Sir W. R. Hamilton

By Augustus De Morgan

An obituary published in the Gentleman's Magazine and Historical Review, vol. I. (new series) (1866), pp. 128-134.

Sept. 2, 1865. At Dublin, aged 60, Sir William Rowan Hamilton, Astronomer-Royal for Ireland.

An old article in a review, written on the subject of this memoir, reminds its readers that each of the three kingdoms has its Sir William Hamilton. The Englishman was noted for his patronage of art; the Scotchman was among the first in philosophy; and the Irishman was among the first in mathematics. In this race it is clear that England, if placed at all, comes in a bad third. Her representative is sufficiently described in the view quoted, as ``holding a distinguished place among the virtuosos of his time.'' But Scotland and Ireland have added each a great man to the rolls of fame, and each honours the memory of one of those who make lasting marks upon the subjects which they studied. Those subjects are so different that no comparison can be made.

William Rowan Hamilton belonged to a branch of the Scotch family, which settled in the North of Ireland in the time of James I. He was born August 4, 1805 [see note]. His father was Archibald Hamilton, a solicitor at Dublin, a man of character and ability. His mother was Miss Sarah Hutton, of a well-known Dublin family, related to the late Dr. Hutton [see note]. When at a very early age, the boy showed signs of talent, and his father placed him with his uncle, the Rev. James Hamilton, curate of Trim (who died about 1847), with whom he remained until he went to college. This gentleman must have been a Hebrew scholar, for he wrote on the Punic passage in Plautus. His nephew had made some progress in Hebrew at four years old. The father had intended him for the East India Company's service, and the uncle must have been well able to prepare him; for, besides some knowledge of Latin and Greek, the boy, at the age of thirteen, had gained the rudiments at least of French, Italian, Spanish, German, Syriac, Persian, Arabic, Sanscrit, Hindustani, and Malay. Very likely he knew but little of some of these languages; and we might have supposed that little the least possible, if some positive evidence had not been produced. A Dublin examiner in Hebrew declared that, at seven years old, he showed more knowledge than many candidates for the fellowship; and the Persian ambassador, to whom the boy wrote a letter of compliment on his arrival at Dublin in 1819, declared that he did not think there had been a man in England who could have penned such a letter in Persian. We may add, that in six months he taught his eldest son Hebrew enough to gain a premium when he entered at Trinity College.

In mathematics he was nearly self-taught. He fell in with a Latin Euclid at ten years old; at twelve he became acquainted with Newton's Universal Arithmetic. From fifteen to seventeen he was employed on the Principia, the Differential Calculus, and the Mécanique Céleste. His studies were rapid, and his own thoughts produced the germs of his subsequent writings. A paper on Optics was presented to the Royal Irish Academy in 1824, and was followed by the request that the author would develope the subject more fully. This gave rise to the celebrated papers on Systems of Rays. Hamilton entered Trinity College, Dublin, in 1823, and rumours of his genius had then begun to spread. These, in a short time, reached the University of Cambridge, where they were fixed in the thoughts of many by those which circulated concerning another young Irishman. Robert Murphy began residence at Cambridge in October, 1825, and was said, and truly, to have given marks of talent very unusual at his age. The early promise was made good in both cases; though Murphy's subsequent career was cut short by death twenty-two years before that of Hamilton. In both cases the exaggerated expression of an admiring witness of their early proficiency is recorded. Dr. Brinckley [sic], about 1823, said of Hamilton, ``This young man, I do not say will be, but is, the first mathematician of his age.'' Another Irish mathematician, who had found out Murphy's talents, said to a patron of his, ``You have a second Sir Isaac Newton in Mallow: pray look after him.'' These prophecies are recorded after verification, and sometimes, if it be not a bull, produced by it. They are exceedingly common: every boy who shows anything like genius is the object of them: those which succeed gain public admiration; those which fail are sure of comfortable oblivion. Dr. Brinkley was, as our account says, ``habitually sober and truthful in speech.'' We remember him well, and his quiet manner; and we will undertake to say that he went no further than - ``If the young man goes on as he has begun, he will become,'' &c. &c.

