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formerly to have been assumed, an approxi- of his Lectures are almost painful to the mate one. But, unless the earth's orbit eye. were exactly circular the true place of the Hamilton had, at one time, serious intenstar will not be the centre of the hodograph. tions of entering the Church, and was, more To enter into further details on this subject than once, offered ordination. The following we should require geometrical diagrams or letter, written to the Editor of the Irish analytical symbols.

Ecclesiastical Journal, and published in that The discoveries we have already described, work, contains a very singular attempt to and the papers and treatises we have men- elucidate one of the grandest questions contioned, might well have formed the whole nected with the Christian religion. work of a long and laborious life. But, not to speak of the enormous collection of ms. “ ON THE ASCENSION OF OUR BLESSED LORD. books, full to overflowing with new and origi

" Whitsun Eve, 1842. nal matter, left by Hamilton, which have been handed over to Trinity College, Dublin, sacred season, turn naturally on that seeming

Sir,—The meditations of a Christian, at this and of whose contents we hope a large por- pause in the operations of divine Providence, tion at least may soon be published, the when, as at this time, the disciples who had works we have already called attention to seen their Lord parted from them, and taken barely form the greater portion of what he up into heaven, were waiting at Jerusalem for has published. His extraordinary investiga- the promised coming of the Comforter. You tions connected with the solution of algebraic will judge whether the following remarks, in equations of the Fifth Degree, and his exami. part confessedly conjectural, but offered (it is nation of the results arrived at by, Abel, occupy any portion of your columns

season commemorates.

, in connex

hoped) in no presumptuous spirit, may properly Jerrard, and Badano, in their researches on ion with the events which the Church at this this subject, form another grand contribution to science.

There is also his great paper on “ It may be assumed that your readers are Fluctuating Functions, a subject which, disposed to adopt, in its simplicity, the teaching since the time of Fourier, has been of im- of the 4th article, that Christ did truly rise mense and ever increasing value in physical again from death, and took again his body, with applications of mathematics. Of his extensive flesh, bones, and all things appertaining to the investigations into the solution (especially by ascended into heaven, and there sitteth, until he

perfection of Man's nature; wherewith he numerical approximation) of certain classes return to judge all Men at the last day.' They of differential equations, which constantly will not be inclined to explain away the dococcur in the treatment of physical questions, trine of the Ascension of the Lord's Humanity, only a few items have been published, at in- into what some have sought to substitute for tervals, in the Philosophical Magazine. Be it, --a ceasing of the Godhead to be manifested sides all this, Hamilton was a voluminous in the person of Christ. Far rather will they correspondent. Often a single letter of his oc

be ready to believe that the 'glorious' Ascen

sion was the epoch of a more bright manifes cupied from fifty to a hundred or more closely tation of God in Christ, than any which had written pages, all devoted to the minute con- been vouchsafed before though perhaps rather sideration of every feature of some particular to angelic than to human beings; and that no problem; for it was one of the peculiar merely figurative, though in part a spiritnal characteristics of his mind, never to be satis- sense, is to be assigned to those passages of Holy fied with a general understanding of a ques. highly exalted, and seated at the right hand of

Writ, which speak of Jesus as having been tion, he pursued it until he knew it in all its God. As God, indeed, we know that Heaven, details. He was ever courteous and kind in and the Heaven of Heavens, cannot contain auswering any applications for assistance in him; yet it is also declared that Heaven is His the study of his works, even when his com- Throne, and Earth is His Footstool : and Scrippliance must have cost him much valuable ture and the Church seem to attest alike, that time. He was excessively precise and hard the risen and glorified Humanity of Christ is to please, with reference to the final polish of now in Heaven, as in some holiest place, where his own works for publication; and it was worshipped ; his power, his name, and his pres

God is eminently manifested, and eminently probably for this reason that he published ence dwelling there. so little, compared with the extent of bis in

“A local translation of Christ's Body beiog vestigations. His peculiar use of capitals, thus believed, it is natural to believe also that italics, and other typographical artifices for this change of place was accomplished in time, the purpose of imitating in writing and type, and not with that strict instantaneity which as closely as possible, the effects of emphasis may be attributed to a purely spiritual opera

tion. and pause in a viva voce lecture, will be

Accordingly we read that at least the evident from almost any of the extracts which the Apostles were witnesses - was grad.

