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lijcdh 13

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1

DUBLIN UNIVERSITY PRESS SERIES.

HAMILTON,

IVKRSm OP DUBLIN, , ETC. ETC.:

'RRESPONDENCE, IIINGS.

VES, M.A.,

AFTON-STREET. A.rERNOSTER-ROW.

MoLth )'i,7 .1

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DUBLIN :

PRINTED AT THB UNIVERSITY PRESS,

»Y VON80NBY AND WBLURICK.

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PREFACE.

*

3E biographical portion of this volume was brought to a close and printed earlj in 1887. This fact will account occasional references in it to persons and events which are in exact accord with the present state of things. The uent and larger portion of the volume consists of a ion from a very extensive correspondence between Sir W. Hamilton and Professor Augustus De Morgan. To make selection has involved the expenditure of much time and The quantity of material was so great that I have had ixdude matter that possessed inherent value, either because in subject unsuited to this work, or because, being mathe- cbI, the investigations carried on were too abstruse or too ded. The general reader will perhaps complain that I introduced more than enough of mathematical investiga- but he will, I hope, withdraw this complaint when he calls d that it was as scientific men that the writers corre- ed, that it would be unjust to them if their correspondence mted should not retain this character, and that the mathe- discussions did in fact most often afford suggestion to lay of thought which, passing beyond the boundaries dence, prompted the wit and the learned and pleasant P which all readers wiU enjoy. Its possession of the ^ts last mentioned was the circumstance which determined k> place this correspondence in immediate connexion with liography. In some instances I have given a condensed Uent of the mathematical matter under discussion. For

vi Preface.

suoh statements I have, in important cases, been indebted to the soientifio knowledge of Mr. G. L. Oathcart, M!. A., F. T. 0. D., who has also by his advice and information saved me from printing what had either ceased to be of interest to the scientific reader, or had been afterwards published by flie writers themselves. I cannot but take this opportunity of pub- licly expressing my gratitude to Mr. Cathcart for a seirvioe from which the readers of the correspondence wiU derive much benefit, and which cost him a sensible addition to the labours of his well-occupied days.

Another great service to me and to this work demands my ample acknowledgment, although that acknowledgment cannot now be received by her who had so amply earned it. Miss Emily Anne Napier, of whom I feel it an honour to have been a friend and distant kinsman, voluntarily undertook to perfect for me the chronological arrangement from the beginning oi the original letters of Sir W. B. Hamilton and his friends, and to make year-lists of them, noting the principal contents of each letter. This task, calling for great accuracy, method, and perseverance, was fully accomplished by her, notwithstanding interruptions from illness and from many other calls of friend- ship and benevolence. It was not unlike the service rendered by her admirable Mother to her Father, the Historian of the Peninsular War, and I am deeply sensible of the extent of the obligation under which it has laid me.

To my friend Dr. Ingram, S.P.T.C.D., I must here express renewed thanks for continuing to this volume the invaluable advantage which my work has derived from his revision of the proof-sheets, and from the indication of errors detected by bis wide and accurate knowledge.

In the first volume a note was made of the fact that I was indebted to a friend for the Index appended to it. I feel now at liberty to state that the friend referred to was Mrs. Edward Dowden, and in thus rendering her my thanks for a valu- able service spontaneously offered, I am happy to have the

Preface, vii

^fxfftaniiy of mentioniBg that in the course of my labours I haye leoeiYed unfaih'ng assistanoe from her distinguished faofibandy wheneyer I was at a loss as to a poetical allusion, or as to any point connected with literature.

The Index of the present, as of the second volume, has been carefnlly prepared by Mr. T. W. Lyster, B.A., of the National library of Ireland, to whom I am also indebted for most efficient aid in drawing up the list of Sir W. B. Hamilton's vorks, and of publications connected with them — a list which vill be found more complete than that of the Boyal Society.

I should fail to perform an act of justice were I not, in regard to Mr. Q. Weldrick, of the University Printing Office, and his principal assistant Mr. Booney, to acknowledge grate- fully the invariable attention I have received from them, and the care they have taken in directing the printing of this work. Nor ought I to omit my thanks to the Beaders and CSompositors engaged upon it for the pains they have taken to secure its freedom from typographical errors. All have worked as if they ^eie taking a willing part in honouring the memory of an illnstrions countryman; and, although misprints, inevitable in any large work, and particularly in one introduciDg extensively mathematical formulae, are to be met with in these volumes, it 13 trusted that they may fairly claim credit for a more than average correctness of typography.

Lastly, I renew the expression of my heartfelt obligation to the Board of Trinity College for their liberality in taking upon themfiehes the expense of publishing this work, intended to be A fiiU record of the scientific achievements, the varied attain- ments, and the personal character, of an eminent alumnus of the Uniyersity of Dublin, and aleo for their grant made at the beginning of my undertaking of the sum of £100 towards the payment of amanuenses employed by me during the course of my vork.

Of the imperfections of that work, resulting from my not Doing a mathematician, and from other deficiencies, I am fully

viii Pre/cue.

conscious ; but I commit it to the public in the confidence that its materials, being the authentic documents of the minds of Hamilton and his friends, will constitute it an enduring monu- ment of the man as well as of the mathematician, and in thankfulness to the Source of all blessings that I have been enabled, through a long period not unbroken by illness and trial, to cany on to the end my humble part in building it up.

R. P. G.

1, WiNTON Road, Lsbbon Park, Dublin, March 9, 1889.

CONTENTS.

Hezzopbikt fboh a Photoobaph of th£ Bust by Foley ik

THB LiBBABY OF Tbiftty Collbge, Dublik, . . /rontUptece.

Pbefacb, page ▼

COBBIGElfDA, „ XXXVi

CHAPTER XXXIX.

THB DABOLE— LITEBPOOL MEETIVO — ^TISIT TO WEBTVOBELABl).

[1854.2

PACI

Letters from Professor Sedgwiok — Auguste Gomte^Theory of Qnadrinomes, of Tetrads — Kirkman — Eleetro-magnetism — Dr. Llojd — Engaged on nDmerons trains of inyestigation — Appointment of his nephew to Looghorew — Grant from Board of T. C. D. in aid of publication of Lectures — Dr. Lnby and Dr. Lloyd thereon — ^Visit to Dr. Lloyd at Kilcroney — Dargle Hexameters — Speech at Bristol Meeting of the British Amodation: French Mathematics, Abb6 Moigno, Professor William Thomson, M. Foucault — ^Yisit to Windermere: Dovenest, Rydal Mount, Mrs. Fletcher of Lancrigg, William Pearson, Mr. and Mrs. Richard Napier — Carlingford : Mr. and Mrs. Disney — Deaf and Dumb Boys — Lady Campbell: Her books, kindness in life being spared, ^ 1

CHAPTER XL.

COBBESPOHDENCE WITH AUBBEY DE TEBE — ^WITH THE NICHOLS— CIPHEB —

XB8. WILDE.

[ISSS."]

A. DeVere's Letters on his Conformity to the Church of Rome — The Nichol family — British Association Meeting at Glasgow : On the con- ception of the Anharmonic Quaternion, &c. — Visit to Brodick Castle —His Hamilton descent — Sonnet to my Daughter — The Observatory visited by Mr. Robert O'Brien and his children—* Mary and Alice !

Contents.

PACK

thongh before that day ' — Mrs. Wilde — The Problem of Hipparohns — Patriotic Grief— Ellen DeVere and Dora Wordsworth — Cohkbspoh- BENCB WITH A. De Veee. Letter from A. De Vere : Old letters, Eliza Hamilton, Mrs. Wordsworth, his Sister — From Hamilton : His reli- gious views have diverged from A. DeV/s, but the friendship remains — ^rom A. De V. : Thanks for this assuranoe — From Hamilton on DeY.'s Lines to Burns' Highland Mary and other poems — From A, De V. on his Highland Mari/y Farewell to Naples ^ Colonisation, Psyche — From Hamilton: His three loves — From A. De V. : early praise, Confession — FVom Hamilton : Relinquishes writing on the past — From A. De V, : Anticipations of Future Glory and Beauty, The three worlds, Lord Belfast's Poem, Speranza — From Hamilton : Conclusion— CoEKESPOKDENCE with the Nichols. From Hamilton to J. N. : his modest estimate of his own poetry, his Cipher — From J. P. N, : His estimate of Hamilton — From Hamilton to J. P. N: Cipher — To J. N. : Herschel, A. DeVere, De Morgan — To J, P. N. : Parsonstown Sonnet, His daughter, < Despair of the Sea ' — From /. P. N. : Friendship in later life, Invitation to Loch Awe — From Hamilton to J. N, : Indignation at a review of Tennyson's Poetry, Scientific Correspondence with Russia, Lord Carlisle's pleasan- try, Logic ; necessity of assuming principles, Ptolemy's Almagest^ . 20

CHAPTER XLI.

VISIT TO CHELTENHAM— ICOSIAN CALCXTLUS — CORBESPOKDENCE WITH AUBEET SEVERS — LETTEKS OK MATHEUATICAL SUBJECTS.

[1856,1

Lady Hamilton's illness and his own depression — Guest of John Graves at Cheltenham, meeting Mr. Grove — Meeting of the British Association — Papers on Scheffler's Der Situations Kalkul and on Gauss's Disquisi'- tiones Arithmetics — The Icosian Calculus — The Icosian Game — CoEHESPONDENCE WITH A. De Vere. FrofH Hamilton : Appreciation of Essays mostly Theological — From A. De V» : Speranza's most amiable letter. Sir A. De Vere's poetry, Wordsworth's opinion of his sonnets — From Hamilton: Typographical accuracy — Estimate of A, De V.'s character — From A, De K. .• Scotch worldliness not like American or English, Defence of the Roman Church, Impressions as distinguished from opinions and convictions — From Hamilton: Pleasantry as to non- version, does not pretend to be unbiassed — From A. De V, : Asserted lack of Passion in his own poetry. Criticism of Henry Taylor, Dut}' of rising above impressions — From Hamilton : Dr. T. R. Robinson — Theses on Romanism — Absorption in mathema- tical investigations — From A, DeV. : Theological and Mathematical Science, Urges Hamilton to write Philosophical Sonnets, Illustration

Contents. xi

PACB

from the sea of the Wrath and Love of God, The past a delicate thing — HamiUon to Dr, Itobinson : M. Houel, * Tellipse de M. Hamilton ' — HamiUon io Dr. JAoyd: Lord Northwick, John Graves's ' Paradise of Booksy' CopemicuSy complex nombersi greatest common measure of two quaternions, Ghiuss's Disquisitiones ArithmetictB, extensions to ^oatemions, Scheffler's Situations Kalkut — Letter to J, T, Graves : Grassmann's Ausdehnungslehre, Moebios, loosian Calculus, Eirkman onPolyedra, 51

CHAPTER XLH.

LETTESS OK QUATEBIHONS — AUBBET DETEBE'S *lfAT CAS0L8 '— BBITI8H ASSOCIATION IN DUBLIN. CORBESPONDENCE WITH SALMON.

Mrs. Smythe of Farmleigh: Linnaeus, First chapter of Genesis — Letters on Quaternions — Anticipations as to the Calculus of Quaternions — Prints for distribution memorandam correcting mistaken ascription to him of a mathematical paper bj J. T. Graves — Vanity — Cobbespondence WITH A. DeYebe. Letter from A, De V»: J. W. Newman, Robert Wilberforce, Tenioe, May Carols — Letter from Hamilton : Essenti- ally a Protestant, no scoffer at Popery — Letter to Mrs, Wilde: Romanism tends to the introduction of a Tetrad into the notion of the Divine Nature, this tendency idolatrous, A. DeVere's English Misrule and Irish Misdeeds — British Association in Dublin under Lloyd's Presidency — Hamilton contributes a Paper On some Applications of Quaternions to Cones of the Third Degree — Professor Henry J. Smith's concurrent results — Communicates also Icosian Calculus and litho- graph of Icosian Game — Remarks on geometrical and symbolical imaginaries — Loyalty to his friend Dr. Lloyd — Letter from Mrs. Lloyd — CoBBESPONDENCE WITH Dr. Salmon. Grassmanu, Moebius, letters contain some matter worth preserving, his Appendix C, the Aim of Quaternions, pleased with Salmon's stout self-coniidencc Letter to Dr, Ingram : Salmon, Jaoobi, Houel, wish as to Salmon, Mac Cullagh's quaternion-pleasantry as to Ingram. P,S, of a letter to Dr. Salmon. Three things Salmon would admit in regard to Quaternions, disclaims the notion of Quaternions superseding deter- minants, the two not identical, law for the terms of a descending series representing weU-known integrals. Quaternions a method of Polar Co-ordinates, careless of priority, instance in a formula of Henry Smith — Lord Brougham, his inaccuracy as to facts, his great speech at Grantham on the unveiling of Newton's statue — Hamilton applied to officially by Lord Monteagle for his opinion on Decimal Coinage — ^Drafts a Bill — Letter on the subject — Paper On the Calcula^ lion of the Numerical Values of a certain class of Multiple and Definite Integrals — Two long letters on the same subject addressed to De Morgan — Mode of transition from Double to Quadruple Algebra, . . .75

xii Cofitents.

CHAPTER XLIII.

FESTITAL OF POETS — VISIT TO EDOEW0BTH8T0WN — DONATl'S COMET —

PROFESSOR TAIT — ^BURNS' CEKTEVART.

[1858.']

PAcm

Growing size of the Elements of Quaternions — Festival of Poets — ^Torquay j — Desoribes singing of birds — Aubrey De yere*s religious earnestness I — H. Taylor's poetical tribute to him — Professor Hennessy, Dr. Waller, ' Dr. Anster, Mr. Grenell — ^The Earl of Carlisle — ^Visit to Edgeworths- town — Sonnet, 'To Mary Edgeworth' — Dangerous illness of his daughter — Hon. Mrs. Ward — Professor Tait introduced to him by Dr. Andrews of Belfast — Letter from Tait on Quaternions — From Dr. Robinson — Hamilton's opinion of Tait's work in Quaternions — Descartes — Invited to attend the Bums' Centenary Festival at Glas- gow— Letter on Bums, 97

CHAPTER XLIV.

CALVIKISM—DATING OF SCIENTIFIC WORK — PORTRAIT — HERSCHEL ON QUATRR- N10K8 — ^hansel's BAKPTON LECTURES — BRITISH ASSOCIATION AT ABERDEEN.

[1859.']

Hamilton's opinion of Calvinism — Letter to Professor Jellett on accuracy in recording dates — Mansel's Bampton Lectures — Letter to Dr. Lee — Science of the Infinite — Visits Rhyl — Visits with his daughter the Moravian establishment at Fulneok — Attends Meeting of the British Association at Aberdeen — ^Meets Clerk Maxwell — On an Application of Quaternions to the Geometry of FresnePs Wave- Surface — Quater- nions applied to Physical Hypotheses — Visits Balmoral — Death of Dr. J. P. Niohol — Lectures at Fulneok — Portraits of Hamilton — Sir J. Herschel's Cry of Distress— Hersohel's satisfaction with Hamilton's reply, Ill

CHAPTER XLT.

ANBARHONIC COORDINATES — GEOMETRICAL NETS IN SPACE— 0E0XETEE8 IN THINITI COLLEGE — CIRCLE^SQUARING — ^ATTBRET DBVERE's * INISFAIL.'

[1860,'\

Correspondence with Dr. Hart on Anharmonic Coordinates — Geometers in Trinity College— Mr. James Smith the Circle-Squarer — Elementary

Contents. xiii

PACE

Proof that Eight Perimeters of the Inscribed Polygon of Twenty Sides exceed Twenty-fhe Diameters — ^Death of Archianna Hamilton— Visits the ooonty of Wicklow — Cokrespokdence with A. DbVere. Letter

from A, De V, : D. F. Mac Carthy's translation from Calderon'a ' Autofi Sacramentales ' — Letter from Hamilton : De Vere's * Select Specimens of the English Poets,' Sir A. De Vere's Tragedies — LeUer

from A. De V.: His own poem ^ Iniafail,' Irish History, . . .123

CHAPTER XLVI.

BBCOeNITIOHS FEOM ABROAB — ^HOKO&ART DRGRBR AT CAMBRIDGE ^TAIT —

INGLEBT— SIBKUAN.

\_1861.^

BeUavitis — Meihauer — Accepts from Dean Graves a Vioe-Presidentship of the Boyal Irish Academy — Offered hy the Vioe-Chanoellor of the Uniyersity of Cambridge the Honorary Degree of D. C. L.— Hesitation in acceptance — Receives the honour in distinguished company — Presented to the Prince of Wales — Yisit at the Observatory from Professor Tait — Miscalculation as to the time which his work on the Elements of Qtiatemions would occupy, and the magnitude of the book — Relations of Hamilton and Tait as authors on the subject — Comet — Social Science Congress— Lord Brougham — Makes the ac- quaintance of Dr. Ingleby — Attends Meeting of the British Associa- tion at Manchester — Visits Rev. T. P. Kirkman — His estimate of Kirkman — Devotion to study — Criticism of a passage in D. F. MacCarthy's translation of Calderon's ' Love the Greatest Enchant- ment,' 129

CHAPTER XLVIL

EXPENSE OF PBIITTIKG— ROBEB's E88AT — AM0I7NT OF 8CRIBE-T0IL.