We will not record the details of a college career unexampled in brilliancy, as a conjoint specimen of literature and science. It is unique in having obtained the judgment of optimé at examinations both in a branch of literature and a branch of science - Greek and Physics. This distinction, very rarely given, answers to the Cambridge myth - we doubt whether there be any foundation for it - of a Senior Wrangler of unusual goodness being officially pronounced incomparabilis. His career as a student was closed in an unusual way, while he was studying for both the gold medals, with the intention of afterwards competing for a fellowship. The greatest distinction, beyond a doubt, which an Alma Mater can offer to one of her sons is, to cut short his career as a student by declaring that she must have him as a teacher; and this distinction was conferred on Hamilton. In theory, the same thing is sometimes done at Cambridge and Oxford; for a Bachelor of Arts is still in statu pupillari. Many smiled when Mr. Airy, then only B.A., took his seat as a University Professor among the Heads of Houses in the Golgotha of St. Mary's. But the distinction conferred on Hamilton was still more unusual. Mr. Airy, in spite of his pupillar rank, was Fellow and Lecturer in his college: Hamilton rose from the very benches of the lecture-room to the Professor's chair. In 1827, he was elected Professor of Astronomy, on the resignation of Dr. Brinckley [sic], an early encourager of his talents.

This appointment gave rise to remark which lasted his whole life. He was not especially addicted to astronomy; he was not at all given to practical astronomy and the management of an observatory: it was not either hoped, expected, or desired that he should become so. His University saw the importance of attaching the rising genius to itself by a permanent tie, and acted a wise part in postponing the claims of astronomy for a season. The event has justified the course taken: the renown which Hamilton has conferred on the Dublin University, the influence of his name, example, and teaching, in the formation of an Irish school of mathematicians of a force which no one could have predicted, have been worth many times the best results which could have been obtained from the utmost rivalry which Dublin could have offered to Greenwich, Cambridge, Oxford, or Edinburgh in practical astronomy. He lectured on astronomy most admirably, and superintended an assistant in the ordinary work of an observatory. In his later years he had classes at the Observatory for instruction in the theory and use of the instruments.

Young Hamilton accordingly started in life at the age of twenty-two, as Andrews' Professor of Astronomy and superintendent of the Observatory near Dublin. The post was not, in the strictest sense, offered to him; but such a discussion took place at the managing board of the College, that his tutor, Dr. Boyton, wrote immediately to press him to become a candidate. He did so, and the result was announced within a week. He took up his residence at the Observatory, with his sisters for his housekeepers. These ladies inherited the talent of their parents. One of them, ``E. M. H.'' long deceased, was well known in the pages of the Dublin University Magazine, as well as by a volume of poems. From this time his life, apart from scientific labours, presents but few events. He was knighted by the Lord Lieutenant (Normanby) at the first Dublin meeting of the British Association. He afterwards received a pension of 200l. a year. [Footnote: This pension has been continued to his widow.] In 1833 (April 9), he married Miss Helena Maria Bayly, daughter of the rector of Nenagh, of an old family in the south of Ireland. This lady survives him, with the three children, two sons and a daughter, who were all the offspring of the marriage. In 1837 he was elected President of the Royal Irish Academy. We pass over the various medals, degrees, and diplomas which he received from academies and universities. These things are the distinctions of the individual while he lives, but after death the honour attaches to those who gave them.

Sir W. Hamilton never was a Fellow of the Royal Society: the reason was, we believe, that he could not afford the annual payments. His income was small, and he resided far from London. It is one of our anomalies that the distinction which is considered as the highest scientific order of knighthood, is, in truth, also a sign of pecuniary capacity: and F.R.S. testifies to a money-power of four guineas a-year, combined with other merits. So, in different degrees, do all the other combinations of letters which we see in title-pages: and to an Irishman of very moderate means, the Royal Irish Academy would probably be as much as he could manage. It would be well if the Royal Society were to admit Irish and Scotch members, actually residing in their own countries, and supporting thier own national academies, at a reduced rate.

In the earlier part of his career Hamilton occasionally had a pupil residing in the house. He did not court this mode of adding to his income; and we may close this allusion by recording that in this manner commenced his acquaintance with his dearest friend, Lord Dunraven.

