29 AUGUST 1885, Page 19

11111 LATE SIR W. R. HAMILTON.* This is the second

volume of Mr. Graves's fall, laborious, and deeply interesting memoir of Sir William Rowan Hamilton, and it is to be followed by a third, which will complete the work.

Probably the first feeling of many readers will be that the ground-plan of the biographer is somewhat too extensive, and that one volume would have been more satisfying, because less exhausting, than three. Mr. Graves himself is not insensible to the force of this objection ; but we think his answer will be found satisfactory in the main to all but those whose first and last demand of a work of this kind is that it shall conform to the

recognised traditions of artistic biography. As the writer says

in his preface, the object of his work " is not simply a record of the events of the life of Sir W. R. Hamilton, and of the series of his scientific productions, but a record incorporating in addition writings which express the opinions held by a man of powerful intellect and wide cultivation on metaphysics, on literature, and on matters of general concernment." A more eclectic method would certainly have been a more popular one ; but the series to which these volumes belong aims at something better than mere popularity, and our own deliberate opinion is that Mr. Graves's choice has been a wise one. To those who are capable of appreciating Hamilton's marvellous achievements in mathematics, or of sympathising with his fine taste in literature, very few of the pages in these volumes will seem altogether superfluous.

The present volume covers the period between Hamilton's twenty-eighth and forty-ninth years, the record beginning with his betrothal and marriage (1832-33) ; carrying us on to 1853, the year which witnessed the publication of his memorable Lectures on Quaternions ; and including the period of Hamil- ton's most eager and fruitful activity. In the former volume of

Mr. Graves's biography, the interest, though largely scientific, was preponderatingly literary ; here, though largely literary, it is even more preponderatingly scientific. Poems and criticisms upon poetry do not disappear from Hamilton's letters —indeed, there is something almost amusing in the manner in which he breaks away from some high mathematical speculation and relieves himself with a sonnet—but they are much less

frequent than of old, and their place is filled by algebraical formulas, which, it must be admitted, have a somewhat de- pressing look, but which were to him quick with an interest as vital as that of poetry. His correspondence with Wordsworth had inevitably become more intermittent, but there was no weakening of the old friendship, and in his letters to Mr-

Anbrey de Vere, which are fairly numerous, there are many Wordsworthian passages. In these later years Hamilton had evidently found courage to indulge in occasional mild criticisms of the idol of his youth, and in one letter (p. 132) a stricture upon Wordsworth's not very intelligible classification of his poems is illustrated by a reference to what must have been a very unusual outbreak on the part of the Rydal poet Hamil- ton writes :—

"I think I admire Keats, Shelley, Coleridge, and Wordsworth at least as much now as ever. But Wordsworth more than any of the other three requires a little previous tuning of the reader's mind to be enjoyed and appreciated aright. After a longer interval than usual, I took up a volume of his works the other day, in a very lazy humour, and in a spirit of merely passing the time, in which one ought not to approach high poetry. I lit on the first of the Poems founded on the Affections.' I wish Wordsworth would let us find out for ourselves what his poems are founded upon ; and so wished his daughter in a conversation on that subject at Rydal Mount last September, and put him in a rage by hinting that her father was sometimes at a loss whether to refer her to the 'Poems of the Imagination' or Poems of the Fancy' for some particular passage."

It is not very easy to imagine Wordsworth, the dignified and imperturbable, " in a rage ;" but it is not difficult to imagine that if anything could so reduce him to the low level of the ordinary human being, it would be a slight put upon his pet classification. Revile the great " Ode " as unintelligible, " The Idiot Boy " as childish, and he could be serenely calm ; but the distinction between works of fancy and works of imagination was too sacred —perhaps because too vulnerable—to render it possible that he should endure a flippant allusion to it without betraying strong emotion.

Most of the literary matter in this volume is to be found in the course of the previously mentioned correspondence with Mr. Aubrey de Vere, some of whose letters to Hamilton, as well as

• Life of Sir William Rowan Hamilton, Kt., LL.D., Sc. By Robert Pereeval Graves, M.A. VoL II. Dublin University Press Series. Dublin: Hodges, Figgie, and Co. London : Longmans, Green, and Co.

those of Hamilton in reply, are exceedingly interesting. It is, however, as a record of strenuous and triumphant labour in the field of scientific speculation that this instalment of the bio- graphy is mainly remarkable. In the previous volume, we left Hamilton at the age of twenty-seven, when, after an easy

mastery of the mathematical problems ordinarily supposed at the time to be within the field of academic training, he had won European fame as a scientific discoverer by his theory of conical refraction. The story told in the present volume is so crowded with splendid and varied achievement that it is hardly possible to do more than mention certain heads under which Hamilton's chief mathematical work naturally falls.