first part of the act of Ascension,—the part of we have made from his works. To such ual; their gaze could follow for a while their an extent did he carry this, that some pages / ascending Lord: nor was it instantly, though it

may have been soon, that a cloud received | Jesus take his seat at the right hand of God, him out of their sight. And to suppose that the than the Spirit fell upon the Apostles. The remainder of that wonderful translation was finished work, of ascending up on high, may effected without occupying some additional time, have been followed instantly by the receiving seems almost as much against the truth of of gifts for men. Christ's patural Body,' as that it should be at "Should this conjecture be admitted, of the one time in more places than one,' which latter Ascension not having been completed till the notion a rubric of our Book of Common Prayer Day of Pentecost, although commenced ten days rejects as error and absurdity. The Cloud which before, it might suggest much interesting meditahovered over Bethany was surely not that tion respecting the glory,' the great triumpb,' Heaven where Jesus sitteth at the right hand with which our Saviour Christ was then exalted of God; and to believe that his arrival, as Man, into God's Kingdom of Heaven. May not the at the latter, was subsequent to his arrival at the transit from the Cloud to the Throne have been former, seems to be a just as well as an obvious but one continued passage, in long triumphal inference, from the Doctrine of the Ascension of pomp, through powers and principalities made His Body.

subject ? May not the Only Begotten Son’have “ But how long was it subsequent? We dare then again been brought forth into the world, not, by mere reasoning, attempt to decide this not by a new Nativity, but (as it were) by Procquestion. · That place to which the Saviour has lamation and Investiture,—while the Universe been exalted, and which, although in one sepse beheld its God, and all the Angels worshipped 'Heaven,' is in another sense declared to be him? And would not such triumphal progress 'far above all heavens,' may well be thought to barmonize well with that Psalm, which has albe inconceivably remote from the whole astro- ways been referred in a special manner to the nomical universe; no eye, no telescope, we may Ascension, and whieh speaks of the everlasting suppose, has pierced the mighty interspace : Gates as lifting up their heads, that the King of light may not yet have been able to spread from Glory might come in thence to us, if such an effluence as light be suf “Many other reflections occur to me, but I fered thence to radiate. And, on the other forbear. Ifanything unscriptural or uncatholic hand, it must be owned, that, vast beyond all shall be detected by you in the foregoing rethought of ours as the interval in space may be, marks, or (in the event of you publishing them) Christ's glorious Body may have been trans- by your readers, the pointing it out will be reported over it, in any interval of time, however ceived as an obligation by, Sir, your obedient short.

servant, “Reason is silent then; nor can we expect to

“W[illiam] R[owan] Hamilton]." find, on this point, a clear revelation in Scripture; but do we meet with no indications ? Does Like most men of great originalty, HamilHoly Writ leave us here entirely without light? ton generally matured his ideas before putI think that it does not: and shall submit to you ting pen to paper.

“ He used to carry on," a view, which it seems to me to suggest. “ First, it is clear from Scripture, that the As. says his elder son," long trains of algebraical

mind, cension of Christ had been entirely performed before the Descent of the Spirit on the Day of during which he was unconscious of the Pentecost. Thus, in a well-known verse of that earthly necessity of eating: we used to bring sixty-eighth Psalm, which the Church has con. in a snack' and leave it in his study, but a nected with the Service for Whitsunday, and brief nod of recognition of the intrusion of which St. Paul bas quoted in reference to the the chop or cutlet was often the only result, Ascension; in the first sermon of Peter to the and his thoughts went on soaring upwards. Jews; and in other passages of the Bible: the I have been much with him in his periods of obtaining of 'gifts for men,' the receiving from the Father the promise of the Holy Ghost, is mathematical incubation, and would divide spoken of as a result or consequence of Christ's them into three, thus :-First, that of conhaving ascended up on high,--having been ex- templation, above indicated. Second, that of alted by the right hand of God,-having as- construction. In this he committed to cended, as did not David, into the Heavens. paper (or, if nothing else were at hand, as The act of ascending occupied therefore no when in the garden, a few formule written longer time than that from Holy Thursday to

on his finger-nails) the skeleton, afterwards Whitsunday. " But may it not have been allowed to occupy results arrived at. Third, the didactic stage.

to be clothed with flesh and blood, of the 80 long a time as this? No reason à priori can be given against the supposition ; no passage of Having now completely satisfied himself of Scripture, no decision of the Church, so far as the correctness of the results (and sometimes I know, is against it. The very close connex- having retraced and simplified the method of ion announced, in the texts above alluded to, discovery) he proceeded to consider how to between the Ascension of Christ into Heaven, teach it, and this by experiment. I was so and the Descent of the Holy Ghost upon Earth, long with him in his periods of mathematical appears to me an indication in its favour. For incubation that I knew, almost by the tones the purely spiritual nature of the later descent prevents the necessity, almost the possibility, of of his voice and the expression of his eyes, our supposing it to have occupied time at all. when the didactic period had arrived, and No sooner, it may reasonably be thought, did generally anticipated it by fetching the black


board to whatever room he might be in. The We give here, as curiously applicable to audience generally consisted of the Obser- Hamilton himself, another of his sonnets, vatory assistant and myself.