\1862.'^

Alarmed by the cost of printing the Elements — Consults Dr. Hart — His feelings towards Dr. Salmon — The Board advances a second £100 — Rober's construction of the Heptagon — Dr. Haughton and Conical Refraction — Homer's Method — Hamilton now a solitary worker — His Aunt Sydney — His Sons, 138

xiv Contents.

CHAPTER XLVIII.

SCIENTIFIC ITEMS — CONCLVSIOH OF THE DETERS C0BBE8P0in>ENCB — TWB ROTAL IRISH ACADEMY AlTD THE ROTAL DUBLDT SOCIETY.

PAGB

LtUer from Tait: Conical Refraotion, Prof. Bolzani, enormous value of Quaternions to Physicists — Letter from Hamilton : Energy and Work, Negative foot-pounds of work done by gravity — Frost and Wolsten- holme*s * Treatise on Solid Qeometry' — Osculating twisted oubics — General centre of applied forces — His originality attested by Dr. Salmon— Advice respecting Scientific work to his son Archibald — Beyers' contracted multiplication — Herschel's anticipation of Hamil- ton's triumph—CoNCLuaioN of Cokhespomdencb with Attbrkt Db Vbre. Letter from Hamilton : Experience of mathematical work during pain. Letter ft^om A, De V, : The heart never grows old — Hamilton's last letter to A. De K: De V.'s < Hymn for Good Friday,' sympathy with him in the most vital doctrines of Christianity. A, De V.*s last letter to Hamilton — Sonnet by A. De V., In memory of Sir William Itotoan Hamilton^ after reading again his letters — Memoranda by Hamilton respecting the Meeting of the Royal Irish Academy, July 6, 1863, 149

CHAPTER XLIX.

EXCURSIOir IK WICKLOW — DR. INGLEBY AND KETAFHY8ICS — HAMILTON'S POETRY — DECLARATION OF llEN OF 8CIENCB.

Extreme diligence in mathematical investigation and correspondence — Excursion with his daughter to the county of Wicklow — Reminiscence of visit with Wordsworth to Glendalough in 1829— Dr. Hart consults Hamilton as to Plana's investigations regarding solar heat at different points of the earth's surface, and his own results on the same subject — Hamilton bears testimony to Dr. Hart's talent for simplification — Statics really a part of Dynamics— Foucault's Pendulum Experiment — ^The Plumb Line Experiment — Dr. Hart suggests leaving physios for a second volume of the Elements — Retracts the suggestion — Hamilton again anxious about cost of publishing — Letter to Dr. Robinson on the subject— Robinson's reply — ^Calculation as to date of the Hejira — ^Wordsworth's claim to be descended from King Alfred — Turns to Metaphysics— Correspondence with Dr. Ingleby. Ego and Non Ego, Perception, Walter Scott's mistake about the Septuagint, Sense of Sight, Sense of Touch, Coleridge on Berkeley, Sir W. Hamil-

Contents. "xv

PAGB

ton of Edinburgh, Hamilton asserts that he sees distance, Dr. Ingleby on Reciprocal Causation, Descartes — Letter to Mr. Barlow* Hamilton's Reid, Hallam, De Morgan, Des Cartes' ' Ego cogito, ergo sum ' — ' My only power is mathematics ' — Not^ : Hamilton on Wordsworth and Tennyson — Hamilton's Poetry — Mourey's relation to Quaternions — Cipher — Declaration of men of science— Clerk Maxwell^-^Hamilton's value for intellectual freedom, 163

CHAPTER L.

PKOFBSBOR CATLEY — fiAMILTOlT's LATBST SdENTIPIC WORK — LAST ILLNESS—

HONOUB FBOM AMERICA— DEATH.

\1865,'\

Feeling with which he enters on his last year — Sonnet by his younger son — ^Intentions as to conclusion of the Elements of Quaternions — Profes- sor Cayley : * Principle of Equivalent Moments ' — Dr. Salmon's con- fidence in Hamilton's mathematical accuracy-— Hamilton refers to Professor Jellett for testimony as to Mac Cullagh's having arrived at the Principle in question — Jellett testifies that he had — Cayley accepts the rectification of his enunciation — Modification of last sentence printed in the Elemente of QtuUemions — Dean Graves's Theorem on Binomial Coefficients — Hamilton's generalization of it — His last con- tribution to the Proceedinge of the Royal Irish Academy : ' On a New System of Two General Equations of Curvature . . . deduced from Gauss's 2nd Method, &c.,' and ' Three Verifications of Measure of Curvature' — Note: Record of investigation in manuscript— Ulness — The printer's bill — Visits the International Exhibition in Dublin — Attack of gout — Rallies and resumes work — Kind neighbours— Honour from America — Placed first on the list of Foreign Associates of the American Academy of Arts and Sciences — Official Letter from B. A. Gould, private letter — Hamilton's letter to Dr. Hart communicating the intelligence — Dr. Salmon's congratulatory letter — Hamilton's acknowledgment to 6. A. Gould — Last illness — Death — Funeral — Inscription on Headstone — Surviving members of his family, . .193

CHAPTER LL

CHARACTEKESTIC8 OF HAMILTON AND OF HIS WORK.

Letters of condolence from Sir J. F. W. Herschel and Professor Augustus De Morgan — Extracts from brief Memoir by De Morgan — Hamilton the ' Irish Lagrange.' Fourier's characterisation of La^ange — Dean Graves's Eloge — Corroboration of it by Herschel — Eloge by Rev. Charles Pritchard, President of the Royal Astronomical Society — Article by Professor Tait in North British J2«9tetc— Memorial Sonnet by Aubrey De Yere, ' Friend of past years, the holy and the blest,' . 214

xvi Contents.

CHAPTER LII.

(supplementary.) a eatherdtg of f&aoments.

t>AGB

Applies to himBelf Henry Taylor's character, in Edwin the Fair, of Wulfstan — Hamilton not unpractical — Applies to himself Ptolemy's characterisation of Hipparchos and Juvenal's precept for a wise man's prayer — His claim in regard to causing pain to others — True ground for tolerance^Sonnet at the dose of a period of solitude, ' Draws to an end a melancholy while ' — His wife's weak health — ' An abstract idea' — His domestic affection — His interest in children —Instance — His truthfulness — Instance — Kindness to dumb animals — Incident of the Dove — Physical courage — Instance — Once contemplated a duel — Alleged interchange of compliments between Wordsworth and Hamilton — Ruled paper — Mathematics applied to Metaphysical reasoning, Coleridge, Kant — Quaternion stanza in Beattie's Minstrel — W. £. Hamilton's msxoranda of his Fathe&'s habits : Prepara- tion for Lecturing, Procrastination, Illustration, Inspiration of Scrip- ture, Resurrection of the body, Duty of laymen as to advocacy of religion— Professor Sylvester * On Hamilton's Numbers,' . . • 228

CORRESPONDENCE BETWEEN SIR W. R. HAMILTON AND

PROFESSOR AUGUSTUS De MORGAN.

Pbeliminakt Statement, 244

Vroxn Data of Z«ett«r.

1841.

A. DeM. May 8. Presents his Paper On the Found(ttion of Algebra aa

introduction. Asks for Triplets.

W. R.H. May 12. Algebra the Science of Pure Time. Kant. P.S.— Triplets,

1842. Polyplets.

A. DeM. Jan. 3. Hansen. Logometers. Divergent Series.

W. R. H. Jan. 28. Second Essay on Dynamics.

A. DeM. Jan. 31. Invites Report on Hansen.

W. R. H. Feb. 8. Investigations on a different line from Hansen's. Fluc-

1844 tuating Functions.

A. DeM. Oct. 1 1 . Abstract of a Paper on Triple Algebra.

Contents. xvii

\

\

. Yvmk Z>ate of Xiettar.

W. &. H. Deo. 9. Does not refuse to triplicise. Challenges any other theory

of Pare Triplets to surpass in three points that in- cluded in his Quaternions. Symmetricalnesa of Spaoe the most important. Ist P.S. — Solution of problem as to resultant of forces, &c. 2nd P.S. — Argument against Triplets reconsidered. 3rd P.S. — Would not prevent the study of Pure Triplets. ^ A. DeM. Dec. 16. You all for interpretation. My object to keep to symbo- lic rules. Suspects you have the right sow by the ear. Dec. 30. Fractional Differential Coefficients. Cautions as to health

1845. and work. W.E. H. Jan. 5. Two notes. Geometrical interpretation of A. DeM.'s

Cubic System. A. DeM. Jan. 12. Acknowledgment.

,» Dec. 23. Asks for information as to H.'s quarto publications.

Advises to give correct information to bibliographers.

1846. Mr. (C.) Graves's Paper. H.'s Symbolic Geometry. ^W.R.H. Feb. 2. Quaternions ** a new algebraical geometry.'* Intention

to retire from Presidentship of R. I. A. Time of Easter. Equinox in the year of the Council of Nictea.

A. DeM. Feb. 15. C. Graves's Paper a finished thing. Quaternions a system

in which rotations play the part of co-ordinates. Approves of resignation of Presidentship. Easter. Burckhardt. Chernac's Crihrum Arithmeticum, Mistake of Gregorian Committee. Arbogast's

\ 1847. method of derivations.

„ April 12. Appeals from a charge of piracy in Logic brought against

him by Sir W. Hamilton of Edinburgh. The two Sir W. EUmiltons constantly confounded.

W. R. H. May 7. Researches respecting Quaternions, Manner in which

the mathematical notion of Time leads to a general conception of Numerical Sets. Mind on the present subject less analytical than synthetical. '* Geome- trical Fraction " of one set of Papers the same as ** Quaternion " of another. Offers Paper on Law of Circular Hodograph. Interested at present in some applications of Quaternions to Physical Astronomy. y, July 10. Death of his Uncle James. Coincidence. Hopes that

, Quaternions will simplify physical astronomy.

A. DeM. July 12. Is there a mental dynamics ? Action of Moonlight.

Stories of ghosts. No doubt of the applicability of 1848. quaternions.

,, Aug. 17. Appeal for Second Part of Memoir on Dynamics.

W. R. H. Aug. 21. Feels that he ought to write a quaternion io treatise on

mechanics. Pressed to write a book on Quaternions.

VOL. Ill- b

xviii Contents.

From Date of Zjetter.

1849.

A. DeM. April 28. Mr. Wentworth Erck. Co-ooBine. Solution of a^-2d;= 6

to 103 decimal places. „ Ang. 30. Professor Young's loss of his post at Belfast.

NW. R. H. Sept. 24. Professor Toung. Commissioner Hargreave. Peacock's

observation that Functions and Quaternions have several analogies. Infinitely many solutions of p«=-l. ^A. DeM. Sept. 26. Professor Toung. Hargreave. Algebra itself a func- tional calculus. Some loose thoughts (algebraical). Parentheses. Chancery suit. Swing-swang integra- tion. W. R. H. Oct 3. Answer to one of the <' loose thoughts." Mr. Hargreave. A. DeM. Oct. 5. ** Closed circuit'' question. Illustration of boys and

beadle. W. R. H. Oct. 10. Some electrical phenomena of circuits not unlikely to

correspond with A. DeM.'s law. Theorem respect- ing Gauche Polygons. Curious to see a demonstra- tion of either theorem by co-ordinates. A. DeM. Oct 11. A searcher for things mental not material. Pascal's

theorem about the hexagon. Nov. 12. An enigma for W. R. H.'s daughter. 1860.

April 6. Iielative$. Motto of Cambridge and Dublin Mathemati- cal Journal,

W. R. H. April 9. Generalisation of A. De M.'s theorem.

A. D. M. April 14. [Two Notes.] The two Sir. W. Hamiltons reciprocal

polars. More on the theorem.

W. R. H. April 18. Continued discussion of the same theorem.

„ Oct. 19. The Calculus of Quaternions includes all ordinary

Algebra. Points in which Algebra and Quaternions 1851. are distinguished.

„ Nov. 26, Thanks for Paper on '* Recent Discoveries on the Inven- tion of Flulions." Vindication of Leibnitz from charge of plagiarism gives him pleasure. Suspects he has been plagiarised from. Book on Quaternions advancing rapidly. Asks for references to works having connexion with the subject of quaternions. Relations between Double Algebra and Quaternions.

A. DeM. Nov. 26. Reason for shrinking from the subject of Triplets.

Death of F. Baily. Sir W. Hamilton of Edinburgh. Quaternions must contain the double algebra. Plagiarism. Omission in published list of W.R.H.'s Time paper. Wheatstone an authority on German writers. Leibnitz. Laplace.

W. R. H. Dec. 1. Use of ^ - ^ in geometry. Wheat^tone.

A. DeM. Dec. 4. Acknowledgment.

99

>»

Contents. xix

Vtoim Date of Ijetter.

W. K. K. Deo. 8. Asks for criticisin of the metaphysics of the early articles

of his Lecturer. „ Deo. 10. Objeot of Leetwre%. A fatal fault in Double Algebra.

A. DeM. Dec. 15. Acknowledgment.

W. R. H. Dec. 16. Despairs of writing anything good on the kUlaiy con- nected with quaternions. A. DeM. Deo. 17. Will set you at rest about the history. W. R. H. Dec. 18. Fears a mistake in a quotation from Persius. Walker's

Logic. A. DeM. Dec. 20. Q,uotation correct. Scientific poems. W.R.H. Dec. 23, Walker's Logic. John Walker.

„ Dec. 24. Has in the last year composed only four sonnets. Could

neyer write verses on the death of a blood-relation. „ Deo. 24. Dep6t. French accents. Qreek accents. English spel-

. ling-

^A. DeM. Deo. 27. Thanks for Sonnets on Tetraetyt and Garden, John

Walker. Dep6t. Accents. Peacock's Report on Analysis. Gauss. About 1831-33 there was a revival of pure algebraical speculation. The gener- alities of Sir W. R. H.'s paper incapable of being transferred elsewhere. Special features of quater- 1862. nions.

W. R. H. Jan. 3. Polyplets. Geometry at the last moulded and fixed my

conception of ijk, yet abstract speculation led to it. ^A. DeM. Jan. 4. Find Quaternions no child's play. All that is peculiar to

Quaternions beyond the reach of anyone except yourself to daim. Nothing in Gauss to suggest quaternions. Ohm on Algebra, translated by Ellis. Give definitions. Tour alleged defect in double algebra a defect in symbols. Encloses order for Ohm's book.

Private reason for knowing that Gauss had not antici- pated quaternions. Baron von Walterhausen. Acknowledgment. Up all night for eclipse.

Mathematicians and amusements. Mathematical book- sellers. Gauss's Disquisitiones Arithmetics. J. Walker. Gauss's Quadratic residues.

W. R. H. Jan. 8. Style of Lectures on Quatemione. Do not assume much

previous knowledge of mathematics.

y, Jan. 10. Gauss's quadratic residues. Solution by quaternions of

the topical problem of Apollonius.

A. DeM. Jan. 10. Lends Mourey. French likely to claim quaternions for

Mourey.

W.R. H. Jan. 13. Servois nearer than Mourey to such an anticipation.

Argand. Fran9ais. Buee. P. S. — Mourey's proof of the existence of a root. History of <v/- 1.

b2

W.R,H.	Jan.	5.
i>	Jan.	6.
91	Jan.	7.
A. DeM.	Jan.	7.

XX Co7itents,

1)	Jan. 26.
>>	Jan. 27.
A. DeM.	Jan. 28.
W. R. H.	Jan. 31.

From BaU of IaMjw.

A. DeM. Jan. 15. Criticism of Servois. Mourey nothing else but a part of

double algebra. \ ,) Jan. 18. Criticism of Sonnets. Functions of } in common algebra.

Instance. History of \/ - 1.

W. U. H. Jan. 21. Combination of science and imagination personified in

Herschel. Careless of criticism of my poems. Sensi- tive as to my mathematics.

A. DeM. Jan. 22. Geodetic lines observed in Dublin Observatory. Asks

for description for Annual report of Astronomical Society. Priority question fully discussed.

W.K. H. Jan. 26. Hopes as to Quaternions, and opinion of their present

state. Gauss's biquadratic residues. Eummer.

Origin of the word *' Panic '* from Polyeenus.

Change of mode of address. Lady Campbell. Euclid in Greek. Bishop Butler's observation about caution to avoid being mistaken.

Pan's horns.

Suppresses suspicion as to plagiarism on himself. Gener- ous treatment by eminent men. Explanation as to himself and the Graveses in relation to De Morgan and Triplets. Mac Cullagh and Quaternions. Polyeenus's Stratagems, Once invented a Luoianic dialogue about the Kape of Helen. *' Reviewers Reviewed."

A. DeM. Feb. 2. Suppose your race susceptible as to priority. His own

nativity. Mulcahy on the altitudes of modem geometry. Murphy. Salmon. Geometry taken root in Ireland. Suspicion of others copying infe- rentiaUy.

TV. R. H. Feb. 9. Proof of a theorem of Desargues. Pure geometry in

Ireland. Mulcahy. Eton and Learning. Irish susceptibility. Prejudices against Quaternions. Anecdote. MacCullagh's question. Salmon.