"Conjugate Functions," "Algebra as the Science of Pare Time," " Characteristic Function applied to Dynamics," " Report on Jerrard's supposed Solution of Equations of the Fourth Degree,"* " Dynamics of Light," " Fluctuating Functions,"—such are the titles which summarise the dis- coveries or inventions of the years previous to 1843. In that year, when Hamilton was but thirty-eight, was made the great

discovery which eclipsed all that had gone before it,—the dis- covery involved in the calculus of quaternions, which, as his biographer truly says, " will always be connected with his name, as the discovery of flexions with that of Newton, and the system

of co-ordinates with that of Descartes." There is, too, a unity in Hamilton's mathematical life which adds to the effect pro- duced on us as spectators by its mere largeness of scale. Most of the discoveries which preceded quaternions had been fore- runners of the great invention, or, at least, foreshadowings of it; and the twenty-two years which intervened between 1843 and the year of Hamilton's death, 1865, were spent in so developing, perfecting, and applying the new calculus as to make it an instrument of discovery for successive generations in all after-ages. Mr. Graves gives two deeply interesting letters in which Hamilton himself tells us of the time, place, and sur- roundings of the great achievement. In 1865, he writes to his son Archibald,—

" I happen to be able to put the finger of memory upon the year and month—October, 1843—when, having recently returned from visits to Cork and Parsonstom3, connected with a meeting of the British Association, the desire to discover the laws of the multiplica- tion referred to regained with me a certain strength and earnestness, which bad for years been dormant, but was then on the point of being gratified, and was occasionally talked of with you. Every morning in the early part of the above-cited mouth, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself used to ask me, Well, papa, can you multiply triplets ?' Whereto I was always obliged to reply, with a sad shake of the head, No, I can only add and subtract them.' But on the 18th day of the same month —which happened to be a Monday and a council day of the Royal Irish Academy—I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal, to which she had perhaps driven ; and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close, and a spark flashed forth, the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery."

Hamilton's prevision of the importance of his discovery has received ample confirmation from great authorities, but it stands now, and will for ever stand, independent of all external but- tresses. Professor W. K. Clifford writes :—" Quaternions are the last word of geometry in regard to complex algebras," and among those who in labouring towards the development of the calculus have carried onward the torch which Hamilton lighted are Kelland, Tait, Haul, Laisant, Bellavitis, Padelletti, Moebius, Bolzani, Benjamin Pierce, Arthur Cayley, and Pro- fessor Casey, of Dublin.

Nor must it be forgotten that besides pursuing the greatlines of study and discovery with which his name is most promin- ently associated, Hamilton was continually diverging into minor paths of investigation, often in order to oblige those who applied to him for help and sympathy, and sometimes because his duty as President of the Royal Irish Academy demanded that he should at least partially master the subjects of papers read before that body. The reader may be briefly referred to the Index, under the heads Hargreave, Euler's Theorem, Ellipsoid, Mallet, Ch6seaux, Nadler, Probabilities, Lunar Theorem, Ohm, Kane, Apjohn, for illustrations of Hamilton's versatility, and an extremely interesting account of a conversation with Faraday (pp. 95-6) must not be overlooked.

The range of Hamilton's powers was indeed almost unique.

• Closely connected with this paper was Hamilton's subsequent "Memoir on the Argument of Abel." See page 185 of volume under review. We are impressed almost as much by his obvious potentialities as by his actual achievements. That he would have done memorable work in the field of metaphysical science, had not mathematics made so stern a demand upon his powers, will, we think, be evident to those who peruse the remarks on Kant in the earlier part of the present volume, especially the exposition of Kant's philosophy (pp. 103.105), which is as adequate as it possibly could be within the limits of a letter. Of the extra- ordinary merits of the portentous letter on Triads (pp. 363-375) we cannot stay to speak. Suffice it to say that it is a production of amazing energy, and is instinct with that intellectual zeal which is in itself an augury of success.

The private life of Hamilton during the years covered by this volume was not specially eventful, nor was it altogether un- clouded. In some portions of his work Mr. Graves has had a difficult task, and he has performed it with great tenderness and delicacy, which contrasts pleasantly with the brutality of some recent biographers. The value both of this volume and of its predecessor has been much enhanced by one of the most admirable indices it has ever been our pleasure to consult.