He “ those fourteen-lined productions," as he was not so much teaching, as throwing his says, “ to which I attach but little value on mind into a didactic attitude. I amused him the artistic side, although some of them are once by saying that his lecturing us on equa- associated with happy or mournful moments, tions of the fifth degree reminded me of the and which at all events may, to a man's self, lion preparing for action by whetting his serve as instruments of culture, and may claws on the bark of a tree.

man strove

He have some social or other interest to those appeared to enjoy intensely arithmetical cal who know him chiefly as a writer, or thinker, culations. I never saw him look so perfectly on subjects of a very different kind.” happy as when running like a sleuth-hound on the track of some unhappy decimal which To Adams (Discoverer of Neptune.) had marred the work, and unearthing it in Sonnet on Unselfishness in the Pursuit of Truth its den. .. I cannot otherwise express

and Beauty. his attachment to his own ms. volumes than by saying that he loved them. He once, at a core, & Zev, ualwrpá por áróðos, fyyuhoas poi avrnu luncheon party of students at the Observa

αδυνάτων εράς. . tory, ranged some thirty of them on the When Vulcan cleft the labouring brain of Jove, chimney-piece, and, turning to the students, With his keen axe, and set Minerva free, said, “These books represent much of the The unimprisoned Maid, exultingly, happiness of my life.”

Bounded aloft, and to the Heaven above A good idea of the process of “incuba- Turned her clear eyes, while the grim Worktion above mentioned is given by the fol.

To claim the Virgin Wisdom for his fee, lowing extract from a letter to å mathematical friend. Hamilton is speaking of And hide in Lemnian cave her light of love,

His private wealth, his property to be, one of the most beautiful discoveries con

If some new truth, O Friend! thy toil distained in his last work on quaternions, the

cover, general symbolical solution of a vector equa If thiné eyes first by some fair form tion of the first degree; and he writes, in

be blest, 1859, the day after the discovery was

Love it for what it is, and as a lover made :

Gaze, or with joy receive thine

honoured guest : “While I was walking, on business of an

The new found Thought, set free, awhile may other sort, through Dublin yesterday, the ques

hover tion again occurred to me.

Gratefully, near thee, but it cannot

rest. “Puræ sunt plateæ, nihil ut meditantibus obstet”

The following final extract, from a letter I nunc, et versus tecum meditare canoros."

written in 1858, gives a very clear insight I was not so rash as to attempt the composition into the view Hamilton took of his own disof a Sonnet in the streets; though, in accept- coveries, and of the comparative value which ance of a challenge from a Lady, long ago, he attached to methods and results. There beside whom I was sitting in a Music Room, I is no doubt that, in the case of quaternions did dash off a Sonnet before the performance at least, he sought mainly to improve his had ceased. But those days are over :-happily? Yes, so far as the getting a little more

methods, and almost studiously avoided the sense, and less sensibility, is concerned. treatment of new subjects; and the result is,

" The problem, however, (though not the that in his hands alone the development Sonnet,) baunted me, as it happened, yester. attained is extraordinary : day, while I was walking from the Provost's Hlouse to that of the Academy; and though I " I reminded the R. I. A. that, so long ago as wrote nothing down, that day, (for I had an 1831, I had communicated to that body an Eximmensity of other things to attend to,) I re- tension of (what is usually called) Herschel's sumed it this morning; and arrived at what Theorem: namely, the following extended you might call, in the language of your last, a Formula. . . By making the two particular * perplexingly easysolution (in the sense of assumptions ... my formula becomes being very UNLABORIOUS, for I do not pretend that which is, if I remember rightly, one form of the reasoning does not require close attention). Herschel's Theorem. .. In speaking of

