: and it was to this theory of Conjugate Functions that he afterwards prefixed the more general essay, of which we have been speaking, as calculated to throw additional light upon Mr. Graves's paper, as well as to suggest a true theory for the science at large. For a distinct view of the object aimed at in that essay, we refer the reader from our slight hints to the general introductory remarks by which it is preceded: those remarks admirably fulfil the intention of their author. We have nowhere met with a piece of composition more remarkable for lucid arrangement of thoughts, and for accuracy and symmetry of expression.

Such is the sketch which we promised of the contents of Sir William Hamilton's principal works. Since the publication of the last of them, a longer pause than had been usual has succeeded, and we had begun to ask, what is Sir William Hamilton doing? Every one, indeed, must know that an indefinite series of productions equal in weight and originality to those we have passed in review is not to be expected from any intellect; but as we were aware that our friend's stores of scientific work, either completed or planned, were by no means exhausted, a moderate degree of impatience, we own, tempered by some anxiety lest previous over-labour might be the cause of the cessation, was rising within us. We have, therefore, hailed with pleasure the indications, in late numbers of the Philosophical Magazine, of renewed activity on his part in the way of publication; these re-assure us as to his being in working order: and, freed from apprehension on this score, we will not refrain, in regard to the projects of a higher stamp, which we know Sir William Hamilton to have had on hand, from making an appeal that they be not allowed to lie too long without being brought to book,- ad umbilicum. We are the more induced to say this, because we are free to confess, as to our friend, that we do not consider him exempt from our national sin of procrastination. Should curiosity tempt him to read our notice of himself, we are sure that after the praise which we have felt it his due to give, he will be quite refreshed by the hint of a fault; and we trust that, if conscience second us, he will in gratitude set himself to act upon our suggestion. From the publication of some of his completed papers, we know that he has been hindered by the desire not to press with disproportionate weight upon the limited funds applicable by the Royal Irish Academy to the expenses of printing.

And now, one word upon a subject which we could have wished to avoid, and for touching upon which we are afraid we shall incur our friend's displeasure, but upon which we have too strong a feeling to allow us to be silent. We allude to what we consider the very inadequate income upon which Sir William Hamilton has to live: inadequate as it appears to us, both to his individual claims and the station which he fills. Sir William Hamilton is the possessor of no patrimonial fortune, neither has he been enriched by marriage: he has been restrained from entering into the ministry of a church to which he is conscientiously attached, and to the most lucrative dignities of which he might naturally have looked forward, by a fear, which does him the highest honour, if not of any incompatibility between the functions of a clergyman and those which he now discharges, yet at least of affording ground of offence on this score to weaker brethren, or to enemies of the church: he has been precluded, we believe indeed by compact with the university, but at all events, we will say, by a due consideration of his present standing, and by justice to his own intellect and to the rightful claims upon it of the scientific world, from aiding any longer his pecuniary resources by the task of tuition: and upon a net income of less than six hundred a year, he has not only to support and provide for his family, but to maintain, for the credit of himself, his university, and his country, a hospitality upon which the demands are rendered the greater by his eminent merits and extended reputation. We know too well the dignity and unworldliness of our friend's character, to this that he will remonstrate on this subject, concerning which, intimate as we have been, we have never heard from him a word of complaint; we also know that in this hurrying world such a character and such conduct are too apt to be neglected or admired, rather than advocated and rewarded; and therefore, feeling that the occasion is exactly one upon which a friend's voice is alone likely to break a silence which ought not to last, we have taken the present opportunity of speaking our word of appeal; and we trust that, humble as it the quarter from which it proceeds, it will not be addressed in vain to the justice and the liberality of authorities, who have at heart, we know, the reputation of our national institutions, and upon whom will be reflected a lasting credit from any set which shall brighten the life of a man now certain of holding a distinguished place in the scientific annals of his country.

The outward form of our friend is the artist's share; perhaps, however, we shall not trespass beyond our dominion by adverting to the ``ample dome'' which Sir William Hamilton's head presents,- its wide compass, its full-orbed development, its lofty elevation,- a physical type, and if the phrenologists be right, an organic index of the capacious mind, with its harmoniously balanced faculties, there inhabiting. Our task we will now bring to an end by grouping, with as much faithfulness as we can, the features of his mind and character.

Professor Sedgwick, when President of the British Association at Cambridge, illustrated his own liberal spirit - every one knows his manifold ability to judge - by referring publicly to Sir William Hamilton as ``a man who possessed within himself powers and talents perhaps never before combined within one philosophic character.'' Of these powers, however, we believe that we may rightly name that of generalization, as the power which holds the predominant place, and is possessed by Sir William Hamilton in a degree which has been seldom equalled. It is that of which his mathematical works are eminently the product, and which makes mathematics to him a region over which metaphysical thought bears a presiding sway, and where imagination can successfully exercise her creative and combining energy, in devising new relations and higher laws. That he perceives the philosophical obligation afterwards to authenticate these relations and laws by induction, and to demonstrate them by the employment of a strict deductive process, and that he has the power also to fulfil this task, and the disposition to expend upon it the necessary amount of labour, frees him from the imputation of deficiencies which have often depreciated the fame and diminished the usefulness of those explorers in the high priori path, with whom the powers we have above referred to, of generalization and active imagination, were not similarly balanced; but who, after all, because they possessed these highest and most living faculties, will ever be allowed to stand in the first rank of scientific genius. It is this possession by Sir William Hamilton of imagination and metaphysical insight, in addition to the powers more commonly the exclusive property of men of science, which have made his mind and conversation a source of peculiar interest, as we know has been the case, to Coleridge and to Wordsworth, the latter of whom has often, in our hearing, testified the admiration and regard he entertains towards our countryman.