A. l>eM. Feb. 12. The equilateral hyperbola. The ellipse. Modem geo- metry worked on a system of signs, Salmon's working of general propositions. Ridiculers of Quaternions. MacCuUagh's question. Objects to phrase " Six points in involution."

W. R. H. Feb. 13. De Morgan ** On the Connexion of Involute and £ volute in

Space." Ball at the Castle. Allman, Jukes, Anster, Lady Kane.

,, Feb. 14. Euclid. Thales. The equilateral hyperboloid. Com-

ment on De Morgan's Paper **0n the Connexion, &e." The circle not a degenerate ellipse, but an ellipse a deformed circle.

Contents. xxi

Vrom Pate of I<etter.

A. DeM. Feb. 15. The Circle and the EUipse. Self-nmilarity in both.

Also in the Screw, which it was a failure of Euclid not to introduce. Cylinder. Ring. Self-cutting Ring. Incloses note to Mr. Salmon — ^really a valu- able writer. Lady Kane.

W.R.H. Feb. 21. Mr. Salmon. [Letter from Mr. Salmon of Feb. 24:

Proof of anharmonic theorem, readiness to employ the most oonyenient instrumentality. Quaternions now a bow of Ulysses which no one can bend but the owner. Reply by W. R. H. : Proposes comparative exhibition of dijSerent mathematical methods.]

A. DeM. Feb. 23. A table of contents a palisade against mere talkers. Irish

more given to pure speculation than the English.

W. R. H. Feb. 25. Difficulty in printing.

yy Mar. 15. Is the word ** eliminanf your invention P

„ April 2. Speech in honour of Moore. His '* rebellious" poetry.

No harm in it. „ April 15. Mesmerism. Miss Edgeworth, Herschel. Believing one*s

eyes. Conical Refraction. Dumaa' **M§moiresd'un M^decin.** Lord Clarendon. Babbage.

A. DeM. Aprill5. Gnn^B History of Pkytical Science. Differential Calcu- lus. Laplace. Format.

W. R. H. April 16. Southey's saying about proof-sheets. Sydney Hamilton

of Trim, infant pupil in Sanscrit and Persian. Mathematical examination papers.

A. DeM. April 16. Clairvoyance. Oood notion of fluxions from Oresmius,

Episcop. Lexov.

W.R.H.*Aprill9,20. Walter Scott on extraordinary events. Herschers

' Collection of Examples.' A theorem. Astrology. Algebra of bi-couples. „ * April 22. Definition of the differential of a function of a quaternion.

Equation in quaternions representing an arbitrary surface of revolution.

A. DeM. * April 23. Comment on definition of differential. Suggests another

mode of differentiating a function. Will require a year after book is out to follow you. Sir W. Hamilton of Edinburgh. ' Rowan.* Astrology. Guy Mannering. Alexandrian Sorcerer.

W. R. H. *April 26. Comment on A. DeM.'s method of differentiating a

function. Challenge. Three advantages of his own method.

'■A. DeM. •April 27. Sceptical about (a + ^)« , &c. A difficulty. When both m and

n are fractional what possible form of development ?

^W. R. H. •April 29. No possible form of development analogous to the usual

one. In quaternions there is a development.

* Letters with an Asterisk are to be found at pages 623-632.

xxii Contents,

\

Froxn Date of Iiatttr.

IN

A. DeM. * April 30. Doubts about ^« . There is a deyelopmeut, but which of

an infinite number P „ *May 1. Beply to yours of April 19. Cannot interpret W. Scott

on extraordinary events. Instances of coincidences.

Astrology, n'^ ^n intruding roots. Cardan's result,

page 623. „ May 3. Geometry and its algebra in T. C. D. Punishment for it

in the next world. W. li. H. May 3. Determination of the differential of the square-root of a

quaternion. ,, May 6. Priority. Proposes to cite DeM. Not pleased with

Bronwin's citation of * Hamilton's Theorem.' * Curse

of Kehama.' Latin poem by Leibnitz. A. DeM. May 6. Walker could ^AinA; about logic. My own claim. Partial

interpretations may solve problems. ' Hamilton's

Theorem,' Herschcd's. The extension Hamilton's.

Citation. Letter to Sir W. H. of Edinburgh.

ihrooTcuris, ovaiOt x(ip<vcnip- Heb. I. 3. W. R. H. May 8. Heb. i. 3. Walker's Logic.

„ May 9. Henry Crabb Robinson. HerscheFs Theorem P

A. DeM. May 10. Herschel's Theorem. Heb. i. 3. Intends to apply the

theory of probabilities to St. Paul's alleged authorship

of this Epistle. W. R. H. May 12. To whom are divine honours to be paid P Regrets having

entered into religious controversy. A. DeM. May 16. De Morgan not de Morgan. Reason for not taking M. A.

degree. Worship of Jesus Christ, meaning of ^ wor- ship.' < Honour.' Anecdote. Portsmatic system,

Libri.

,y May 21. y^- 1 of multiple interpretation. Whewell's name for

interrupted inversion. Wanted a short and sound interpretation of a theorem. Fermat's Method of maxima and minima. Kepler.

W. R. H. May 24. Multiplicity of interpretation of (^) " • DeM.'s proof of

a cited equation satisfactory. ,, May 26. Possibility of a visit to Greenwich. In 1838 climbed into

the Ball at St. Paul's. Effect of the wind. Coinci- dence with an expression of C. Dickens. Another coincidence with an expression of Tennyson. Dinner- rhymes. Biquatemions.

A. DeM. May 27. Will not be at Greenwich. Dinner-rhymes. Cannot

keep to Swift's vein. First surgical operation under mesmerism.

* Lettei's with an Asterisk are to be found at pages 623-632.

Contents, xxiii

ftom Sate of Ijetter.

A. DeM. May 31. Shadow of a pole at sonaet.

W. R. U. June 2. A new sort of variations of definite integrals. Ganchy.

libri. Fellowship ExaminationB oonduoted in English. "xA. DeM. June 8, 9. ^x ^ 0. Partial solutions of equations. Algebra not

nuide for geometry. Double algebra is of a surf aoe, single algebra linear, double areal. Quaternions with the three rotations ought to be the triple algebra.

W. R. H. June 12. Results respecting a particular sort of yariation of a

definite integral. Investigations respecting differen- tials of functions of quaternions more general than that respecting the differential of a square-root.

A. DeM. June 15. Men to whom Lectures on Quatemiom shoidd be sent. ,, June 20. Dr. Logan. Libri. Eirkman's mathematical mnemonics.

Catechism of mathematics. Libraries. Airy, prince of methodise.

W. R. H. June 23. Expectations in connexion with Quaternions as regards

electricity, magnetism. Polarity. Mnemonics. A formula hard to be remembered. Politics.

A. DeM. July 1. Lodges a paper on Syllogism considered as a composition

of relations. A play on words. „ July 11. Oppressive heat. Chasles: Qiomitrie SupMeure, Liou-

ville's Monge. Poinsot's Theory of Rotation. Justin Brenan v. Logic.

W. R. H. July 12. Dublin election. Beautiful aspect of city and river.

The Bi-tensor of a product of Biquatemions.

A. DeM. July 14. Politics. My reform of the House of Commons.

Theory of decision by votes. House of Lords. In English hands, not objecting to a moderate mixture of Irish and Scotch, anything would work well. Macaulay on the House of Commons. Libri. Prince Boncompagni. Gerard of Cremona, Translator of Ptolemy. Negative quantity in Arabic algebra. „ July 16, 17. GD = 10^^ Reinhold's 2b^/<s Dtrec^tonum. My Mnemonic

for the hard-to-be-remembered formula. Suggests a sonnet. Libri.

W. R. H. July 20. Politics. Robert Hutton. T. Drummond. The Ballot.

A. DeM. July 23. The Time$ on Libri. Jewels of criminal law in France.

Prof. Toung. Maynooth.

W. R. H. July 23. Dublin politics.

„ July 26. Admits deep prejudice in politics. Reminiscences. Claim

of family descent. Maynooth.

A. DeM. July 27. Politics. How I would tinker the Constitution. Evil of

subscriptions. Opposition to Maynooth grant founded on a subversive principle. Reinhold's Tabula Joccunda,

XXIV Contents.

TxKxtEL Date of Ijetter.

W. R, H. July 28. Against mnltiplying oaths. Bribery.

A. DeM. July 31. Epigram on the Dnke of Norfolk and curry powder.

Tour Seal. Lucas Paoioli's Summa di Arithmetica,

The last day of letters prepaid in money. W. R. H. Aug. 3,4. Calculation unfavourable to the notion that the asteroids

are fragments of an old planet. Such calculationa

not his most useful employment. His birthday and

his younger son's. ,t Aug. 8. Lithograph of G. Wolfe's autograph of ' Not a drum was

heard.' Preface. First or Third Person ? Lady H.

and his daughter desire to see De Morgan. A. DeM. Aug. 9. Asteroids probably parts of a ring. Bibliography.

Errors in Description. y, Aug. 10. Reasons for First Person. Advice as to Preface. Scotch

Ancestry. Dr. Parr to Sir James Mackintosh. W. R. H. Aug. 11. Two Solutions of your puzzle for my daughter. Her

birthday. „ Aug. 13. Chasles on imaginaries. Time of publication of book. A. DeM. Aug. 16. Only two solutions of the puzzle. Dates. W. R. H. Aug. 20. Paper on the Ascension. As Trinitarian as Athanasios.

Sermon by Salmon. A. DeM. Aug. 23. F. Baily's correspondence. Tour handwriting diminish- ing. Tour Trinitarianism. Tour * sermon.' Mr.

Robinson and belief in the Devil. Mrs. Flamsteed's

Valentine. W. R. H. Aug. 26. Ely Sonnet. Sir J. Hersohel's to HamUton. A. DeM. Aug. 30. The Wolfe lithograph. A Peacock a Phcsniz. The

Three Churches in the Ely Sonnet. Herschel a man

of poetical elements. W. R. H. Sep. 1. Explanation of Ely Sonnet. Bishop Terrot. Abp.

Whately and the memorial window in Castleknock

church. A. DeM. Sep. 1. Bad practice of printers putting books a year forward.

Theology. An agreeable lull. W. R. H. Sep. 2. Satisfaction about the Wolfe autograph. My Preface a

bore. A. DeM. Sep. 3. Paradise Lost necessarily Tritheistic or Arian. Whately

and emblems. I would not abolish superstition and

mysticism. My notions about burial. W. R. H. Sep. 16, 17. Belfast Meeting of British Association. Carlingford.

Renewed interest in Quaternions. A. DeM. Sep. 20. Given X-land, what constitutes an X-man ? Chancellor- ship of Oxford. Walton, opponent of Berkeley's

Analyst : son of Isaak W. ? W. R. H. Sep. 25. Return to Dublin. A. DeM. Sep. 27. Portfolios. History of infinitesimals in England. Leibnitz.

Newton.

Cofitenh. xxv

>»

W.R.H.	Oct.	3.
9>	Oct.	4.
A. DeM.	Oct.	5.
W.R.H.	Oct.	8.
A. DeM.	Oct.	23.
V.iLH.	Oct.	26.

From Date of Ijotter.

W. R. H. Sep. 29. Salmon on Temporal Blessingfl. National Sins and Jndg-

ments. Irish mniden. Gift of a Douay Bible. Charitable supposition of R. C« Priest.

A. DeM. Sep. 29. Enquires for Boole about Dublin printers. Cheek upon

printers. Oct. 1 . Salmon's argument that religion was intended to develop

the inquisitiye faculties sound, but involyes the con- sequence that differences of opinion were also intended* A difference with Salmon. Irish Exodus — pun. Answer to application for subscription towards a R. C. purpose. Dublin University Press. Boole.

Bishop Berkeley. Walton. ' Fluctions ' and ' fluxions.'

Irish bulls. Boole has got hold of the true connexion of

algebra and logic. Ckiuche Polygons.

Editions of Berkeley. Infinitesimals in England. Newton.

Four colours will colour any possible map. Asks for a sketch of the history of Double Algebra.

v/- 1. Grassmann.

A. DeM. Oct. 29. Cannot comply with request, (hussmann (Nebuchad- nezzar). Sir W. H. of Edinburgh and his charge about Plouoquet. Translate for me your German.

W. R. H. Oct. 30. Begun Preface-writing.

A. DeM. Not. 8. Series and mean values.

W. R. H. Nov. 16, 18. Triplets worked at in 1835. Bight now to record this in

Preface. A. DeM. Nov. 20. Admits his right. Not at the Duke's funeral. The

procession. -W.R. H.Nov. 24, 25. Tour Triple Algebra and my Triplets. Fundamental

difference between them. My notion of triplets as

old as 1830. A. DeM. Dec. 15. Do not be uneasy about priority. Grass and mutton.

W. R. H. Dec. 18. Admits nervousness as to anticipated controversy. When

it comes the vexation is over. Trisection of an angle. Is it impossible by Euclid P Gauss.

A. DeM. Dec. 24. Your priority- vexations a reflection on Lady Hamilton.

Proposed resolutions of British Association. Gauss's discovery of a method of inscribing a polygon of seventeen sides increases my disbelief in possibility of trisecting an angle. Tells a story.

Argand true author of Double Algebra, not Bu^e. Asks for any information to the contrary relative to Bu6e.

Double Algebra. Bu^e, De Morgan, Wallis.

Buee, Wallis, Warren. Am afraid of virtual discoveries.

	1853.
W. R. H.	Jan. 8.
>9	Jan. 26.
A. DeM.	Jan. 27.

A. DeM.	Feb. 6.
W. R. H.	Feb. 9.
A. DeM.	Feb. 11. Feb. 12.
W. R. H.	April 1 . April 4.

xxvi Coyitents.

From Date of liOtter.

W. R. H. Jan. 28, 31 . J. T. Orayes confirms recollections about Argand. Buee,

Warren, Wallis. Been reading Grassmann with admiration and interest. Burprising that Grassmann failed to hit off Quaternions. „ Feb. 1. Verification of recollections about Argand. Not quite so

enthusiastic to-day about Grassmann. Comparison of his own work and Grassmann's. Take a side, and care for nobody. Arago and the watch. Willing to be mentioned favourably. Skin so thick it can neither be pierced nor tickled. Thirtieth anniversary of my starting for Cambridge. Comparison of work with Grassmann's. Argand did not anticipate De Morgan. Extract from Latin poem of Leibnitz. Theorem suggested by hints from Cotes and HerscheL German intellect. Tobacco-smoke. Difficulties of exten- sion to experts used to it. D. F. Gregory. Sir W. H. of Edinburgh cannot abstract quantity. Leibnitz. Inquiries.

Returned from fairyland, an investigation in the applica- tion of bi-quatemions to the inscription of polygons in surfaces. This day would have been birthday of Sister, who vdob a poet. Claims for himself only poetical temperament and feeling.

A. DeM. April 14. Objects to his limitation of his own pretensions to poetry.

Corrects expression about birthday. All opposite terms in logic come under phu and mmtM. Vnirer- $al-f particular +, &c. Recommends change of occu- pation from quaternions. A four-course suooession.

W. R. H. May 5. Dlness of children.

A. DeM. May 9. Table rapping. Our thoughts are read.

„ May 21. Poetry runs in families more than mathematics. Lady

Lovelace and the Difierential Calculus. Verses from Morgan's Horolagiographia^ and Hylles' Arithmetic.

W. R. H. June 30. Feelings after printing off a book. Anxiety about a

word. Observations at Dunsink quinquiseoted by Royal Commissioners. Mr. Charles Thompson.

A. DeM. July 2. A new Double Algebra. The two Sir W. H.'s, + 1 and

- 1. Argand' s lamp. Rotation of intellectual crops.

W. R. H. July 7. A new symbol of operation, !«.

A. DeM. July 11. Your new subject not recreation. The sailor's three

wishes. Difi'erential equations.

W. R. H. July 16. Book [Lectures on Quaternions) actually out.

A. DeM. July 18. Punning suggestion of letters to be added to Sir W. R.

H.'s name.

W. R. II. July 25. Method of least squares and theory of probabilities.

Suspects fallacy in himself and Encke.

Contents. xxvii

From Bateof Itetter.

A. DeM. July 29. Dispntes < both you and Encke.' W.R.H. July 29, 30. Agrees with DeM. as to fallacies.

y, Aug. 18. Suggests abridgment in De Morgan's argument (2){^.

and Int. Cole.) as to theorem of mean value.

Error in Moigno's Lemons de Calctd Differential. A. DeM. Aug. 19. Admits difficulty. Homersham Cox. The principle of

fluxions always gives light. „ Aug. 22, 23. Problem in probabilities as to set of books. Imperfect

cerebration. W.R.H. Aug. 22, 24. Inverse Probabilities. The Comet.

A. DeM. Aug. 26. Mrs. DeM.'s sight of the comet with naked eye.

Thundering error in my Probabilities. Everyone

makes errors in probabilities. Laplace, Poisson.

Illustration. W. R. H. Sept. 7. A theorem of Laplace. Royal visit to Dublin. The

previous one of 1849. The first Great Exhibition

in Dublin. Interview with the Prince Consort. A. DeM. Sept. 12. Presents tract on Probabilities. My thundering error.