During the year 1865, Sir W. R. Hamilton declined in health. The last occasion on which he appeared in public was the opening of the Dublin Exhibition. An attack of gout soon followed, under which he languished, though still able to work, until June, when a second and very sudden attack brought him into a dying condition and closed his life on the 2nd of September. He retained his faculties to the last: not only his intellectual power, but his keen apprehension of dates. He remembered that a Dublin physician, who was called in late in his disorder, had been in the house ``a quarter of a century ago,'' which turned out to have been the fact to the very year.

Before giving a few words to his scientific labours, we shall attempt some description of his personal character. Hamilton was a man who combined different talents to an extent which is often attributed, by exaggeration, to the possessor of one powerful faculty: but in his case there is abundant evidence. He was scholar, poet, metaphysician, mathematician and natural philosopher. Highly imaginative and fluent of tongue, he was an orator in all that he knew; even in mathematics, to the details of which he could give almost a rhetorical cast in a letter. In metaphysics he was very well read, and could talk in a way which suggested a comparison to Southey, and a difference. Hamilton one day preached to Southey on this subject until the latter remarked, as they passed a ploughman, ``If you had been Coleridge, you would have talked to that ploughman just as you have been talking to me.'' He has left a large collection of unpublished papers; and it is to be hoped that some of them will relate to other studies besides mathematics.

Hamlton was not only an Irishman, but Irish: and this with curious oppositions of character. He was a non-combatant: there was too much kindness in his disposition to allow any fight to show itself. Impulsive and enthusiastic, with strong opinions and new views, he was never engaged in a scientific controversy. In this matter he was the Scotchman, and the Edinburgh Sir W. Hamilton - never quite out of hot water - was the Irishman. William Rowan Hamilton's preservative was his dread of wounding the feelings of others. In his youth, ``Defender of the Absent'' was his nickname. One person, who must not be named, wrote against him in an ignorant manner; and for once he replied, and pointed out how unfit his opponent was to be a critic. But afterwards, and long afterwards, he spoke with great remorse of his proceeding: ``He found,'' he said, ``that he had hurt the man's feelings;'' and he exerted himself to get a pension for the widow. He had a morbid fear of being a plagiarist; and the letters which he wrote to those who had treated like subjects with himself sometimes contained curious and far-fetched misgivings about his own priority. But, with all this, there was a touch of the national temperament in him. An Englishman who never strikes, can, nevertheless, clench his fists, which the most warlike Frenchman cannot do: an Irishman who never gets into a row may give quick but quiet symptoms of opposition of opinion, and of what, were it more than a rudiment, would be called pugnacity. We may seriously illustrate this by Hamilton's first thought, on seeing the commencement of a bit of verse written in the visitor's book at Glendalough:-

``From soft Shillelagh's shady vale come down - ''

``Soft shillelagh!'' said he: and he took his pencil and added,

Hard sticks on many a bald and tempting crown.''

Hamilton was apt to work by fits and starts. He has been known several times to work fourteen hours in one day, standing nearly all the while; but there were intervals of comparative inaction. The laudatory article to which we have referred, accused him of procrastination: we may add, that he was the most methodical procrastinator who ever lived. What other specimen of this class was much given to keeping copies of his letters? - aye, even of letters which were never sent? Sometimes a letter was written and copied which was not sent for months, and then only the first sheet, with promise of the rest. It has even happened that the letter was knowingly never forwarded at all, and that when, long after, he found reason to wish to send it, he could not find it, and sent the copy instead. But with all this, he made more notes than anyone, and was exceedingly particular about minute accuracy of points, crosses, and dates in the most trifling memoranda. His first lectures on Quaternions, to our knowledge, had a dozen sheets printed off by December, 1851, and appeared only in the middle of 1853: the second set, which will probably appear by the time this account is printed, took a much longer time in passing through the press. The proof-sheets were held in hand until the author had satisfied himself about himself, and about others: and neither was easy work.

We have said he never had a controversy. The nearest approach we can find is that when churchwarden - an office he accepted on condition of a sinecure - he was involved in a defensive discussion with Archbp. Whately - a man greatly admired by him - who objected to the insertion of a certain stained-glass window in a church. When a piece of road was placed under his superintendence, he insisted, like a mathematician, upon the stones being broken until they would pass through a gauge. His papers were in most picturesque confusion, but he knew how to lay his hand on any one he wanted: he could detect the removal, were it only by a quarter of an inch, of any one out of hundreds, and any such offence against the laws of his study would throw him into what our informant calls a ``good, honest, thundering passion.''

