BOOKS.

SIR WILLIAM ROWAN HAMILTON.* Tam volume brings to a conclusion the massive and monu- mental biography of Sir William Rowan Hamilton, the pre- paration of which has occupied so many years of its writer's life; and Mr. Graves is to be heartily congratulated upon the successful and satisfying completion of his great achievement. There are doubtless some not wholly unsympathetic critics who will maintain that the achievement is too great, or, as they would put it, too bulky; and it must be admitted that in an age when books are many, and leisure to read them increasingly scanty, a biographical work covering more than two thousand large octavo pages does stand in some need of defence against the charge that it is too much of a good thing. Perhaps the best defence is provided by the plea that any one attempting a really adequate biography of Hamilton was bound to satisfy two classes of readers,—thoae who are mainly interested in Hamilton's personality, and in his contributions to literature which so admirably reflect it; and those by whom he is remembered chiefly as the inventor of Quaternions, and as one of the most profound and prescient mathematical thinkers and workers of modern times. Kr. Graves has done justice both to the man and the mathema- tician, and the fair-minded reader will hesitate to resent the copiousness rendered necessary by this double duty. The im- portant question to be asked concerning any literary portrait is not, "What is the size of the canvas ?" but, "Is the picture lifelike and real ; does it present the man to us in his habit as he lived, and make us feel that we have been of his society ?" If such inquiries be made with regard to Mr. Graves's biography of the great Dublin savant, the only possible reply is an emphatic affirmative.

In matter which appeals to the first of the two classes of readers just mentioned, this volume is necessarily less rich than its predecessors. The second volume brought us up to 1853, in which year Hamilton had his forty-eighth birthday. He died in 1865 at the age of sixty, but though he was an assiduous worker until a comparatively short time before the end, his most memorable labours, and the majority of his most interesting experiences, belong to the earlier period;- and without any diminution of the scale of his work, Mr. Graves has been able to give us the entire remaining portion. of the • Life of Sir William Rowan Hamilton, including Selections from his Poem', Correspondence, and Miscellaneous Writings. By Hobert Perceval Graves, ALA. VoL ILL Dublin Hodges, Figgis, and Co. London: Longmaus, Green, and Co

biographical record in fewer than two hundred pages. This is followed by two chapters giving the verdicts upon Hamilton's work expressed by great contemporaries, and gathering up some interesting fragments of reminiscence ; while the rest of the volume—rather more than half—is devoted to a correspond- ence between Hamilton and Professor De Morgan, extending from 1841 to 1865, which, in addition to the interest it possesses for the mathematical student, is by no means lacking in characteristic sayings upon personal and general topics.

The last twelve years of Sir William Hamilton's life were, as we have said, comparatively uneventful. To Hamilton himself, probably the most interesting, and certainly the most gratifying incident, was the conferring upon him of the highest honour which the learning of the Western World had in its power to bestow. "It was," writes Mr. Graves, "after the tremendous conflict between North and South was ended, and both divisions of the continent had been by it welded into one nation, that the first truly national Academy of Science in America was formed. One of its earliest duties was to draw up a list of the most eminent scientific men throughout the world, upon whom the honour of Foreign Associate should be conferred, and by a two-thirds majority it was decided that the place should be occupied by the name of William Rowan Hamilton." The honour came only just in time, for when Hamilton received the official notification, his last struggle with disease was well begun. It evidently gave him great delight, and lie received it not merely with gladness but with an unfeigned surprise, the outcome of the characteristic modesty which never deserted him ; speaking of the event in a letter to a Trinity College friend, as "to me so sur- prising a thing that I might be apt to treat it as incredible, if I had not been long acquainted with the writer of the com- munication." This modesty of nature which always prompted Hamilton to self-depreciation rather than to self-assertion, was not, however, inconsistent -with an outspoken desire for and delight in the fame which assured him that his labours were recognised and valued,—indeed, both his modest estimate of himself and his keen appreciation of the higher and truer estimation of others were manifestations of that exquisite sensitiveness of nature which was one of his most powerful charms. One of the most eager welcomers and enthusiastic students of the epoch-making Lectures on Qwzternions was Professor Peter Guthrie Tait, who at that time held the mathematical chair at the Queen's College, Belfast, and was comparatively little known to the outside world, now the distinguished Professor of Natural Philosophy at the University of Edinburgh. Professor Tait had in view the publication of a set of examples in Quaternions which might afford popular proof of the utility of the calculus, and to this plan Hamilton gave his entire and hearty sanc- tion. At this period (1858), however, he was himself engaged in preparing his Elements of Quaternions, and for some time he was seriously troubled by forebodings that the weight and interest of this work might be discounted by the prior publica- tion of the work of his younger fellow-labourer. The anxiety was very characteristic, and not less so was the beautiful con- siderateness with which Hamilton refrained from any word of complaint or remonstrance. The former proved to be needless, and the latter soon received a fit reward, for the master found in the disciple a nature not less loyal and generous than his own. Professor Tait "not only took an early opportunity of publicly acknowledging, in ample terms of homage, the supremacy of the discoverer in the territory of Quaternions, but gave frank engagement not to anticipate Hamilton's publication." This engagement was carried out with scrupulous honour, though neither Hamilton nor Professor Tait had any anticipation of the delay which it would involve. The author of the Elements of Quaternions seriously miscalculated the time required for its completion, for as a matter of fact, the work was not published until after the death of its author, and Professor Tait's Examples did not see the light until 1867, after nine years of patient waiting.