The theorem of Laplace. What I have not seen. W. R. H. Sept. 28. British Association Meeting at Hull. Beverley Minster

and Flamborough Cliffs. PhiUips and Sedgwick.

York. Bolton Abbey. Belfast. Carlingford. A. DeM. Oct. 4. Guild of Literature and Art. C. Dickens. F. Baily's

handwriting. Lord Brougham and Quaternions.

Conundrums. W. R. H. Oct. 31. Death of a friend. Guild of Literature and Art. ^^^A. DeM. Dec. 10. Invention of Double Algebra.

W. R. H. Dec. 15. Telegraphic experiments in connexion with his second

son. His cipher. Dr. Hincks. ,, Dec. 17. Daughters.

1854. A. DeM. Jan. 10. Death of his daughter. Homer's Method, and its author.

W. R. H. Feb. 20. Homer's method. Secretary Drummond. Solution of a

linear and partial differential equation in bi-quater- nions. The existence of two arbitrary functions a startling departure from the analogy of the older algebra. Carmiohael.

A. DeM. Mar. 4. Arbitrary functions queer fishes : example.

W. R. H. Mar. 7. A transformation of the integrals involving only one

arbitrary function, y, Mar. 14. Mathematical blundera of Auguste Comte. His capacity

of admiration. A. DeM. Mar. 26. Comte's verbosity and self-sufficiency . His * final system

of Knowledge.' April 18. ' Dupin's proof (regarding the lines of curvature on a

system of orthogonal surfaces) diabolical. Tiie

97

xxviii Co7itents.

From Date of Zjotter.

words *• synthetical ' and ' analytical.' Derivation of

name of Easter. W. B. H. April 24. Dupin's genins. Le bon diable. De Morgan a Hippo- potamus. A. DeM. April 29. Dnpin a decent devil in mathematics. Intends to write

letters of advice to young mathematicians, wil^ a

Hippopotamus on the title page. W. R. H. April 25. Quaternions a Calculus. A. DeM. April 29. Quaternions certainly a Calculus. My course of teaching.

Infinitesimals. W.B.H. May 12, 20. Calculation with quaternions, geometrical interpretation

in the background. Simplest way of proving by

calculation the modular theorem. „ May 25. The Electro-magnetic Quaternion. (Quaternions furnish

a Calculus of Polauities). ,, May 27. Withdraws the epithet Electro-magnetic as assuming too

much. Dr. Lloyd. A. DeM. July 10. Rule for giving an extempore lecture. Stevinus. Joseph

Fenn*8 * Instructions, &c.*, at the Dublin Society,

1772, uses notation of the difiFerential calculus. W. R. H. July 14. Mourey's proof that every algebraic equation has a root.

Versors, tensors. A triplet-system. „ Aug. 11. Cipher. Asks De Morgan if he would be stakeholder. A. DeM. Aug. 12. Anything but decipherer. Tables of quarter squares.

1855. The PoUto.

W. R. H. Jan. 3. Payment by Board of Printer's bill. ' Extensions of Quater- V nions.' Would require some time to read. Easy to you.

A. DeM. Jan. 6. A shorter demonstration is time saved in teaching.

Example of arguing in a circle. Double algebra and

quaternions. W. R. H. Jan. 9. Find I can understand my own researches on Dynamics.

Connected this method with quaternions in 1845. A. DeM Jan. 15. A remonstrance. Read an old paper of my own not

knowing its author : pleased with it and gratified by

this testimony to myself. „ April 29. A fundamental method of Newton generally unknown.

Gives the problems. Carmichael on the Calculus of

Operations. Who is he? Rouse out from the

quaternions. W. R. H. May 2, 4. Up all night with the moon. 'He' or <It' of an infant.

A ' young pagan,* Mrs. Wilde : her son Oscar.

Her remark on the Observatory. More sociable. A. DeM. May 16. ' It ' for a baby. * Shortened.' Sponsors' undertakings. W. R. H. July 11. Decimal coinage: Mr. Lowe. Maria Edgeworth's pun.

Her age. A. DeM. July 13. Puns. Pitching into a joker a good service. Jokes on

serious subjects.

Cofitents. XXIX

Vrom Sate of Xi«tter.

A. De M. Sept. 5. Refers to his owb article on Brewster's NtwUm. Lying

fallow. Sheepshanks. Ballads: CuriositieB in the history of popular ballads. Simplicity an ultimate attainment. EncUd 1. 47. Eelland. Airy.

W. R. H. Oct. 2, 24. Glasgow. Jessop on Decimal System. ' Morning Regis- ter.' Extensions of Quaternions.

A. BeM. Oct. 29. The « Fine Old Irish Gentleman.' Decimal Coinage :

Lord Monteagle, Article in National Review, Mr. Jessop. Galileo. Anti-Romanist joke.

W. R. H. Not. 1. Decimal Coinage. Abduction of Miss Arbuthnot.

A. DeM. Nov. 4. The abduction case. English legal-headedness. 1856. ,y Mar. 3. The words of the ^ Fine Old Irish Gentleman.' Additional

stanza by De Morgan.

W. R. H. June 11. A protest against omission of his name from Grant's

History of Physical Astronomy, Jacobi. Donkin. Cayley. Houel.

A. DeM. Deo. 26. Death of Sir W. Hamilton of Edinburgh. Obituary

notice by A. DeM. The creed of the Decimal 1867. Association. Isonosical lines.

„ Jan. 12. Air of ' Irish Gent.' in A. DeM.'s musical notation.

Note* Petrie on this notation. y, Jun. 18. Sir W. H. of E. on Mathematics.

W. R. H. Mar. 22. Early days at Glasnevin. Varenii Qeographia Oeneralis

edited by Isaac Newton. Instance of historical inaccuracy on a recent and public occurrence.

A. DeM. May 4. Newton's Yarenius. Story for story. What is history ?

Libri.

W. R. H. May 20. Salmon and Quaternions.

A. DeM. June 15. Salmon's name. Tour son. Affirmative and negative

as applied to propositions: definition must be enlarged.

W. R. H. June 24. The Times, Its powers of f aoe.

A. DeM. July 3. Bulk of the 2Vme« staff Irish. Newspapers mirrors. ,y Aug. 3. Quaternions not for ladies. Approves W. R. H.'s

Decimal Coinage Bill. Archibald Smith. Preserv- ing letters. Specimen of my folly in a letter to Mansel. Wills. Logics and Mathematics.

W.R. H. Aug. 7. Terms with Salmon. With MacCuUagh. Notion of

writing a Tract on Cones of the Second Order treated by Quaternions. Asks for opinion.

A. DeM. Aug. 14. Opinion as to such a book.

W.R.H. Aug. 14, 17. Abandons the project. Notion of another tract. Letters

to Salmon. British Association. A. DeM. Aug. 21. British Association. Am not in sympathy with physical

philosophers. Object to travelling. ,, Nov. 15. What curves cannot include a space ? No news to tell.

XXX Contents.

Vrom Bataof l40tt«r.

W.E.H. ^ov. 16, Dec. 4. Definite Integrals and Transfonnation of Series.

Theorems (A) (B) (C) (D) (E). A. DeM. Nov. 20. Cauchy's 'principal valne.' Carves that do not inclose

space : elementary proof. Proof that every equation

has a root. W. R. H. Nov. 23. Cauchy's proof. Monrey's method. Writing merely to

free the mind mntually allowed. Professor Stokes on

Definite Integrals. A correction. A. DeM. Nov. 27. Every convex spherical polygon has its supplemental

polygon. Cauchy's proof. Mourey's. Argand. Airy

and 'v/- 1 . Herschel on a certain discord. W. R. H. Nov. 28. Correcting misprints. Definite Integrals. ^A. DeM. Deo. 6. Airy's paper on \/- 1. * In all haste.* W. R. H. Dec. 18. G. Stokes on my Definite Integrals. A. DeM. Dec. 19. Your last letters [on Definite Integrals] a memoir in

themselves. W. R. H. Dec. 14. Transition from Double to Quadruple Algebra. „ Dec. 22. Herschel's wit in re Decimal Coinage. ,, Deo. 23. A convert to Divergents.

1858.

A. DeM. Jan. 1. Comment on letter of Dec. 14. Vindication of Cauchy.

The French and Divergent Series. Four sorts of Series.

W. R. H. Jan. 4. Cauchy, admire his mathematical talents. My investiga- tions by quaternions respecting families of surfaces the germ of a new Calculus of Partial Differentials. Great importance of ' alternating series.* Where Mourey succeeded, where he failed.

A. DeM. Feb. 20. The logicians too mathematical. Organ- tuning by beat«.

March 1. Pascal's Theorem. Projection. Apol- lonius.

W. R. H. Mar. 3. Pascal's Theorem. Moebius.

A. DeM. Mar. 7. Projection. Pascal's Theorem the fundamental instru- ment. „ Mar. 23. The police and the Trinity College lads. A shillaly

tournament.

W. R. H. Mar. 30. Tour construction of hyperbola derivable from Pascal's

Theorem, which I have considered fundamental. Pascal above Chasles in inventive genius.

A. DeM. Aprill. Newton's equation. Chanting it. Whewell's letter- puzzle.

W.R.H. ApriH, 6, 10. Cipher. Series for/ {x + A) with a foreign and arbitrary

constant. Silver wedding. A formula of Laplace analogous to mine.

A. DeM. April 11. Anticipation of your theorem by Murphy. Anticipation

of life.

Contents. xxxi

Ftom I>ate of Iietter.

W. R. H. April 14. Admits antioipation by Murphy of one of his theorems. . A more general series.

A. DeM. May 16. The two sides of Logic, mathematical and metaphysical.

W. R. H. May 26. Annonnces finishing and despatch of his long letter on

Definite Integrals.

A. DeM. June 3. Read through your 72-page letter: 'a collection of

memoirs, a real inroad into the territory of divergent series.' Alternation safety in series, not convergency. Motto from Hohbes for my tract on Logics and Mathematics. Sir W. Hamilton of Edinbuxgh and * quantity.'

„ July 27. The two Sir William Hamiltons. Logic of the word

*of.' Anagrams. Newton and Huyghens. Syllo- gism implying relation in copula. A near relation. London air. Logical examples. P. M. A. 0. F.

W.R.H. Sept. 13, 14. Visit to Trim. Daughter dangerously ill. Dr. and Mrs.

Butler. Oct. 13. My differentials what Newton 1859. would have caXiedJliizions.

jy Jan. 3. Additional conclusions respecting Definite Integrals.

Hon. Mrs. Ward.

, , Mar. 1 1 . Monthly Notices of Royal A stronomical Society. Reports ?

A. DeM. Mar. 27. Do not write much in Reports. Main : Donati.

„ No date of time. New date of place. Chalcot Yillas. J. Smith and

circle-squaring. Tour short proof. Daughter's restoration to health. Advice to her.

W. R. H. Oct. 9. A plea for Italics and Capitals. Duty to Insurance

Offices.

A. DeM. Oct. 11. Insurance Offices : a distinction as to duty towards them.

Elimination. Transition. Illustrations.

W. R. H. Dec. 1. Deference to your criticisms.

1860. A. DeM. May 26. An outcry for information as to himself. Report I shall

circulate. Where was Sam Johnson in 1745-6 F W.R. H. July 9. Touring in Wicklow.

A. DeM. Nor. 6. Received your letter (of October 29 on Geometrical Nets

in Space). Reviewing Sir W. H. of Edinburgh in AtheruEum, He certainly never read Euclid I. 1. to understand it. G. Dickens knew it better. Dec. 18. Glad the affair (with Tait) is so well arranged. My con- troversy with Mansel. Very good opponents. Bad practice of establishing exact science by quota- 1861. tions.

April 29. Tried pleurisy. Sir W. H. and * some at least.'

W.R.H. May 1. Gout does not disturb my mind. TEOTA. Lady Hamilton

wants to see A. DeM.

9»

91

xxxii Contents.

N

Tkom Date of Xiotter.

A. DeM. May 31. Mr. Smith wants more killing. Convincing Mr. Smith.

Father 0' Flaherty's pig. A jingle. Lady Hamilton would be disappointed in seeing me. Another Lady Hamilton terribly bored by me. Mr. James Smith coming to London. Bhyme to Timbnctoo. Pun on Airy.

W. R. H. June 30. My daughter's remark on my posting in one evening

notes to two Lady Hamiltons. ' Geometrical sighs.' Challenge to De Morgan. A puzzle from him. I, Aug. 10. My daughter pleasantly angry. Irish Church Canon.

A. DeM. Aug. 12. The anger will oool. Delight in defying control: example.

W. R. H. Nov. 9. Compares the Lectures with the unfinished JElemente.

1862.

A. DeM. Mar. 6. Inferential non -affirmation.

W. E. H. Mar. 8. Berkeley's criticism on remarks of Newton. Newton not

consistent in his philosophy, I stick to ihejintte

quantities, Thomas Simpson. A. DeM. Mar. 11. Newton shuffling. My autograph for Miss Helen.

W. R. H. Mar. 14. Have adopted Finite Differentials.

A. DeM. Mar. 15. Differentials. Laoroix. Legendre. Limits.

W. R. H. Mar. 18. Dispute your negative. Lagrange unreasonably objects

to modem use of the word lirnit. My differentials not infinitesimals. Philosophy of the Infinite. Science of the Infinite.

A. DeM. Mar. 23. Is differential to be used for infinite multiple of a diffe- rential. Supports his negative. Suggests the word primo-raiumals instead of differentials: also terms

for Yi K c^d A*

W. R. H. Mar. 25. Is quasi universal usage in favour of considering a diffe- rential as an infinitesimal? Lacroix. Peacock. Cauchy. Moigno. When was ' Differential ' natura- lised ? Euler.

A. DeM. April 1, 7. Ranges the authorities on both sides of the differenticd

question. Date of introduction of Diff. Calo. into Cambridge, x rate of y.

W. R. H. April 19. Berkeley in earnest against fluxions as well as against

matter.

A. DeM. April 20. Infinitesimals before Leibnitz. Newton got hint of

fluxions from intensionists.

W. R. H. April 22. x rate of y won't serve me. Infinitesimals may be intro- duced into quaternions. The only question as to differentials. Weight of authority on your side.

A. DeM. April 24. Hart's rectilinearity. A joke. My objection to your

practice as to differentials. Hey diddle diddle^ Qi'sec^ partim, partim Latins.

Contents. xxxiii

Prom Dtttoof Iiettcr.

W.R.H. July 2. Differentials of qnatenuons. I treat them as infinitesimals

in integration. A. DeM. Jnne 4. Change of local date in verse.

W.B.H. Sept. 15. Rober's inscription of a heptagon in a circle. Homer's

method.

A. DeM. Sept. 18, 23, 29. Homer. Young. Hair-compasses. Rheticua of Pitis-

COS. Cavendish. Involution and other articles in JBngUsh Cyelop€Bd%a, Conies or qitaricB, Infinity : twice as many pints as quarts in infinite space 'f

1863. Amosgepotically.

„ April 3. Infinitely small qnantities P

W. K.H. April 16. line at infinity in given plane. Plane and circle at

infinity in space. A. DeM. April 26. Expediency of waiting. Cambridge Undergraduates.

Infinity a light to guide. „ July 31. Collecting my queer books. Whewell's apothegm. „ Oct. 21. Beyer's contracted multiplication. Short methods don't

pay. Mr. Weller. W. R. H. Oct. 23. Those can use who don't want it. A. DeM. Nov. 10. Col. Oakes's rule for multiplication.

W. E. H. Oct. 24. Homer's Method. Complex Evolution P Complex Invo- lution.

A. DeM. Oct. 28. Evolution and Involution. Teachers of calculation.

James Smith. 666. Cabbala.

W. K. H. Nov. 10. Cotes's Harmonia Mensurarum, Ratio. A duplicate

ratio. Briggs, Napier. Modulus. Modular Angle.

A. DeM. Nov. 14. Cotes probably not intentionally unjust to Napier.

Napier did not use Naperian logs. Object to Halley's and Cotes's Mensura rationxs. Cotes and Newton infinitesimalists. Newton a momentarian.

W. R. H. Nov. 17. Napier's ' Canon Mirificus.' Importance of distinguish- ing between Ratio and Quotient. A Quaternion, geometrically considered, a Quotient of Vectors, but do not choose to call it a Ratio of Vectors.

A. DeM. Dec. 31. Ratio and Quotient. Duplicate ratio. A riddle. Two

papers. Another riddle. Shakespeare tercentenary.

1864. Note.

W. R. H. June 8. Logic of two Controversialists, Roman Catholic and

Protestant. Father Tom. A. DeM. June 22. The two controversialists. Middle term in a syllogism.

Anti-root. Signal-factor. ^W.R. H. June 24. The controversialists. Anti-root. Signal-factor: Argand,

Peacock. Double Algebra interprets too much.

Algebraic geometry requires imaginaries. Expected

once to find in Quaternions a new set of geometrical

imaginaries. No such instance.

VOL. HI. 0

xxxiv Contents.

"BxQxn. Dat« of Letter.