The religion of a modern man of science is a difficult subject to mention in most cases. When the man is officially attached to the Establishment he has an official orthodoxy presumed for him, unless he take pains to get another character; this imputed correctness he may deserve in any degree, from nullity to totality. When free of trammels, no one pretends to guess what he may be, and biography generally treats the subject in terms either loose or guarded. In the case of Hamilton there is no occasion to state anything but the simple fact, known to all his intimates, that he was in private profession, as in public, a Christian, a lover of the Bible, an orthodox and attached member of the Established Church, though of the most liberal feelings on all points. He had some disposition towards the life of a clergyman, but preferred to keep himself free to devote all his time to science: he was offered ordination by two bishops. It is rarely that a man of genius, who has devoted much time to metaphysics, finds himself quite in harmony with the belief of the multitude in all but its denunciatory part: he may keep prudent silence, but he seldom volunteers assent to private friends of different opinions. And this without any affectation. In the matter of right and wrong, Hamilton was very simple-minded. To say that he was truthful would be only a part of the truth: his aptitude to entertain misgivings, already alluded to, made him often think it right to express his opinions to avoid the possibility of being misunderstood. But it may be said that it was not he and others who differed, but his opinions and the opinions of others: his tolerance was perfect. He delighted in music, in playing with children, in reading their fairy tales: and by rolling hoops, leaping, walking round on the parapet of the Observatory, and other remains of old gymnastic practice, he provoked a staid Scotchman of science to call him an overgrown boy. His hair was, in youth, of a dark, curling, and silky chestnut colour; his eyes were violet, his hands were fair and soft, his finger-ends broad. He was of middle height, with a broad chest. His voice was distinct, sweet, and powerful.

He very much liked Goldsmith's writings, and we think points of similarity might be traced between him and the author whom he so much admired. But the parallel would break down altogether in one point: Hamilton spoke as well as he wrote. He relished the extremes both of simplicity and splendour, though in his own habits and manners as plain as possible. He thought much of the comfort of others, and lightly of his own. When some housebreakers were caught on the premises, and detained until they could be carried before a magistrate, he amused his family by directing that the felons should be asked whether they preferred tea or milk for breakfast. A full memoir of his private and public life would present a genial combination of intellectual greatness, moral goodness, and piquant peculiarity of thought and manner, all brightened by never-ceasing benevolence of feeling, and toned by rare gentleness of manner.

Our notice of Hamilton's scientific character must be brief: and it is not in our power to dwell on those parts which are not in evidence before the public. The scholar, the poet, and the metaphysician must be set forth in some large and well studied memoir, or not at all. Hamilton himself often said, ``I live by mathematics, but I am a poet.'' Such an aphorism may surprise our readers, but they should remember that the moving power of mathematical invention is not reasoning, but imagination. We no longer apply the homely term maker in literal translation of poet: but discoverers of all kinds, whatever may be their lines, are makers; or, as we now say, have the creative genius.

Hamilton was once called the Irish Lagrange, and the comparison was a good one. The styles of mathematicians differ as much as the styles of poets; and Hamilton is distinguished by that power over symbols, combined with elegance of expression, which is so remarkable in the writings of Lagrange. The mere list of his scattered writings, which we are afraid we cannot make very perfect, is as follows [see note]:-

There is one separate work, the Lectures on Quaternions; Dublin 1853, 8vo (about 900 pages). In the Transactions of the Royal Irish Academy, as follows (we take the dates on the titles of the separate copies, which best show the time when the results were widely made known to the world, but the dates of communication are sometimes several years earlier):- In 1828, 1830, 1830, 1833, the Theory of the Systems of Rays, and three supplements; 1830 and 1831, Error in a Received Principle of Analysis, and note; 1834 and 1835, two Papers on a Method in Dynamics; 1835, on Algebra as the Science of Pure Time; 1838, on Abel's Argument concerning the Roots of an Equation of the Fifth Degree; 1842, on Fluctuating Functions; 1843, on Equations of the Fifth Degree; 1847, on Quaternions.