So simple does this solution appear, that 'Herschel's Theorem,' I believe that I follow I hesitate as yet to place entire confidence in an usage, which of course he did not originate, it; and therefore, till I bave fully written it but against which he has never complained. out--for at present it is partly mental, -and In my own case, however, I did complain, have given it a complete and thorough re- although (as I hope) gently, that a much less examination, I hesitate to communicate it to general formula of mine, which had indeed you."

occurred in the same short paper of 1831 ...


had been cited, in a then recent number of the from letters which we have received from Cambridge and Dublin Mathematical Journal, Hamilton himself. We have derived some under the title of “ Hamilton's Theorem.” What assistance from articles, or sketches, in the I meant was merely this ;—that although I had Dublin University Magazine (Jan. 1842), no desire to have any theorem of mine so named, yet it was scarcely just, in my opinion, the Gentleman's Magazine (Jan. 1866,) and to select, out of a single and short paper, a the Monthly Notices of the Royal Astroformula which involved only one functional nomical Society (Feb. 1866). The last of characteristic, one symbol of operation, and one these, especially, is an admirable tribute to ultimately evanescent variable; and by the Hamilton's memory, but is somewhat marred manner in which the formula so selected was mentioned, or by the title under which it was

s by inaccuracies in the note on the nature of cited, to ignore, or even virtually to reject, the quaternions. And we must express our much more general equation, which (as you see) obligations to W. E. Hamilton, Esq., C. E., involved two functional signs, two operators, the elder son of Sir William, for many facts and two ultimately evanescent variables. So, and documents; and for his kindness in don't cite anything as “ Hamilton's Theorem,” verifying the statements we have made if you wish not to tread upon my corns! I as to his father's ancestry and early hishope, indeed, that it may not be considered as

tory. unpardonable vanity or presumption on my part, if, as my own taste has always led me to first of these sketches, the Rev. R. P. Graves,

We are glad to hear that the author of the feel a greater interest in methods than in results, so it is by METHODS, rather than by any

one of Hamilton's oldest friends, and brother THEOREMS, which can be separately quoted, that of his former colleague in the University the I desire and hope to be remembered. Never- Bishop of Limerick, is about to write his theless it is only human nature, to derive some biography. The prospect of such a volume pleasure from being cited, now and then, even leaves us but one wish to express, that the about a “ Theorem, especially when : : : the authorities of Trinity College may publish, quoter can enrich the subject, by combining it with researches of his own."

as speedily as possible, if not all, at least all

that is most valuable in, the mss. of the most In concluding, we have only to express a distinguished among the many great men hope that we have rendered intelligible to who, as students and professors, have shed the general reader, though perhaps in but lustre on the University of Dublin. small degree, at all events the nature of We conclude with an extract from the some of the grand investigations of this Opening Address (Session 1865–6) of the illustrious man. Of course there will ever President of the Royal Society of Edinbe many who, though (or perhaps because) burgh, of which Hamilton was an Honorary totally incapable of understanding anything Fellow. lofty or difficult, will sneer out over such pages the cui bono of ignorance. They can “ Sir John Herschel once wrote thus:not see one of the sources of the vastness of 'Here whole branches of continental discovery modern commerce in Newton meditating are unstudied, and, indeed, almost unknown about gravity, another in Watt patching a choly truth. We are fast dropping behind. In

even by name. It is vain to conceal the melantrumpery model. To their narrow vision mathematics we have long since drawn the rein the designer of a new easy-chair or the in- and given over a hopeless race, etc.

? Hamilton, ventor of a new sauce, a lucky speculator or while second to none, was one of the earliest of a sensation-novelist, even, it may be, a that brilliant array of mathematicians, who, mountebank assuming the guise of a philos- since Herschel wrote, have removed this opher, is the grandest of the human race; stigma, and well-nigh reversed the terms of but, while science lasts, the name of Hamil his statement. Another was the late Professor ton will hold an honoured position among ranks of British science which will not soon be

Boole. . , . Their death has made a gap in the those of her few greatest sons.

filled; and our sorrow is but increased by the We have endeavoured to give, in brief recollection that they have been removed in the compass, a trustworthy account of Hamilton full vigour of their intellect, and when their and his works. Of himself the account is passion for work was, if possible, stronger than easy, being mainly quoted from his corre- ever.” spondence. In our account of his works we have endeavoured, so far as we could, to avail ourselves of extracts from his writings. In several cases this was impossible; and we must warn the reader not to judge of the Art. III.-1. The Book of Ballads. Edit. importance of the subject by the extremely ed by Bon GAULTIER. Seventh Edition. small fragments which we have been forced Edinburgh, 1861. to give as popularly intelligible specimens. 2. Firmilian. Edinburgh, 1854. Many of the preceding extracts are taken 3. Tales from Blackwood. Edinburgh.