A. DeM. June 26. Case in whioh both middies may be partionlar. Double

algebra one of the perfect oommon algebras. Quater- nions one of the triple algebras. W. R. H. July 4. Vision. Habitually a double-seer. Binocular vision not

necessary. Amount of obligation to tou/ch. Visible distance. Do we believe we see the very trees ? A. DeM. July 17. Strictly unooular. Not aware of difference from a short- sighted person with two eyes. Obligation to touch. Can draw a straight line and circles. W. R. H. July 19. Tour * Unocular ' a right correction of my ' monocular.'

< Homofocal,' ' GonfocaL' A. DeM. July 31. Seeing the very objects. So words for objects. Distance

recognisable without touch. A second eye would add to quantity of nervous action. Illustration. Peroxide of hydrogen. W. R. H. July 4. Hamilton of £. on Reid. Interested in Hamilton's Philo- sophy. A. DeM. July 9. Hamilton of E. interesting even in Logic when quantity

is not in question. At Oxford. Originality of thought of putting sign of quantity to the predicate. W. R. H. July 9. Agree more with Ingleby than with Hamilton as to Per- ception of an External Uniyerse. Axioms ascribed to Euclid probably not genuine. Sir W. Hamilton's view of Philosophy differs essentially ftx>m mine. A. DeM. Sept. 22. The Declaration of Scientific men. Herschel's stinging

answer. W.R.H. Sept. 23, 30. Herschel's intention in refusing to sign. Sir John

Bowring. A. DeM. Oct. 2. Herschel objects to Declaration as mischievous. Declara- tion translated into English. Illustration. Cui bono. Herschel not a timid man. J, Dec. 13. Pension for Professor Boole's wife and daughters.

Influence of the Irish in the House of Commons. Acknowledgment of kindness.

Contents. xxxv

APPENDIX. YoL. II., page 537 : —

Two POPULAR ACGOUirrS OF THE QUATEBNIOIT CALCULUS :

PACK

1. From Sir W. R. Hamilton to Rev. James Hamilton, . . 633

2. Elementary Sketch, 635

Vol. II., page 543: —

Masdleb's Ceittral Sun, 637

Vol. III., pages 199, 200 :—

Additions to ConUnU qfJSlemenU of Quaternions ^ . . . 640

Intended Notes A, B, and C to Elements of Quaternions, .6-11

Brrata in Lectures on Quaternions and in Elements of Quaternions, 642

Vol. III., page 200 (Note 2) :—

Memoirs in which Determinants are used, 643

Vol. II., page 103 :—

Eant's Philosophy : Fragment of a draft of a letter to A. De Vere,

Esq., 643

List of Papers, Memoirs, Addresses, and Books purlished ry Sir William Rowan Hamilton, and op Notices op Communica- tions; also op Posthumous Purlicationh, and of Books dealing with quaternions, 645

INDEX, 659

COKRIGENDA.

VOLUME III.

The reader is particularly requested to make tbe following corrections in the ^tals at the top of the pages specified i~

Pages 61, U, W, . . . /or SO read 61.

„ 88 ,.6l„ 62.

„ 117, 119, . . . „ 68 ' „ 6i.

„ 127,129,181,138, „ 54 „ 66.

„ 186, 137, 189, . . H fi6 „ 6e.

„ 141,143, . . . „ 66 „ 67. Page 7, line 22./or latter read later.

„ 7, note, lifter ' aupra * insert Vol. II.

„ eO, line 21, for deserters read dissenters.

„ 69, L 25, after integers /or comma imert — .

„ 136, 1. 14, /or Chai-les Mansfield read Clements Mansfield.

„ 879, L 17,/or Havll, Great Southampton-street, read Uavil-strcet, Soutltanipton-street 472, 1. 21 ^fler function iiuert O,. 693, 1. 26,yor October read November.

11

[Minor errors are left to the intelligence of the reader].

LIFE

or

SIR WILLIAM ROWAN HAMILTON-

CHAPTER XXXIX.

THE DAR6LE. LIVERPOOL MEETING. VISIT TO WESTMORLAND.

(1854.)

The last preoeding chapter of this work reoorded the publieation^ ten years after he had discovered the CaloulaSy of Sir William B. Hamilton's Lectures an Quaternions^ and the reception by him from his scientific brethren of most gratifying testimonies to the value of the work. Both the publication and these results of it must have been an immense relief to Hamilton's mind and spirits. And indeed that relief had been greatly needed ; for, as may be remembered, his intellect had been long continuously tasked, and he had passed through a period disturbed by much care and emo- tion. Early in the year 1854 he received from an old friend a letter of thanks for a presentation copy of the book, which, though containing a disclaimer of the ability to read and judge of it, could scarcely have been less welcome to the author than homage from the highest mathematical authority. Its writer was Pro- fessor Sedgwick, the veteran geologist, who in it expresses, in his own natural and vigorous style, his affectionate feelings towards Hamilton, and in regard to himself manifests the indomitable spirit which, carrying on a constant battle with ill«health, was one of the many charms of his noble character. I here give thia letter, and add a sequel of shortly subsequent date and equallj diaracteristic.

VOL. 111. B

2 Life of Sir William Rowan Hamilton. [1854.

T^om Professor Sedgwick, f.r.s., to Sir W. B. Hamilton.

' Cahbbidob, March 26, 1854.

^ How long your Lectures on Quaternions has been at my rooms is more than I oan tell you : but here it is before me, with " the author's afiPectionate regards" written on the title-page. I am very oblivious ; so I may have thanked you before ; but I have no remembranoe of having sent you a former letter of thanks, and I now do thank you with my whole heart. Your book is quite out of my depth, and I am far too old, and too busy in the works of my own craft, to think of learning to swim in the wide ocean of your mathematical speculations ; but I can, and do, wish you good speed, and I trust that your life, spent so nobly in soaring after truth, may be continued to you in honour and happiness for many years to come. I have had a miserable winter. In the October Term I lectured (my thirty-sixth Course) to the largest class I ever had at Cambridge ; and I always had a good class, even during the twelve or fourteen years when the professorial lectures were, generally, in a state of great depression. Now they are much re- vived. Perhaps the crowded state of my lecture-room excited me too much ; or perhaps I this year had a warning that I am becoming old, and unfit for my former tasks. Be this as it may, I did break down during the middle of my course ; and I was forced for fifteen days to be as mute as St. Anthony's congregation in the Gulf of Genoa (surely it was there or thereabouts that he preached to the fishes ; but you can, I dare say, eliminate the fact without the help of quaternions). During the said fifteen days my inner man was washed by streams of rattling cathartics ; and as for my poor head, they cured its congestion by sucking all the blood out of it by help of leeches applied three different times to my temples, the back of my ears, and the back of my neck. I then finished my course, though in a languid and unsatisfactory manner. The general reduction of my system made me unusually sensitive to atmospheric impressions, and before the end of Term I caught a cold which assumed, in a day or two, the type of bronchitis. For twenty-nine days I remained a prisoner in my own room, and in a state of miserable stupefaction. The weather then became milder, and about the middle of January (muffled to the ears, and with a respirator over my mouth and nose) I went to my house at

AEiAT. 48.] Letter from Sedgwick. 3

Norwich ; and under the oare and love of a nieoe* I gradually came ronnd, and again tried to spread my sails to the wind when the weather was nuld and the son was warm. I retomed to Gam- bridge early in this month. I am still a grombler. A remnant of bronchitis still clings to my chest ; suppressed gout takes away my sleep ; my Iddneys are doing their work in a grating fashion ; and I have every day, especially every night, long fits of coal- black melancholy. A quaternion of maladies ! Do send me some formula by help of which I may so doctor them that they may all become imaginary quantities or positively equal to nothing. Any change will be for the better. Try some transformation or other ; for I am at present both stupified and demoralized. I send you this dissection of myself as a kind of lame apology for not having thanked you sooner. Your book was, I believe, on my table among a multitude of parcels I found there, about three weeks since, when I returned from Norwich. GKve my best remem- brances to Professor Lloyd and the other members of the dear late Provost's family. Ever, my dear Sir William, truly and gratefully yours.

' P. 8. — I may well talk of getting old, for on the 22nd of this month I entered on my 70th year, and I have now resided very nearly half a century in Cambridge. I was a green Freshman in 1804.'

From the Same to the Same.

* CAiiBBrDOS, April 19, 18M.

' Yerses I have none to send you, for I never wrote a line of poetry in my life — at least in my own Yorkshire tongue. My master, under the stimulus of birch, did force out of me some Latin lines that would scan ; but I dare say he never had a drop of poetry from me. No muse ever rocked my cradle : but I love good poetry and good poets, and I do fervently thank you for your last letter and the enclosed poem. To offer you one of my geological Papers would be like asking you to lunch on a dish of brick dust. I have, however, f oimd a copy of my letters to Wordsworth, which are a little more popular than my Paper read at Somerset House. I am not so imreasonable as to ask you to read them. I only ask you to

* Uifts Isabella Sedgwick. B2

4 Life of Sir William Rowan Hamilton. [1854.

read from page 51 . . . 53, and the oonoluding words begmning' page 90.

* Pray accept this small and humble offering as a mark of my regard and mj affectionate remembrance of jonr kindness.

' Ever, mj dear Sir William, tmlj and gratef ally yours.'

Sedgwick's 'charming letter/ as Hamilton called it, was forwarded, on account of the message at its close, to Professor lioyd, and with it a note of De Morgan's, in his correspon- dence with whom he had found occasion to criticise some assertions of Auguste Gomte's in connexion with mathematics. What passed between Hamilton and De Morgan on the subject may be found in its place at the end of this volume, but I insert here Hamilton's reference to it in his note to Lloyd.

From Sib W. B. Hamilton to Pkofessou Llotd, d. d.

* March Z\, 1854.

* . . • De Morgan I have, I think, not seen of tener than once, or say twice, in my life, but the triplets and quaternions threw ua into a very free and familiar correspondence ; and I spoke to him of Comte lately with a degree of freedom, which might well have been cbX^bA. flippant^ if my criticism on one part of the wiitings of so celebrated a man had been in any way designed for publicity. Some of the mistakes may be mere slips of the pen, but others (I still conceive) indicate a confusion of thought on Gomte's part, on subjects which he professes to treat of.'

In May Hamilton wrote an important letter to John T. Graves, in which he comments on Mr. Graves's theory of Octavea (a theory arrived at independently by Mr. Cayley), and proceeds to announce that *one of my recent extensions of Quaternions gives a theory of quadrinomes^* and, *I have found also a system of Tetrads.' A postscript refers in appreciative terms to the re- searches of the Bev. T. P. £irkman, and on this account I insert it in a note, leaving the main body of the letter for a place in

ACTAT. 48.] EUdro-Magnetism. T. P* Kirkman. 5

Hamilton's Boientifio oorrespondenoe.* The same most be the deetination of some still more important letters to Dr. lioyd* They set forth what he eaUs a oonjecture soggested by Qna- temions which might prove ^a phyaioal disoovery respecting the mutual action of two elements of the same, or of two diffe- rent (electro-magnetio) currents, considered as exerting (in addition to Ampere's attractive or repulsive force) a certain directive force, or as producing a system of two contrary couples.* He afterwards saw reason to doubt of the physical applicability of what he had called provisionally his electro-magnetic Quaternion ; but Lloyd continued to assign to it a high possible value in re* lation to the theory of Electro-magnetism. Dr. Lloyd's words

* May 31st. — I am greatly interosted with your electro-dynamic Quaternion. It seems to me to promise {not a new physical dis- covery, but what is yet moro interesting) a theoretical explanation of the fundamental facts of electro-magnetism. . . . The similarity (or agreement) to these [Biot's laws, representing the action of an infinitely small magnet upon a magnetic pariicki] of the laws which govern your vectors, give, I think, ground for hope that you will be able, through it, to explain the true physical relation between the electric current and the magnet. And if so, the discovery will indeed be a great one.'

I add here a postscript to one of these letters to Lloyd, in- dicating the fertility at this time of Hamilton's mathematical imagination :—

* ^May 16, 1854. — I have little more than looked into Kirkman's Pluqua- tendons (Philosophical Magazine, end of 1848), but am sure that they are very interesting, and ought to be studied, if the octaves are to be pursued. You know I object to his use of the word (tquatemions, which I wish to reserve for a + V^l (^y Q and Q' being quaternions. Bid you ever consider whether he has been sufficiently cautious in his use of the association principle f And must his oorious '* imaginary duads " finally remain as such P Are his final conclusions about sums of squares confirmed P He is a very clever feUow. My son William Edwin has lately received another science honour in T. G. D. Salmon's Came SecHims he knows a good deal about, and is now entering seriously on the Differential Calculus, of which I must soon tell you my definition.'- Elements of Quatemianif pp. 99, 100.

6 Life of Sir William Rowan Hamilton. [1854.

^May 30. — ^P.S. This month of May has been an unusually original (if not an unusuallj busy) one with me, whatever good may or not have oome out of this last speculation. At least four distinct (though not unconnected) trains of inquiry have opened themselyeSy though I may not be able to pursue any of them far at present ; and I could not continue the writing of a letter to- Carmiohael* this morning, which had been begun yesterday even- ing without perceiving a fifth line of future investigation. All this, however, is unfavourable to routine duty : and, besides, we are at present in much anxiety here about the health of my dear little daughter/

A cheer was given to Hamilton's spirits this summer by two events : in July the living of Ijoughcrew was, through his influence^ conferred by the Lord Lieutenant, Earl De Grey, on the Bev. James Alexander Hamilton, son of the uncle to whom he had been so deeply indebted for his education; and in August the Board of Trinity College relieved him of all remaining liability for the expense of printing the Lecturer on Quakmions. They had previously contributed £200 towards this object, but a balance of £100 remained due, and the prospect of having to pay this sum was the source to Hamilton of much anxiety. Hir oause was warmly advocated by Dr. Luby, Dr. Todd, and Dr. Lloyd, and the vote in favour of the grant was unanimous. Dr. Luby had previously written to Hamilton, saying: *I cannot con- ceive that the Board would suffer you to be at any loss by the publication of a work which is so noble a monument of human science, and which does so much honour to our University.' A pleasant note from Dr. Lloyd, of subsequent date, makes the following reference to what passed on the occasion. * I have often

* The Rev. Robert Carmichael, mentioned here, was a Fellow of Trinity College, who carried on original researches in the region of Claatemions, and corresponded with Hamilton on the subject. One formula (!>■ - i2>« -jl>f) V^ Or connected with the celebrated equation of Laplace, Hamilton proposed to call * Carmichael's Equation' : see Proceedings^ R. I. A. Hamilton somewhere notes, concerning Carmiohael, that *he often made mistakes, but that he had the tem<» perament of genius.' His life was oat short at the earlj age of 31.

ASTAT. 49.] Vtsti to Kilcroney.

thouglit smce I saw you with equal pleasure and pride of the Quaiemian you told me of , whose unit- veotors are (not f , jy k^ but) H., J., Li. ; * and I made some use of it at the Board the other day in solving the problem of GfilPs account ! I must add, however, that the members did not need much demonstration to arrive at the conclusion which they came to.'

Dr. Lloyd at this time lived in a country house called £ilcroney , situated near the entrance of the Dargle, and here he and Mrs. Ldoyd hospitably received many distingoished persons, foreign and native, whom the eminent qualities and accomplishments of the host and hostess, and the rare loveliness of the surrounding woods, and waters, and mountains, attracted as visitors. Towards the dose of August, Hamilton took the thought of going to see these faithful friends, found them at home, and was easily persuaded to stay the night.

In the following Hexameters he puts on record the incidents of his visit. They were sent to Mr. Thomas Disney, who, by lines of his own in the same metre, had provoked Hamilton's attempt to repay his friend in kind. It cannot be said that they cope success- fully with the difficulties of the metre. His earlier poem on the Dargle, to which he refers in the letter prefixed to some copies of the latter one, printed for private circulation, maybe found in the first volume of this work, page 147. I reprint, with the Hexa- meters, the prefatory letter: —

From Sib W. B. Hamilton to Thomas Disney, Esa.

* Obsxsyatobt, September 15, 1854.

* You will easily believe that in allowing the following verses, connected chiefly with the scenery of the Dargle, to be printed, though not published, my highest ambition has been to give some moments' pleasure to a few friends and acquaintances, for whom I had at first designed to copy the lines myself, but found that the task would have occupied too much time. If those verses shall fall into the hands of any persons unacquainted with me, I hope

* Hamilton, Jaoobi, Lagrange; supra, p. 117.

8 Life of Sir William Rowan Hamilton. [1854,

that on inspection thej will aoquit me of the presumption of having aspired to riml anj compositions in the same unusual and somewhat foreign metre, which yet I may be supposed to have sought for my own satisfaction to imitate,

* You know that I have never hoped to win any reward from poetry, beyond an occasionally elevating relaxation from pursuits of a different kind, and an assistance towards preserving for my- self , and sometimes communicating to friends, a few records of the pleasurable or painful feelings of what has been, upon the whole, a studious and happy life. My recent attempt at hexameter com- position, notwithstanding its confessedly imperfect execution, haa already enabled me to enjoy more than before (you will say, per- haps, by force of contrast) some passages in the *' Evangeline " of the American poet Longfellow, not to mention here any less popu- larly known writers in that style. But I am so far from supposing that I have surmounted the (by some thought insuperable) diffi- culties of this kind of verse in our language, that these latest lines of mine do not please myself so well as even that early, and indeed boyish poem of my own, on a subject nearly the same, which I venture here to append : althoughi as a record of the sort above referred to, I have chosen in this way to preserve them. You will see that I have abstained from introducing the name of any living friend ; but have thought myself permitted to allude to a dear and departed lady, whose name has become already classical, from its occurrence in the published Memoirs of her deceased and illustrious father.'