These high powers of Sir William Hamilton are served by a memory of unusual vigour; which also furnishes to his conversation, from the various fields of literature, nature, art, and life, felicitous allusion, appropriate example, and illustrative anecdote. That conversation, exception being made that for some audiences it is too wide and elemental in its general character, receives almost every additional intellectual charm from his natural eloquence, from language - his mastery over which is complete - the most varied and often original, from a lively fancy, a free discursiveness, and a clear logic: while the of the man causes it to shine with a light refracted from qualities still more excellent and amiable;- a buoyant cheerfulness, an ingenuous simplicity, a kindly human-heartedness, glad to praise, and glad to receive the reward of genuine approbation, a patient candour, a singleness of fidelity to truth, a love for all that is intellectually or morally noble, and an habitual reverence for every divinely-imposed restraint upon the play of fancy and the speculations of intellect.

The poetical productions of Sir William Hamilton are in our eyes of considerable value: more perhaps, indeed, as beautiful emanations of his character, evidencing the strength and generousness of his affections, and the loftiness of the aspirations and communings of his spirit, than as works of poetic art: yet many of them, we think, prove that had he devoted his powers to this art as a study, he might have gained a high place among our poets. We annex one of his sonnets, chosen not so much to exhibit to advantage his powers of rythm and expression, as to accredit our testimony to the exaltation and generosity of his nature.

In politics Sir William Hamilton has always been a Conservative of enlarged views and steadfast principles, which he has not shrunk from publicly maintaining. As to his religion, we are deeply gratified to have abundant warrant for believing that in conviction, in feeling, and in life he is an attached member of the Church of England, a sincere and devout Christian.

We had thought to conclude our memoir by designating him as ``the Irish Lagrange;'' flattering, however, to his scientific merits as the parallel possibly might be, his own name, we will believe, is his most fitting and honourable designation - Sir William Rowan Hamilton - a name which, we doubt not, will live a long life of scientific reputation, and be proudly remembered by his country as that of a great and a good man. But listen to his own sublime and holy aspiration!

O brooding Spirit of Wisdom and of Love,
Whose mighty wings even now o'ershadow me,
Absorb me in thine own immensity,
And raise me far my finite self above!
Purge vanity away, and the weak care
That name or fame of me may widely spread:
And the deep wish keep burning, in their stead,
Thy blissful influence afar to bear,-
Or see it borne! Let no desire of ease,
No lack of courage, faith, or love, delay
Mine own steps on that high thought-paven way
In which my soul her clear commission sees:
Yet with an equal joy let me behold
Thy chariot o'er that way by others roll'd!

Notes:

¹Mr. J. Hamilton is the author of an essay printed in the Transactions of the Royal Irish Academy ``On the Punic passage in Plautus.''

²In November, 1835. Of this tribute the Academy, as we learned from its minutes, requested afterwards to be furnished with a transcript, which might remain amongst its records; but we have ascertained with regret that the author, for some reason, was unable to comply with the request. The subsequently adopted plan of printing the proceedings at the academical meetings, for distribution among the members, is of great value, as securing the preservation of such memorials.

³It is stated in a note in Blackwood's complete edition of Mrs. Hemans' works that her beautiful poem, ``The Prayer of the Lonely Student,'' was written after hearing one of Sir William Hamilton's Introductory Lectures. The poem takes up the high religious theme at which the conclusion of the lecture reverentially glances. Sir William Hamilton and his sisters enjoyed the personal friendship of Mrs. Hemans; we happen to know that it was a flower sent to her room of sickness, from the garden of the Observatory, which suggested her exquisite lines, ``To the Blue Anemone.''

⁴See the article contributed by Sir W. H. to the fourth number of the Dublin University Review (October 1833, Milliken), entitled, ``On the paths of Light and of the Planets.'' This article, as well as several other papers, by Sir W. H., has been translated into French, and published by Professor Quetelet, of Brussels.

⁵Tome VIII. Livraison 2, page 99. Il y a dans l'analyse precedente un vice radical que echappe a toutes mes reflexions.

⁶Tome VIII. Livraison 1, page 27.

⁷``Report of the Third Meeting of the British Association for the Advancement of Science, held at Cambridge in 1833.'' Page xvi.

⁸``London and Edinburgh Philosophical Magazine.'' June 1833, p. 420.

⁹As we understand the matter, the interior cone emerges as a cylinder.

¹⁰Report of the Sixth Meeting of the British Association for the Advancement of Science, held at Bristol in 1836. Vol. V. Notices, p. 41.

¹¹In the introductions to his Essays on Dynamics, published in the Philosophical Transactions.

¹²Mathematical Researches, by George B. Jerrard, A.B. Strong, Bristol.

¹³Vol. XVIII.

¹⁴Report on the Recent Progress and Present State of Certain Branches of Analysis. Report of the Third Meeting of British Association. We allude to the following expressions at pages 311 and 312 - ``Some parts of it are obscure, and not perfectly conclusive.'' ``If the demonstration of Abel should be likewise admitted.''

¹⁵Vol. XVII. Part ii.

¹⁶Mr. Semple in the ``Metaphysic of Ethics, by Immanuel Kant,'' speaks of our understanding of how geometry and algebra arise, by the theory that space and time are intuitions a priori. This work was published (at Edinburgh) in 1836; Sir W. Hamilton's essay in 1835.

¹⁷Also erklärt unser zeitbegriff die möglichkeit so vieler erkenntniss a priori, als die allgemeine bewegungslehre, die nicht wenig fruchtbar ist darlegt. - Kant. C. d. r. V.

Links:

• William Rowan Hamilton: Some Nineteenth Century Perspectives
• Sir William Rowan Hamilton (1805-1865)
• History of Mathematics