4. Headlong Hall, etc. Bentley's Standard times as well known as Henry Taylor. But Novels, 1837.

this is one of the eternal phenomena of liter5. Gryll Grange. By the Author of Head- ature which never discourages real men of long Hall. London, 1861.

letters, while it ought to teach critics that 6. Reliques of Father Prout. A New perhaps their most important duty is to help Edition, 1866.

to make known those whom the world has

not learned to know for itself. If we proSINCE the days of the prince of biographers, pose to glance now at what was done by the the wise and warm-hearted Plutarch of Chæ three gentlemen just mentioned, for their ronea, very little has been done in literature generation, our object is partly to induce for that parallelism which was so essential a readers to become better acquainted with part of his biographical theory. To take men them at first-hand. Professor Aytoun's of eminence, and place them in juxtaposi- works are, indeed, well known in Scotland, tion; to observe their points of similarity, but might be better known in the South and and of dissimilarity in similarity, so that in Ireland. Peacock, in spite of the admiraeach should be separately more intelligible ble wit and cleverness of his tales, is, we susfrom the comparison of him with the other; pect, little appreciated out of London. -this, the Plutarchian idea, has been less Father Prout is loved and honoured by own fruitful than might have been expected, con- countrymen, and in the literary world of the sidering the just popularity of Plutarch from metropolis his name is a household word; the days of Montaigne downwards. Bishop but, elsewhere, few know how much ,enjoy. Hurd deserves the praise of having advo- ment may be got from his pages. We should cated its study, and of having suggested like to see the reputation of these brilliant some material for the purpose; and Cole- men counter-changed, as the heralds sayridge, in what he called the "landing-places" the Scoth and Irish reputations crossing into of his Friend, so far followed it up, that he each other-and the English intermingling made most ingenious suggestive comparisons with both. We are no friends to excessive between Luther and Rousseau, and between centralization. Indeed, we cherish national Erasmus and Voltaire. We are not going individualism as one of the conditions of to deal just now with men of such magni- literary variety, raciness, and colour. But tude; but we must be allowed to congratu- nationality without intercommunion has a late ourselves on having a good opportunity constant tendency to degenerate into proof applying the doctrine in the case of a vincialism; and provincialism preserves nagroup of distinguished contemporaries re- tional traits not as living things, but as petcently taken away. Within about a twelve- rifactions. The intellectual life of every month three humorists have been blotted country ought to blow over into other lands from the roll of living British men of let- like a wind. The north wind is necessary to ters: Professor Aytoun, Mr. Thomas Love keep the south cool, and the south wind is Peacock, and the Reverend Frank Mahony, necessary to keep the north from freezing. better known as Father Prout. Each of Now, it so happens, as has been already these men represented one of the three king- briefly hinted, that each of our three humordoms : Aytoun, our own bonnie Northern ists had a strong flavour of his own country land; Peacock, England; and Mahony, Ire about him. In an age when so many Scotchland. They were all humorists. They were men emigrate, Aytoun devoted his life to all lyrists. They were all more or less Bo- Scotland. He formed himself on native hemian and eccentric in the exercise of their models, and attached himself to a native gifts. They were all men of classical educa- school of literature. His humour--and it is tion. They were all men of strongly marked humour with which we have to do in this national type. Finally, they had this, too, paper-was essentially Scotch; that is to in common, that they never became exactly say, hearty or even vehement in expression popular, that is, universally popular in the sometimes, but dry to the taste; shrewd and sense in which Thackeray or Jerrold were so, thoughtful at bottom; and based on characbut enjoyed their chief reputation among the ter rather than light and brilliant. He did cultivated classes. Every generation has not shine in epigram. His prose style wantwriters of this peculiar type-writers often ed clearness, terseness, grace. His strong of higher powers and attainments than many point both as writer and talker was humour who are better known,-but who, somehow, proper, fun, a perception of the ludicrous; never pass the line which divides those who but a perception of the ludicrous from a are distinguished from those who are famous. Scot's point of view, in which the intellectual It is curious to reflect that De Quincey never rather than the moral pleasure to be derived had a tithe as many readers as Mr. Harrison from it is the predominant object sought. Ainsworth, and that Mr. Tupper is some fifty Peacock, again, was eminently English in

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