<DARGLE VERSES.

*T0 AK OLD FBIBVD.

* Thanks, old friend, for your lines, in that anoient hexameter flowing : Thanks for describing so well to me the adventures of that night, And whatsoever befell, sinoe alone in the starlight we parted. I have been roaming too, and have met with some pleasant adventures; Suoh will I now reoount : accept the imperfect requital.

* After a morning walk to the nearest skirt of the city, Back by the cool canal, and the long green lane to my dwelling, H using I came ; and enjoyed the distant vision of Dublin, Seen with the valley between, and the ship-studded ocean beyond it, Spires, and the haunts of men, while I stood in unbroken seclusion, Kear that small gate which you know, where the harvest waved, ripe for the reaper.

AiTAT. 49.] Dargle Hexameters.

' Then to myself I said : I'll enjoy the remainder of this day ; Let books rest for awhile, and the still new labour of writing : I will return to men, yet see more of nature this evening. Lately I have not viewed so muoh as the borders of Wicklow. There, where that hill-top appears, from the seaside rising ahraptly, Though from my sight its base by nearer ranges be hidden. Lovely the scenery is, and to me was in boyhood familiar. And with a dweller there, from early youth I'm acquainted : Known o'er the world his name, with our Irish science associate. Yet by his friends beloved, e'en more than admired by the stranger. Worthy his wife to be his, but of her let these verses say only, Her's is the name of your wife, and that of the Daughter of Wordsworth. Yes, I will visit them, and enjoy the scenery near them.

' Easily was I persuaded, when this my resolve was accomplished, And when at evening hour I stood in the friendly mansion. There to remain for the night, and explore on the morrow the Dargle. He, then, and I set forth, on that our pleasant excursion. Leading a child by the hand, for whom at the font we had answered, To us his brother came up, who was one of my old College cronies.* Stoutly we battled it out, our collegiate arena when entering ; Till we from rivals grew friends, and such have we ever continued.

' So we together went on, and remembered beauty received us ; Which, when an ardent boy, I had sought to describe in my verses : Bat had despaired, and now, muoh more, must despair to describe it. Yet, though the air was warm, I longed for a perfecter sunlight, Some old effects, which i missed, to bring out on the canvas of natoie* Kor was the wish confessed by me, at last disappointed : Burst forth the sun in heaven ; wood and water glittered in sunshine*

' Leaving the lovely glen, the prospect expanded around us ; But it was lovely stiU, and only succession of beauty. 2^ot in my friendly guide had the sense of such pleasures been blunted, Kor our home charms despised, from his knowledge of men and of cities. Venice he coold describe, and its first effect on a stranger ; Switzerland had he searched, and many a mountain ascended : Yet he enjoyed, like me, the view that was open before us. As on green slope we lay, we touched upon manifold topics ; Some that referred in part to new speculations of science, None pursuing so far, as to trouble our tranquil enjoyment : — Talked of the planet-spheres, and are they peopled by beings, lifted, like ns, with mind, and, ah ! like us, loving, but sinful P — And, while the sheep on the hill, at our feet, were quietly grazing, Spoke of the Book Diviins, so rich in pastoral image, Lambs, and the heavy with young, and the tender care of the Shrphbkd.

* Bartholomew Lloyd^ Q. C.

lo Life of Sir William Rowan Hamilton . [1864.

* Then we desoended to oroes to the other side of the valley. Boat was there none, us to ferry the murmuring rivulet over : Deftly we picked our steps, on the small rooks, moistened and slippery. And I remembered the Wharf, near Bolton Priory gliding ; Broadly and stilly it flowed, by a long line of stones intersected ; Pleasant passage which gave to me last autumn at sunset, Wishing, from hill that crowned the further bank of the river. On the gray Abbey to gaze, and to muse on the White Doe of Ryktone ; Kre in my wanderings I reached that Btrid, so fatal and famous, Where the pent water boils, and the Boy of Egremond perished. — Parting at length from my friends, I set out on my homeward journey : Here in the twilight arrived, and found your episUe awaiting.

^ Thus have I, mingling thoughts of old times with recent adventures. Simple however they were, and involving nothing of wonder, Told you, in verses rude, and metre to me unfamiliar. Story of those two days, which have passed since we last met together.

'AuguH 26M, 1864.'

The British Association met this year ia Liverpool, in the month of September, and Hamilton attended it, principally with a view of securing that it should make its second visit to Dublin in the year 1857. This he succeeded in arranging. I find, cut out from the Morning Post of September 30, the following report of a speech made by him when proposing a vote of thanks to the foreigners who had attended the meeting. Its allusions to the Abb^ Moigno and Monsieur Foucault give it a personal interest, and the references to poetry, and the poetic treatment of hi» subject, are characteristic of the speaker.

*My Lord Harrowby, and Ladies and Gentlemen, —

* I have been requested to move, that the thanks of this Associa* tion be given to our distinguished foreign visitors. In the first place, allow me to thank you for having thought that I mighty without impropriety, be put forward on such an occasion, and for having shown thereby that you do not consider me as a foreigner. Since I was invited to make this motion, I have had no time even to read the list of our foreign visitors, and must request thenik and you to acquit me of the presumption of pretending to analyse that list, or of doing anything more than state my own personal views. Of the members from America who may be present I shall

AKAT. 49.] Speech at Liverpool. 1 1

say nothing, for in England and Ireland, and I suppose espeoiallj in this great port of Liverpool, we scaroely oount Amerioans as- foraignerB. From the soientific and philosophical writings of the Gennans, I hope that I have learned much in my maturer years ; but when I was a boy the French were my masters and teachers in scienoe. In Ireland, at that time, the higher branches of ana- lysis went commonly by the name of French mathematics; and, in order to study the works of the great writers in that department, I was obliged to learn their language. Having never yet enjoyed the advantage of a visit to Paris, though I have had the honour of being, for the last ten years, a Corresponding Member of the Insti- tute of France, the scientific names of that country have appeared to me pretty much as abstract ideas; but I think that when you look upon the eminent Frenchman at my left hand you will agree with me in considering that he is no mere abstract idea, but a very concrete, and a very pleasant body. (This allusion to the fat little Abb6 Moigno produced great laughter at the moment.) Perhaps you may have thought, any of you who may have- happened to observe me turning over the pages of a book upon this platform, within the last half-hour, that I have been inatten- tive, negligent, and almost rude, as regarded the proceedings of this meeting. But when I tell you that it is a work put recently into my hands, by my present neighbour, the Abb^ Moigno, whom I had known to be an abstract mathematician, but who now turns, oat to be a distinguished physicist also ; and when I add that in this work ("E^pertoire d'Optique"), I find expressed the most candid, intelligent, and, I must say, generous appreciation of what has been done by persons in these countries, you will forgive me- that seeming neglect. As an old member of this Association, it has gratified me to see noticed in this Optical work of a Frenchman an account of experiments in Optics, which first acquired some pub- licity during the first Cambridge meeting of this Association, in the year 1833. And if, with the name of my dear Irish friend '^Monsieur Lloyd,*' the name of •* Monsieur Hamilton" be coupled, I can scarcely be expected to feel less grateful on that acoount. I can remember the time when England was at war with France. I waa a child then, but children quickly learn, through sympathy, the feelings of their seniors. And I remember that France was then, I do not say feared, but respected, as a formidable and gallant

12 Life of Sir William Rowan Hamilton. [1854.

enemy. The Frenoh were then our generous and noble foes; they •are now our generous and noble friends. I trust — ^indeed I feel assured — that in making suoh allusions as these to events which now agitate the world, I do not pass beyond the limits within which the rules of the Association confine its members. The names of Whig and Tory are never heard within our halls ; those party differences which are, perhaps, essential to the working of a free State, find yet no echo here. Some may, perhaps, expect that we should carry out this principle yet further, and that we should realise in our own persons the conception of the Boman lyrist : —

" Si fractus illabatur orbis, Impavidum ferient roinsd."

And our great country ha% stood firm, while thrones were shaken, and nations were reeling around it. But individuals may be ex- oused if they exhibit a less absolute and philosophic calm, and if they suffer to be perceived an ardent, and even an anxious interest, in the fortunes of the land to which they belong, especially in this Society, which, if it be an association for the advancement of -science, is yet essentially a British Association. Permit me, for a moment, to make one other allusion to war, and to name another Frenchman. When Professor William Thomson, of Glasgow, was lately speaking in our Mathematical Section of potential and ■actual energy, and drawing one of Iiis many and happy illustrations from the gunpowder and the cannon ball, I was reminded of some lines of Coleridge's translation of Schiller's play of '' Wallenstein.*' In that great play, and in that beautiful translation, the elder Piocolomini (Octavio) is represented, if my memory serves me aright, as warning against the hazards of civil convulsion that son of his. Max Piccolomini, on whose character the author of the poem appears to have lavished all his love, and to have bathed it with floods of lustre. The father, I think, is represented by iSchiller as saying to the son, respecting the ball when it has left the cannon —

** It is no longer a dead instrument ; It lives, a spirit passes into it."

And I must say that when we in general, and more particularly when a small party of us, of whom I was one, were permitted lately by M. Foucault to attend the exhibitions of his more reoent

AiTAT. 49.] Visit to Westmorland. i j

experiments, the same lines of English translation of German poetry again ooouired to mj remembrance. When I saw the little dJBo of Professor Fouoault possessed with what he was pleased to call "«» esprit de contradiction^^* disobedient, apparently, to ita human former but yet essentially and throughout submissive to the laws whioh the great Creator of all things has been pleased to impress upon matter, I admired anew the activity of the French intellect ; but I looked up with even greater reverence than before to the Supreme GKver of all intellectual and of all higher treasures/

From Liverpool, with his son Archibald as his companion, he proceeded to the Lake Country on a visit to myself and Mrs. Qraves, then residing at Dovenest on Windermere. During this visit he had the satisfaction of being several times received affec- tionately at Bydal Mount by the widow of Wordsworth; he enjoyed at Lancrigg the hospitality of Mrs. Fletcher and her daughter, Lady Bichardson ; and he renewed a long discontinued intercourse with his old friends Mr. and Mrs. Bichard Napier,* then sojourning near Bydal.

A letter, written in a somewhat playful spirit, to his old friend Lady Campbell, discovers in Hamilton the elements which were deeply seated in him of a reverent admiration for woman showing itself in the form of a grave, old-fashioned, gallantry. I have in a former volumef put on record how eminently fitted was Lady Campbell to call forth these feelings. Not a less noble example of womanhood was Mrs. Fletcher of Lancrigg, the principal theme of this letter to Lady Campbell. No one who had ever met her could fail to carry away the impression that he had met in her a woman almost unique for the combination of majestic form and features with a spirit and an intellect in perfect correspondence. Enthusi- astio and yet dignified, strong in will and judgment, warm and compassionate in feeling, she was the ideal of womanly grandeur — a queen of nature's making — receiving, not claiming, universal homage. But I need not to set out in detail her eminent qualities

* SuprOf Tol. i., p. 165. f SvprOy vol. i., p. 359.

14 Life of Sir William Rowan Hamilton. [1864.

•or the influenoe she exerted oyer her Mends. That has been done by the publioationy sinoe her death, of one of the most delightful of autobiographies, enriched by the reminisoenoes of Lady Richard- i9on, its editor, and of her sister Mrs. Davy, daughters worthy of their mother. The act of homage to his venerable hostess which Hamilton records had therefore, it may be seen, the warrant of « special fitness.

JPVom Sir W. B. Hamilton to Ladt Campbell.

< House of the Rkt. Robert Ghayes,

* doyensst, near windbrmerb,

< Friday mgU^ October 6, 1854.

^ Will you believe that I sat next a gentleman here, at dinner yesterday, who asked me if I had lately seen ^'Pamela Campbell''? a name by which you know that I never presumed to call you. You will think that the man must have been very impertinent : but will, I suppose, forgive him and me, when I tell you that lie was Mr. Eichard Napier, brother to the conqueror of Scinde, who is, I believe, a cousin of yours, and who is pleased to claim an acquaintance with me of thirty years' standing. Again, at dinner to-day, but at another house, your name was mentioned by a lady — and a very old and very charming one — who told me that she remembered Sir Guy Campbell since he was " that height " (about the height of the table), and that she knew he had married a •daughter of Lord Edward Fitzgerald. I said that another Quy, son of her friend, had died last year in India, and that his mother had scarcely yet recovered from the grief occasioned by the loss. She inquired whether you had any other children, and I mentioned Sir Edward and your daughters. She wanted then to know whether they had inherited the beauty of their parents. I said that I had always heard that the married daughters, of whom alone I should presume to speak, had been quite ^' the rage," for their beauty, &c., at the Irish Court, and elsewhere. It is time that I should tell you at least the name of the lady who thus catechised me. She is Mrs. Fletcher of Lancrigg, and she is in her 85th year. She took my arm, when we were going in to dinner, and her con- versation was really delightful. She remembers well and vividly many of the remarkable characters of the latter part of the last

KTAT. 49.] Mrs. Fletcher^ William Pearson. 15

centoiy — especdally those oonneotod with Sootlandi and, still more preoiflely, with Edinburgh, where she at that time resided — for example, Dugald Stewart. She has been well acquainted with Wordsworth during a long subsequent residence in this neigh- bourhood; and she, and her daughters (one of whom is lady Biohardson, wife of the Arctic traveller), have also deeply appre- ciated him. (I have visited alone, by moonlight, the graves in Qrasmere churchyard, of Wordsworth and his daughter Dora, and others of his family whom I remember. I have also visited his widow, who received me several times affectionately at Bydal Mount). And yet she (Mrs. Fletcher) is quite open to fresh im- jiressions — for instance, to the merits of Matthew Arnold's poetry. By-the-way, Mr. Arnold and his wife were members of our dinner- party. To sum up all, she (Mrs. Fletcher) has almost the finest eyes in the world, and when retiring in the evening, I asked leave to kiss her hand — an action which I found was considered to be quite comme il/autj and in which my son Archy followed me.

*I vnrite in the bedroom which once was occupied by Mrs. Hemans, and the view from which is lovely. It is nearly time for me to go to bed, especially as I have walked several miles to- day. Good night, dear Lady Campbell, and believe me to remain jour affectionate friend.'

He also met at Doveneet a remarkable man, William Pearson of Borderside, Crosthwaite, and his estimable wife, born Ghreenhow. William Pearson was a self-cultured yeoman, who at this time, after many years spent in a Bank at Manchester, had retired to a small patrimonial estate on the southern border of Westmoreland. Here a stranger might have been surprised to find him surrounded by a choice collection of books representing fully the English poets of all ages, and (in translation) the best G-erman authors, poetic and metaphysical, besides the classical prose works of his country and the best authorities in Natural History. Of the habits of birds and other native creatures around him he was a watchful observer, and he described them in purest English, with a charm that suggested no disadvantageous comparison with White of Selbome. Soon after his marriage, which occurred late in life, he spent a year in Switzerland, and Wordsworth, who had long

1 6 Life of Sir William Rowan Hamilton. [1854.

known and esteemed him, told me that the brief records made bjr him of noteworthy incidents of travel or natural phenomena were models of what a tourist, eschewing the commonplace and the super- fluous, should indite. Wordsworth's poems he particularly loyed for their truth in the expression of the contemplative mind occu- pied with outward nature and its own higher aspirations; he knew most of them by heart, and his spontaneous recitation of them was scarcely inferior in feeling and truthfulness to that of the poet himself.

I should say more of him and of Mrs. Pearson, had not the latter, T)y a biography,* printed for the enjoyment of his friends, preserved from oblivion the character and some of the writings of her husband. I remember that at Dovenest the Yarrow poems of Wordsworth, illustrated by all the ballads which prompted them, afforded delightful subject of discussion to him and Hamilton, and to others taking in it a subordinate share, and that from poetry the keen intellect of the rural philosopher passed on to metaphysics, and urged the scientific sage, not without some reward and satisfaction, for explanations and judgments. The question, then much canvassed, of the plurality of inhabited worlds excited between them a lively difference of opinion; Hamilton, though refraining from a negative conclusion, agree* ing with Whewell in considering that science afforded no analogy in favour of the idea.

Hamilton and his boy accompanied Mr. and Mrs. Bichard Napier across Dimmail Baise to Xesvrick, and proceeded by Whitehaven to Belfast and Carlingford, where he was again the guest of Mr. and Mrs. Disney. In the middle of October he was at home in his Observatory, where the only exciting event of the closing year was a visit from the deaf and dumb boys of Clare- mont Institution, to whom Hamilton and his assistant showed the telescopes and some of the heavenly bodies, receiving afterwards

* PaperBy LetterSf and Journals of WUUam Pearson : London : Eroiljr Faithful, 1863.

AKiAT. 49.] Lady Campbell. 17

in return what he calls * a most delightful and oharaoteristio letter of thanks.' In simple terms it expressed admiration of the proofa of God's Almighty power, and gratitude for the bread, jam, coffee^ and milk supplied to them by Lady Hamilton. De Morgan com- mented in his witty way upon this letter, writing about it, if I remember rightly — * These D.D.s are like other D.D.s in wisely linking together the good things of heaven and earth.'