An indefatigable worker, Hamilton was pre-eminently a social man, and Mr. Graves has done jnstice to this side of his nature—perhaps its most truly characteristic side—by devoting a. large, but certainly not disproportionately large, amount of space to the record of his numerous and ardent friendships. Prominent among these was his long friendship with Mr. Aubrey de Vere, and some of the most interesting of the more personal letters in this volume are those which passed between the friends at and subsequent to the time Of Mr. de Vere's submission to the Roman Church. Never was.

man less of a bigot than Hamilton, but this action on the part. of his friend seems to have been really painful to him ; and.

his reasons for feeling it to be so illustrate so aptly the sensitiveness and desire for sympathy above referred to that. we quote from the letter in which they are set forth with very touching pathos. We print the letter with Hamilton's own.

marks of emphasis, which seem to testify to the mental and emotional tension of which it was the outcome :—

"If then it be painfully evident to both, that under such cir- cumstances there CANNOT (whatever we may both desire) be now, in the nature of things, or of minds, the same degree of intimacy between us as of old ; since we could no longer talk with the same degree of unreserve on every subject which happened to present itself, but must, from the simplest instincts of courtesy, be each on his guard not to say what might be offensive or at least painful to the other : yet WE were once so intimate, • and retain still, and, as I trust, shall always retain, so much of regard and. esteem and appreciation for each other, made tender by so many associations of my early youth and your boyhood, which can never be forgotten by either of us, that (as times go) two or three very respectable FRIENDSHIPS might easily be carved out from the frag- ments of our former intimacy. It would be no exaggeration to quote the words, Heu quanto minus eat cum reliquis versari, quam tui meminisse.' "

To a highly strung emotional nature like that of Hamilton, the sense of pain expressed here was perfectly natural, and it was equally natural that with the lapse of time it should. diminish and pass away. Subsequent letters to Mr. Aubrey de Vere seem to be characterised by perfect freedom as well ashy perfect sweetness, and in them, as in other letters dealing with religious subjects, we feel that we are being brought into contact with a singularly candid, earnest, and devout spirit.

This volume, like its predecessors, has one quality which, while from the reader's point of view a notable attraction, is from a reviewer's point of view almost a fault,—the quality of fullness, which renders it impossible to take note, even by mention and allusion, of more than a tithe of the interesting matter which it contains. Of the three instalments of Mr. Graves's biography, perhaps the second gives us the most vivid impression of Hamilton's greatness; the present volume best enables us to realise the wonderful simplicity and loveableness

of nature by which he was no less distinguished. Like Abou Ben Adhem, he "loved. his fellow-men," and specially did he

love children and animals, who amply returned his affection. His allusions to his own children—especially one or two. passages referring to a little invalid daughter—are very tender and winning ; and there is a beautiful story of his.

sitting down to amuse a little girl of weak intellect, whom his. sister had brought to the Observatory, by playing with her a.

mathematical game of his own invention. "Of course," said he, "I saw that she did not understand it, yet I assure you that many a Duchess could not have carried it off so well She had to me quite the air of one accustomed to Castle

society, who considered she condescended to oblige me

I think her too interesting ; I hope she will not attract any one too deeply to her; but I should fear it for her."

Finally, we would say that the hearty gratitude of all who can appreciate things lovely and of good report is due to Mr. Graves for this simple, discriminating, and sympathetic memoir of one who was in the best and noblest sense of the term a great man. Frailties Sir William Rowan Hamilton doubtless had, but they belonged to the accidents of his nature, not to

its essence ; and those who were best acquainted with them were also those who loved him most warmly and reverenced him most truly. As we cast a look backward over the long record, we feel that the epithet " high-souled " applied to him by Sir John Herschel was not a term of vague eulogy but of accurate definition,—that he was indeed a spirit finely touched to fine issues. Concerning the endowments which enabled him to.

perform the work by which his name will be immortalised in the records of scientific achievement, no fitter words have

been uttered than those of Dean Graves, now Bishop of Limerick, in the course of the eloge spoken before the Royal

Irish Academy :—

" Hamilton was gifted with a rare combination of those qualities which are essential instruments of discovery. He had that fins perception of analogy by which the investigator is guided in his passage from the known to the unknown. This is an instru- ment by which many important mathematical discoveries have been effected. Sometimes the mathematician devises some happy modification in the statement of a theorem, or a method by which its application may be extended. Sometimes by analysing

different demonstrations, he even sees that a particular proposition may be made the starting-point from which he ascends to more than one generalisation. In the investigations of Hamilton we find abundant instances of all the expedients and incidents of inventive sagacity. But he seems also to have possessed a higher power of divination—an intuitive perception that new truths lay In a particular direction, and that patient and systematic search, carried on within definite limits, must certainly be rewarded by the discovery of a path leading into regions hitherto unexplored. Something like this was the unshaken assurance which led Columbus to turn his back upon Europe, to launch upon the broad Atlantic, and seek a new world in the far-off West."