In the Philosophical Magazine are various small papers, to which we give slight reference. 1831 and 1832, Mathematical Optics; 1833, Characteristic function in Optics; 1834, Application to Dynamics of Method previously applied to Optics, 1835, New Theory of Logologues; 1836, Calculus of Principal Relations; 1838, Propagation of Light in Vacuo; Propagation of Light in Crystals; 1842, Mode of expressing Fluctuating Functions by Formulæ; 1843, Theorem of Differences; Investigations connected with the Calculus of Probabilities; Equations of the Fifth Degree; 1844 and 1845. On Quaternions; 1847, Isoperimetrical Problem treated by Quaternions; 1849, New Applications of Quaternions to Geometry; 1850, Polyzones inscribed in a surface of the Second Order; 1852, Biquaternions; 1854, Extension of Quaternions; 1855, Conception of the Anharmonic Quaternion, and Application to Involution in Space; 1857, Icosian Calculus; 1859, Application of Quaternions to the Geometry of Fresnel's Wave-Surface; 1861, Geometrical Nets in Space.

In the first four volumes of the Cambridge and Dublin Mathematical Journal are papers on symbolical geometry, and on quaternions. There is also, but we have not the reference, a mathematical game, which the framer called Icosian: and there are other small tracts.

It is impossible to give the least account of the remarkable paper on rays by which Hamilton first established his reputation. The third supplement contains the memorable prediction of conical refraction. By reasoning it was shown that, under certain circumstances, a ray of light is split by a crystal, not into one or into two, but into a cone of rays. The assertion was tested and verified by Professor Lloyd in 1833. Opticians had no more imagined the possiblity of such a thing, than astronomers had imagined the planet Neptune, which Leverrier and Adams calculated into existence. These two things deserve to rank together as, perhaps, the two most remarkable of verified scientific predictions.

The new method in dynamics is a very remarkable extension or completion of Lagrange's general equations for dynamical problems. The paper on algebra as the science of pure time, is one of those explanations of algebra, in its full extent, which will hereafter be held as a noted feature of our day. The paper on Abel's argument against the possibility of expressing the root of an equation of the fifth degree, is a masterly examination of one of the most difficult of controversies. The paper on fluctuating functions, the name of which is not suggestive, is an investigation of the modes of expressing discontinuity which contains the soundest demonstration ever given of Fourier's celebrated theorem on the subject.

The quaternions are perhaps the things by which Hamilton's name will be most widely known in future times. He was himself a lover of fame: he did not hesitate to avow that he took pleasure in the thought of being remembered for ages. So do many who are able to enjoy the satisfaction, and will never know that their houses were built on sand. But the founder of a new algebra, of great power and flexibility, will be remembered in the daily life of all the mathematicians who use it, and in the history of science even when, if the time should come, the quaternions are supplanted by something yet more powerful. The old algebra, as all know, went through stages of difficulty, consequent upon the appearance of symbols which the mechanism of the science furnished, but which the definitions of the science were inadequate to explain. First came the negative quantity; and when that was conquered, its square root, long called the impossible quantity. In this and the last century the second difficulty was gradually overcome; and algebra, with a field of explanation embracing all lines in one plane, became a fully explained science. But where is the algebra which has a grasp of symbols wide enough to take into its field of explanation lines drawn in all possible planes? Hamilton answered this question by producing the quaternions, as one solution of the problem; and he made his new algebra a powerful instrument of application. We quarrel with the name quaternion; we contend that the system is the triple algebra, in the sense in which ordinary algebra, when fully explained, has been called double algebra. But we accept good things under any names. Such is the glimpse we can give, in an article like the present, of the writings of a man of true and rare inventive genius, - a man whose place among mathematical discoverers we cannot venture to assign: those who see the ultimate consequences of the quaternions will be the proper judges on this point.

There is an article, to which we have alluded and from which we have borrowed, in Fraser's Magazine for January, 1842, which gives a genial and interesting account of Hamilton. It is accompanied by a portrait, representing him sitting in the chair of the Royal Irish Academy. This portrait is not thought to do justice to him, and a marble bust in the possession of Lord Dunraven is to be preferred to it. But the great size of forehead and the intelligence of the expression are strongly indicative; and both the engraving and the photograph from the bust shew humour and a sense of the ridiculous.


D.R. Wilkins
School of Mathematics
Trinity College, Dublin