Headers who remember the terms of friendship which in early years subsisted between Hamilton and Lady Campbell «will have noted with pleasure that he continued to correspond with her, and will be glad to learn that he still enjoyed the advantage of being able to confide to her his inward trials, and to speak to her freely of his spiritual state, receiving in return kindly sympathy and wise counsel. As a true friend, she had not failed earnestly to plead with him his own cause, when she heard of the danger that threatened him of being dominated by a fatal habit ; and now, at the beginning of this year, congratulating him on the publication of his Lectures^ she had written — ' I hear the Quaternions is a wonderful book, and sheds a light on Ireland. You know how I love to be proud of you, so I need not tell you how I rejoiced to hear this.' In Hamilton's letters of this period to his old friend, the portions which are most interesting are such as it would not be right to give to the public, and those of slighter texture would not well stand alone. I must content myself with producing notes referring to small books published by Lady Campbell, which were marked by a beautiful delicacy of touch in description and by justness of feeling, and with extracting one passage from a later letter which incidentally presents a combined retrospect of the external and spiritual life of the writer.

< Obseryatobt, May 17, 1864.

'So while you were seeking to draw me out, on May-day last, to talk too much about what you were pleased to call my '^ wonderful" book, you did not give me the least hint that there was a chanco

VOL. 111. c

1 8 Life of Sir William Rowan Hamilton. [1864.

of my 80 BOOH seeing your "charming" one . . . Now I won't begin to praise you even as an author, and can't say that I find that anyone here is disposed to wotider at your producing a de- lightful book. But I may mention or confess that, living so much out of the world as I do, it was not till yesterday that I heard of the publication of your Cahin by the Wayside, and forthwith pounced upon it at M'Qlashan's . . .

But your book fairly carried the day, or the evening, as I was walking back along the Canal yesterday, after having walked to Dublin some hours earlier by the same path. A couple of mile- stones gave me very pleasant opportunities for sitting down to read more comfortably, and when I got home I was so selfish as to finish the book quite alone. But this morning I showed it to Lady Hamilton. ... At all events she never stopped till she had read aloud the whole to my little daughter, and to a son, who pre- tended to be reading Homer. I have put my daughter's name in the copy.*

* May ISth. — Unquestionably I shall accept with pleasure, not to say with pride, the copy which you promised me of Tfie Story of an Apple; and what's more, that I may have the pleasure of reading it first, as a gift from you, I shall abstain from ordering the book. My son Archy has confessed that he was listening while his mother was reading your book aloud.'

* June 15th. — It was Jellett's turn, as one of the Examiners for Bishop Law's Mathematical Premiums, to give the annual dinner. I sat between him and Mr. Walsh, a clever barrister,* and remarked to the latter that this was the 28th time of my assisting at an Examination Dinner of this particular kind. " What a frightful restrospect I " exclaimed he. " Do you mean the dinners? " I asked him. " No," said he, " but the years." I let the conversation on that subject drop; but cannot altogether regret that I have lived so long, though I have had impatient fits. Or rather, in my serious moods, I feel it to be a subject of deep thankfulness that so much time has been allowed for schooling — a process which as yet has been very imperfectly performed in my own case • . • if I find and transcribe them [some notes written at

* Afterwards Maater of the Bolla.

ASTAT. 49.] Retrospect. 1 9

the oommenoement of the preoedmg year], you will see that, when ihoaghtfolly oonsideriiig the question, I have heretofore reoog- nised, as I still do reoognise, a kindness in life being spared. . . .

P. S. — I have played a few games of draughts this morning with my daughter— dear, sweet, patient child. She has very few source of amusement, but she enjoys flowers, the garden, and the Bible.'

C2

20 Life of Sir William Rowan Hamilton. [1855.

OHAPTEE XL.

OORRBSPONDBNCB WITH AUBRBT DE VERB : WITH THE MICH0L8 T

cipher: MRS. WILDE.

(l865.)

The year 1855 was not remarkable in Hamilton's histoiy, either for soientifio work or for events of importance ; yet there remaina of it extensive record in the form of correspondence. A summary of the f actSy followed by some extracts from the correspondenoe,. may here suffice.

The correspondence between Hamilton and Aubrey DeVere- springs again into activity. It had been interrupted by an illness of the latter from scarlatina which precluded for a time intercourse of any kind. In its oourse — it went on continuously into the succeed- ing year — Mr. De Vere wrote some most interesting letters, giving an account of his gradual change in religious opinion, until his final submission to the Boman Catholic Church. Hamilton declines to discuss the great question controversially, but gives his friend clearly to understand that his own opinions, instead of moving in the same direction, had become more Protestant. Had Hamilton's letters met those of his friend by argument, I should have thought it a duty to print both sides of the correspondence in full ; but besides the limits of space which I am obliged to observe, I have to consider that these letters of Mr. De Vere belong more properly to the history of his own life. It is to be desired, I think, that they may see the light, for undoubtedly they deserve meditation and discussion, as worthily expressing the views which proved decisive with a singularly pure and thoughtful mind. I say this, though myself farther removed, perhaps, from his stand-point than was

jiBiAT. 60.] Aubrey De Vere. The Nichols. 2 1

Hamiltoiiy of whom it is only fair to add that, writing sabsequentlj to another friend, he oalls Aubrey De Yere a ' splendid type of Bomanism.' It is true also that, although the two friends diverged widely as to the Churoh question, they continued to the end to be in harmony in respect to their views of religious philosophy; Hamilton, as well as De Yere, maintaining that, from the constitu- tion of the human mind, Faith had in Religion a function at least oo-ordinate with that of Knowledge.

The meeting of the British Association attracted Hamilton, in the September of this year, to Glasgow, and there, at the ObsOT- vatory of the University, he became the guest of his friend Dr. JTohn Pringle Nichol; and an intimacy thus arose between him And the family of the accomplished astronomer, which continued to be highly prized on both sides. Dr. Nicholas son, now Pro- fessor of English Literature in his father's University, was then a member of Balliol College, Oxford, and already manifested that taste for modem literature, of which he has since given to the public proofs which mark him out as not only a vigorous critic, but a man of poetic power. The confidence which his father had won from Hamilton was now, with full expansion of feeling, imparted to the son ; and the daughter and sister of these men, Agnes Nichol (afterwards to become wife of Dr. Jack, Professor of Mathematics), herself imbued in literature, and exercising in it her inventive faculty, was admitted a member of the band of friends. The correspondence which resulted was frequent and •animated ; but as on Hamilton's side it was mostly occupied with the incidents of the past, a region which the reader has already traversed, I refrain from quoting it, except in brief extract.* One

* It was about this time that John Niohol, Jan., addressed to Hamilton two sozmets, which tended to cement the friendship between them. These sonnets dwelt npon the combination in Hamilton of simplioily and affection with high scientific qualities ; but some imperfections of expression rendered their author dissatisfied with them, and he afterwards condensed their meaning into a single sonnet, which has appeared in the collection of poems recently pnbluhed by him. A similar tribute to the memory of his father may be found in the same volume, and in this connexion will interest the reader.

22 Life of Sir William Rowan Hamilton. [1865.

sabjeet of Ebunflton'B letters to Dr. Niohol and his son was a cipher of his own inyention. Some of the extracts which follow will inform the reader of the great merits of this cipher, the almost unlimited power of variation which it admits of, and the practical impossibility of discovering its key. Hamilton was wont to say that he believed a challenge to the whole world to discover it would not meet a reply.

The communication which Hamilton made to the Mathemati* cal Section of the British Association at Glasgow was a Paper On the Coneq>tum of the Anharmonic Quaternion and on its AppHcaUon- to a Theory of Involution in Space* During the week of the meet- ing he joined an excursion-party to the Isle of Arran, and with a select number of its members was received by the Duke of Hamil- ton at a dijeuner at Brodick Castle, Sir Roderick Murohison introducing him personally, and bespeaking for him the place of honour among the guests. This visit was one of great enjoy- ment to Hamilton. The conversation which passed led to a short but cordial correspondence. Hamilton had mentioned, perhapa quoted, to his host Aubrey De Yere's poem to the memory of the Highland Mary of Bums, and the Duke had the tact to recognise in Hamilton a namesake as well as a savant. Accordingly Hamil- ton afterwards forwarded to him a copy of Mr. De Yere's poem, adding (let it be confessed) his own Dargle Verses^ and made good his title to his name by using and calling attention to the impression on the envelope of his father's seal, which bore the Hamilton crest and motto ; and in reference to his own brandi of the family, in a subsequent letter to the Duke, he took occasion to write : — ' Sir W. B. H. has, with the exception of his two sona William and Archibald, only one living male relative of his own name with any traceable degree of connexion : namely, his cousin the Bev. James Hamilton, who has the living of Loughcrew in If eath, and who (according to family tradition) \a the heir to- a dormant baronetcy.'

On the day he left the Observatory of Glasgow Hamilton com- posed a sonnet prompted by a photograph of his daughter, which

AKAT. «o.] His Daughter. 2 j

he had leoeived as a gift from her on the eye of his departure from home. ThiB sweet and interesting ohild had wound all her tendrils round her father's heart In one of his letters I find him wilting : — ^''I think Lady Hamilton would forgive me for saying that the being I now lore most in the world is my little daughter; ** and elsewhere he declares that he is in the habit of judging the happiness of other men by oonsidering whether they have or have not a daughter. It may be added, that even at this time — she was now only fifteen— she had evinoed much love for poetry, with which she had largely stored her memory, and that having been brought through more than one serious ilbiess, she had been very recently a sufferer from an accidental bum of considerable severity.

' SONNET TO MY DAUGHTER.

' Dear patient child ! upon a "bed of pain Bo lately lying, watched by tender eyes, Thy son-limned fiice and form I dearly prize, Thy gift at parting ; and can see again Thy head bowed meekly o'er some poet-strain. In book out-spread, or some diviner page, Such as would oft thy maiden thoughts engage Ere yet I left thee for the ocean-plain. Not all the wealth of mind, not social joy, When Scottish Science met in converse free With men of other lauds, and welcomed me, Away from thee could all my heart employ. In starry tower, or on the sunny water, I blessed my loving and beloved daughter.

« Obsertatobt, Glasgow, September 24, 185d.'

Late in the autumn of this year a visit wasjpaid to his own Observatory, which stirred into activity remembrances which had not ceased to be cherished by Hamilton, and*enabled him to show the interest of a friend in persons whom he hadjnot before seen. One day in October, Mr. Bobert O'Brien arrived at Dunsink with his two young daughters and their two brothers. Mrs. O'Brien, formerly Ellen DeYere, had desired that her husband and children should be known to Hamilton and his wife, and

24 Lifi of Sir William Rowan Hamilton. [1856.

advantage was taken of their being for a short time in Dublin to make an arrangement for the purpose. Friendly feeling was manifested on all sides, and Hamilton took special delight in showing to the daughters an experiment which he remembered having in the same meridian room shown to the mother, and never in the long interval to anyone else — ^that of a key floating on meroury — and he was prompted, when the visit was over, to oom- pose a sonnet addressed to the two young girls, which in affeo- tionate terms expressed the pleased and tender feelings with whioh he had welcomed them to his house, and joined them to the com- pany of friends, living and dead, whom he Hked to associate with the thoughts of his garden : —

< Mary and Alice I though hefore that day Unmet, when, through this garden wandering, Lately ye trod where Wordsworth once deigned sing Some grand old strain for me, or newer lay Murmured, half musing, or in boyhood's May With Brinkley spent I sweet but solemn hours, Listening his lovely lore of stars or flowers, The thought of you not soon shall pass away ! Your images shall rise before me here, With thoughts of other friends of long ago : Time takes not all things in his ceaseless flow, Fixes and hallows some : and many a year. Since dear ones linked with you I flrst did know, Gives me a poet's right to oidl you dear.

' Obsebvatoby, yovemher 5th, 1855/

In the spring of the year Hamilton met, for the first time, Mrs. Wilde, afterwards Lady Wilde, the wife of Sir William R. Wilde, the eminent physician and Irish archsdologist, herself remarkable as a woman of warm feelings and literarj faculty, shown in patriotic and eloquent contributions to newspapers and other less ephemeral periodicals, and in poems published under the name of SperanzOj and, it may be truly added, as a woman of high sispirations and real genius. The acquaintance rapidly ripened into friendship, and a correspondence ensued in which Hamilton some- times acted as critic of a poem by Speransuiy at other times confided

AEXAX. 60.] Lady Wilde. Hipparchus. 25

to her the stoiy of bis life. The same reasons which have led me to refrain from presenting in print Hamilton's oorrespondenoe with the Niohol family dictate a similar course in this instance. Bat it would be wrong to leave unrecorded the fact that Hamilton was not only interested in the mind of this gifted countrywoman, but esteemed highly her whole nature, in which he recognised many features of native nobility.

It was at the end of 1855 that Hamilton was led by his stndy

of the Almagest of Ptolemy to engage in computations connected

with the Problem of HipparehuSy which set forth the remarkable

acooracy of the observations and deductions of Hipparchus; a

degree of accuracy declined from, rather than improved upon, by

his admirer and commentator of 300 years later date, Claudius

Ptolemy. A specimen of this exercise of Hamilton's powers in

exhibition of the work of these Fathers of Astronomical Science

may be found in Hermathena for 1883. By his study of this

astronomical problem Hamilton was led on to investigate, in an

extended treatise, a geodetical problem, having much affinity,

which had been proposed and solved by the celebrated Snellius in

1617. This treatise remains unpublished. Among Hamilton's

scientific correspondents during this year were, besides De Morgan,

Uoyd, Boole, Cayley, Carmichael, Bomney Bobinson. I find

four pages (61-64), but no more, of a letter to Mr. Townsend,

F.T.C.D., on Co-planar (or Homosphseric) Involution.

An extract from a letter to Mrs. Wilde, with which I intro- duce the non-scientific correspondence of this year, has much bio- graphical and ethical value, as showing that though Hamilton loved praise he also feared it, and that his was a mind which, with regard to politics, was no holder of stereotyped opinions, but capable of growth, and of comprehensive sympathy. After somo remarks (prompted by a letter from his enthusiastic correspondent) on the dangers of the reciprocal admiration of friends — its liability to degenerate into reciprocal flattery — ^Hamilton observes : —

26 Life of Sir William Rowan Hamilton, [i8o5^

From Sir W. E. Hamilton to Mrs. Wilde.

< Obskrtatost, Jwm 30.

^ ... At all events you are no chaplain of mine, but onlj a fair compatriot J whose Irish feelings prompt you to take the most fayourable view in your power of one who is essentially an Irish- man by birth, and life, and labour, though educated by a clergy* man who held the aaoendancy principles (from which, by very slow degrees, I have been through life gradually emancipating^ myself), and who would have regarded repeal as rebellion. It wa& English history, not Irish which I was taught ; and my heart still throbs with sympathy for that great British Empire to which, from childhood, I have been accustomed to consider myself aa belonging as to my country — though Ireland, as Ireland, haa always been the object of my love — and, I think you will admit, of my exertions. G-od forbid, then, that I should even smile, and I pray you also not to think it, at any grief, or sadness, or depres- sion which any feeling of patriotism may have caused you. Edu- cation has much to do with the direction of such a feeling, but I know what it is, without hope or fear of any private gain or loss, to« sympathise with a nation. I was almost literally sick with sorrow at hearing of the disasters in Cabool and the Khyber Pass several years ago.'

Passages from a letter written in the spring of 1885, to his old and kind friend, Lady Dunraven, will, by the mention of the sister of Aubrey De Yere, lead on the reader to the letters whioh passed in this year between him and Hamilton.

From Sir W. R. Hamilton to the Countess Dowager of

Dunraven.

[from a copy.]

*• Obsebtatort, May 19, 1865.

^ How often have I poured out to you in years now long past the secrets of my heart, and how kindly you suffered me to do so^ and responded to, and comforted me !

AKTAT. 49.] Letter to Lady Dunraven. 27

" Lady, who with a mother'i tendemew, And fond indulgent patience, nursinglj Cherished that hope in its frail infancy. • • ."*

* Ton see that I quote from memory [allnding to a yerbal oor- reotion made in his writiiig of the quotation], though I don't forget your most kindly returning me some years ago the original, such as it was, of those that were at least heartfelt lines.

'A Yery unexpected and yet very natural oircumstanoe, or train of oiroumstances, has brought back Ellen De Yere, and of course you, dear Lady Dunraven, with imusual freshness beforo my mind and heart, within the last few days, although you and she had never been forgotten.

* My dear sister Eliza, the poetess, whom I am ashamed to oonf ess that I forget whether you ever saw, but with whom Lady Anna Maria exchanged some friendly notes, died in my arms in May, 1851, having every comfort, spiritual and temporal, which it was possible to procure for her, and with that last poetic satis- faction of the evening sun shining beautifully and gloriously^ as well as comfortingly, in for the few minutes which were her last. We read of the Sun of Eighteousness, and the early Chris- tians accepted the title of Suni&j from the heathens as associated with Him who, on that day, rose from the dead, and triumphed for Himself and for us.

'My sister Eliza left me the most entire control over her papers, which were many, with power to preserve or destroy. To some extent — indeed to a large one — I have used the latter power, by putting into the flames, after reading them, a great number of the sheets of a journal which, I am convinced, would have brought me in some hundreds of pounds if I could have borne to publish it, but which was written for herself ahne^ though in her dying^ hours she gave me permission to read it, and which described too freely, as I judged, though without any particle of malice, our many visitors of long ago to this Observatory.

' But among the numerous papers which thus came into my hands, it is only very recently, after the expiration of four year^ of mourning for my sister, that I have taken courage to open what she considered her pet box of letters^ and had confided unreservedly

• YoL i., p. 610.

28 Life of Sir William Rowan Hamilton. [1866.

to me. If I tell you that I found in that box a large number of letters of m j own, you will make allowanoe for the affection which we felt towards each other, and which was more like that of twins than of a brother and sister whose ages differed by more than a year, but who *' in early childhood, almost infancy, had wandered forth together fancy- fraught."* We loved each other to the last, and I had the satisfaction of being . . • useful to her. Indeed I have burned a great number of letters of hers to me, because I did not like to preserve records of the gratitude of one who de- served a//, and more than all, which it was in my power to do.

' But among the papers of my sister I have f oimd many letters which had not been written by myself ; and among those I must •confess that I have found, and even read, though I have not yet had courage to read through all of them, several letters from Ellen De Yere, and from Mrs. Kobert O'Brien. At this great distance of time it did not seem to me an unpardonable sin, nor even any want of delicacy, to do so ; and I was comforted on that score by finding in one of the most beautiful, but also most secret, letters of the set the remark : '^ I should be glad that no person out of your family should know of this letter." My sister, no doubt, feared to agitate me by showing me at the time that very charming letter ; but surely I may accept, as an anticipatory forgiveness lot reading it, the sentence which I have quoted.

' We are told from the pulpit, and cannot, perhaps, be told too often, of the faults and corruptions of our nature. Most fully, most heartily, do I grant all that from the experience of myself. But I must say that my opinion of the good part of human nature, and especially of the nature of young ladies, has been very •decidedly exalted by the perusal of my sister's correspondence, not •quite completed yet. How much it struck, how much it affected me, to compare the ardent yet discriminative enthusiasm with which Ellen De Yere and Dora Wordsworth (whose grave I kissed by moonlight at Orasmere last autumn) wrote to my sister sepa- rately of their first meeting ! '

• Vol. i., p. 495.

AETAi. 49.] Aubrey De Vere on Old Times. 2^

From Ax7BBET Db Ybbb to Sir W. B. Hamilton.

' KiLLABifBT, J%Uy 25, 1855.

' . . . I cannot say how muoh I am obliged to yon for them [letters of Sir W. B. Hamilton forwarded from the Seven GhurchesJ. They are conyinoing proofs that you have not for- gotten old times. To me old times seem rather to approach one nearer, as one advances in life, than to recede into the distance. To Time may be said, in its degree, what Wordsworth says to a mightier Power —

<> Tbon takest not awaj, 0 Death."

The present it is, not the past, that looks like a vision, except so far as duty and sorrow convert it into a reality.

' The extracts which you sent me [from old letters of E. De* Yere about Gurragh] have for me a deep and touching interest, partly of a different kind from that which they have for you. At first I hardly understood what they referred to, or by whom they were written. Gradually the mist cleared away, and scenes which belonged to my boyhood, but which were the most touching I have ever known, came back to me with the strange pathos of the past. The very features of the beautiful face, referred to in the letter to your sister, seemed to look forth again from the long darkness — not, however, in the radiance of youthful life, but in the yet more beautiful stillness of death — flower-crowned, and with a sweetness that seemed cast down from the region of Immortality.*

* I should wish to hear something more of your sister Eliza. She died, you tell me, in your arms, and four years ago. Had she been long ill P I trust that her death was one of peace and joy, for I believe that there is sometimes a joy as well as peace in death that life knows not of. This, however, is granted or not granted, as G-od sees good for each several person, and no infe- rence is to be drawn from its absence. I shall be very grateful for a copy of your sister's poetry. There are poems of hers which can hardly be forgotten. Those which you tell me my sister singled out for special approbation were, I think, my favourites also, but the Columbus I liked the best of all. Some of the lines of it

* This passage refers to a sister of the writer of the letter, who died at the age of fourteen.

30 Life of Sir William Rowan Hamilton. [1855.

recurred frequently to my memoiy during that long and trying period of change (progress I should rather call it) in my religions convictions, which ended in a change of my religious position — a period in which one seemed to navigate a trackless deep, over which Faith alone could be one's guide (though many a '^ floating wreath impearled" gave good omen), till were heard the voices —

*< Deep-marmnring < land' in musio proud." *

* She must have left many poems unpublished. I have directed my last volume to be sent to you at the address you name. I should have wished to dedicate the volume to you, as some of the poems in it were included in the volume originally so dedicated. It would not have been suitable to do so, however, as several of the poems at the end of the volume express opinions with which I •could hardly expect you to be in sympathy. The present arrange- ment of the poems is, however, but temporary, and those that originally belonged to you will, I trust, find their way back to you ere long in a new edition. . . .

* To return, however, from Poetry to Life .... I am very glad that you made a pilgrimage to see Mrs. Wordsworth last year. She is the most venerable woman in England. I visited her also since her widowhood. She always spoke in the most cordial terms of you, as did the great Bard. He used to say yoa were the only man who had ever reminded him of Coleridge. You were sorry, I am sure, for poor Hartley Coleridge. TTir sister, Sara Coleridge, who died some years ago, was one of my most intimate friends. She inherited no small part of her father's genius. Do you ever read his works now P Wordsworth seems to me to have much more accomplished his mission. . . . It has been a real gratification to me to find that your thoughts have been reverting so much of late to that Past in which my own find so conmionly their home. The modem world, ever rushing into the future, is, I suppose, against all reminiscences on account of their " inutility : " but surely this is but in accordance with its usual materialism. "A painless memory of pain" will probably be part of the inheritance of the Blessed hereafter ; and we are surely the better for anticipating here what, we hope, awaits us in

• Columbus f by E. M. H., see vol. ii., p. 698.

ABTAT. 50.] Hamilton and Aubrey De Vere. 3 1

a happier sphere. All your Tecolleotioos of mj sister give me the same sort of satisfaotion which thej would give to her also, as pre- serving old kindness^ without the alloy of old suffering — ^thongli suffering is less to be called the alloy than the fire which clears the metal from the alloy. It seems to bring her back to me as she was when a girl :

'* There's something oomes to us in life. But more is taken quite away."

^ It is as a girl that I chiefly like to think of her — when Poetry and Thought seemed to give her wings. She has been happy as a wife and mother ; though life has brought its cares to her as to aU who root themselves in it ; yet I do not doubt that she would have been not less happy had she continued to float over the sur- face of life, barely touching it, as of old. Be assured that the feelings she expressed in her letter to your sister in 1838 are those she feels now. . . .

^ As for the Extracts — which I have been reading again since I began this letter— it is a deep satisfaction to me to have them. They oome to me like a strange, and yet near and thrilling voice, from the region which we call the Past, but which is past only in semblance, for whatever has been lives on in its influences, and is destined to live again.'

Fmm Sir W. B. Hamilton to Atjrret De Verb.

< Obseryatoby, Aufftut 4, 1855.

<As to our religious views, you rightly judge that we differ more than we once did. Even if t/ou had stood still, which was (as I suppose) impossible, at the point of Catholicism which you occupied when we used to have the most frequent opportunities of conversing freely on such subjects, and when there was, I think, very little difference of opinion, if any, between us, yet I have not stood still. Yours has been, as I most fully admit, and feel, with respect to yourself, a vital progress, a real psychological develop- ment ; you are now more consistent with your own instincts, and so far subjectively truer. On the other hand, if you knew my mental history, you would be apt to say, or if too polite to sajf it, you would think that I have been retrograding, for at least ten years, since about the time of Mr. Montgomery's change of

32 Life of Sir William Rowan Hamilton. [1855.

profession. The question of progress or retxogression, as regards myself y I do not choose to discuss : but the (mentally) historical factj expressed in words which we may both adopt, is that while you have been becoming, or considering yourself to become, more Catholic, and certainly more Koman, / have been growing gradu- ally more Protestant, and (as you are welcome to call it) more Anglican, than I once had been.

' We are therefore, with whatever regret it may be admitted on both sides, by a twofold motion, less in harmony now with each other than we were in former years, on the subject of our religious feelings, impressions, and convictions — that is to say, on the most important subjects in the world — and I see no probability of this state of things being changed. I suppose that in saying all this I hardly give you any information — none certainly for which your letters alone would not show me that you were already abundantly prepared.

^ If then it be painfully evident to both, that under such cir* cumstances there cannot (whatever we may both desire) be notCy 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 de- gree 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 tinist, shall always retain, so much of regard and esteem and ap- preciation for each other, made tender by so many associations of ray early youth and your boyhood, which can never be forgotten by either of us, that (as times go) tivo or three very respectable FRIENDSHIPS might easily be carved out from the fragments of our former and ever-to-be-remembered intimacy! It would be no exaggeration to quote the words *' Heu quanto minus est cum reliquis versari, quam tui meminisse ! " . . . ^'

* I have been very much gratified, indeed, by the kind message which I have received through you this morning, from one of the two ladies whom I have loved the best in the world — and of whom it is a deep satisfaction to me to know, that one is happily dead, and the other happily living — namely, the objects of my very early, and of my later, but still youthful poems.

^ That I should have seen the one before her death, and have

ACTAT. 60.] Close of an Era. 33

h^xrd to-day through you, at least by a message, from the other^ is 8 matter of quiet joy, and indeed of thankfulness. It seems to aay to me : — " Your past life is rounded ofif ; you have lived for half a century, and the la^t day of it has been made happy by a recognition from one whom you had so very long and so very well remembered. Let that suffice for the past^ and try whether you cannot, for the future, not indeed exert yourself more vigorously (that were unreasonable and hopeless to expect), but at least work more calmly, suffering all agitations about former times on earth to be absorbed in thought of the future eternity." Decidedly I feel it as a close to an era^ although a very consoling close to me, that on a day which to my own imagination, or perhaps fancy (for I am accustomed to have associations with, and to receive im* presfiions from, days that seem to me remarkable), presents itself so much as one of transition^ as that of my reaching the age of fifty, at the same time that my second son, Archibald, attains exactly that of twenty years old, I should receive through you a kind message of thanks from your sister, from whom I had not heard in any way for so very long a time — ^in fact, since 1831. . . .*

I^om Aubrey Db Yere to Sir W. B. Hamilton.

*Auguit 9, 1856.

^ . . These are the things that show us the marvellous depth and strength of the human affections : when we call to mind how commonly they are left without response in this world, or even if responded to, are opposed by invincible obstacles, we cannot resist the conclusion that our whole moral being finds here below but a rehearsal of that great part assigned to it hereafter. On earth there seems no proportion between the strength of the affections and the objects on which, or circumstances under which, they are exercised. Were our life an animal life, man would indeed be the most ill-assorted and incomplete of all animals. But this very incompleteness of our destinies, considered as creatures of time, takes its place among the many proofs that we are made for Eternity; — and doubtless our human affections bum with a fire some portion of which is derived from that Love which is to last for ever, and to be bestowed on no human object, except as koown and enjoyed in and through God.'

VOL. ni. D

34 L,if^ of Sir William Rowan Hamilton. [1856.

From the Samb to the Same.

'DnrciLB, SepUwJber 1, 1855.

' . . . I do not like, however, to let another post go out with- out sending you at least my most cordial thanks for a confidence which is in itself the best possible proof of the sincerity and fidelity of your friendship. It also assures me (and this is a subject of great gratification to me) that, seldom as we have met of late years, you do not distrust the permanence on my part of a friendship which I have always regarded as one of the chief blessings of my life. When we met first, it was at a time when I had formed few friendships; and for this reason, as well as others, I naturally grew into the habit of associating you with all those studies and aspirations which belong to growing youth, but do not desert our maturer life. Later experience has never tended to withdraw my thoughts and affections from what belonged to that early time ; and even to the most intimate of my later friends I have often been tempted to say, as Charles Lamb does in one of his poems, " Why did you not belong to the old, well- remembered times P'' . . .

*' I will take care to communicate to my sister, when I see her next, what you so kindly, and with such affectionate and generous remembrance, say respecting her; and in the meantime I may safely assure you that she has never forgotten you, or remembered you with other feelings than those of the warmest, most grateful, and most admiring friendship.'

Frofn Sir W. B. Hamilton to Aubrey Db Yere.

< Obssevatobt, September 3, 1855, * Monday Night.

' So you wrote those lines to Bums's Highland Mart/, which I

had so very deeply admired, without having the slightest hope

that I shoidd ever know so much as the name of the author !

Surely they were not printed in either of your two former

volumes. I think it was in a number of BlaekwoocCe Magazine

that I first saw them, and very much they struck me ; but I had

not the least suspicion that they were by you. Perhaps such lines

as

<* Honour to Scotland and to Boms "

ought to have made me suspect that they came from a foreign

iBTAT. 50.] Poems of Aubrey De Vere. 35

■

flooroe — ^foreign, I mean, to Sootland; but I must own that I always attributed the^poem to some native Sootchman. I congra- tulate you most heartily upon the authorship of it. To anyone whatever it would, in^my opinion, be a fit subject of congratula- tion. . . .

[Here followed critical remarks on several of the poems con- tained in a volume published by Aubrey De Yere in 1855.]

*I must once more congratulate you, not merely on the poetical skill, but also] on what seems to me the perfect taste with which you have expressed your new views, and the complete absence of bitterness, so far as I have yet observed, even in manner. The change seems to have been no change to you (though I can well believe your statement that it cost you a straggle). The old poems which you have retained appear to be quite at home among the new ones. Yet I think that, if you look back upon that volume which you dedicated to me (and of course you could not have properly paid me the same compliment again), you will understand that / may have almost entirely sympathised with you then, and yet be separated importantly now; as, for instance, with regard to the Blessed Yirgin Mary, whom certainly 1 am not conscious of honouring le%8 than I formerly did, but whom you now honour othei'icise,

' This slight comparing of notes as to our own feelings and your poetry is not designed to draw on any discussion of dog- matic theology. But I remain, my dear Aubrey, affectionately yours.'

From Aubrey Db Yerb to Sir W- R. Hamilton.

^DlKGLE, September 7, 1865.

^ It is a very great pleasure to me to find that you like the poems of my new volume which you have had time to read as yet; and certainly, considering how short a time you have had the book in your hands, you seem to have made yourself marvel- lously well acquainted with its contents, as well as to have read it in a most friendly spirit. It is curious that you should have chanced to see the poem on Highland Mary, It was written during a tour I made in Scotland in the winter of 1845. A volume of Bums was the companion of my solitary way. Both

I>2

36 Life of Sir William Rowan Hamilton. [1855.

for him and for the Scotch people, with their singular mixture of imagination and warm feeling, with their robustness, courage, and perseverance, I felt a great, though by no means unqualified, admiration. I wished to write something in honour of the bard and of his country ; and it struck me that, by making ^' Highland Mary" the centre of the poem, and, as it were, a connecting link running through it, something of heart might find its way into the poem, as well as a certain degree of unity, without which it woidd ^' drag its slow length along" only to weary the reader. It was a sort of farewell tribute to a land in which I had met kind- ness, and from which I had received many impulses of thought and feeling. A Farewell to Naples^ written in a different tone, you will find in the same volume. It is probably too severe, but ought at least so far to confirm what I say in praise of Eome and the other sanctuaries of Italy, as to show that that praise comes from one who does not fancy perfection in every city which is washed by the Mediterranean, and professes the Eoman Catholic faith. By-the-way, I am particularly glad to find that you like the ^rit in which I have touched (at the end of my volume) on points respecting which we should differ. My firm conviction that the Church to which years of thought made me believe it my duty to make my submission (to join a Church is a phrase I could never use) represents the authentic and permanent form of Chris- tianity— nay, that she alone gives to the bodies which have de- parted from her whatever of clear, firm, and orthodox teaching they retain — this belief ought surely to produce no bitterness of tone in the expression of it. To leave such convictions unexpressed would, on the other hand, imply little regard or respect for others, or else very little faith in tt^th as the great gift to man, through which God is pleased to dispense His other gifts. It is, however, a mere absurdity to fancy that, by expressing such convictions in a rude or bullying tone, we can convey them to others, or that we have a right to be surprised at others still thinking much as we once thought. We have neither to impose our sentence as ^judgCy nor to plead in the spirit of an advocate^ but to witness^ in sim- plicity and in manly humility, to whatever of truth God has been pleased to impart to us, and then let that witness fare as it may in a world preoccupied and not zealous for truthy though eager enough for knowledge.

AKTAT. 60.] Thru Feeling. 37

* To oome back, however, to joar remarks on my poetry. . . . Whenever you have time to go through the volume, you may be sure that any remarks you may make on it will be most aooeptable and useful to me, and that whether or not they should prove as favourable as those of your last letter. There are two sets of poems on which I should especially like to know your opinion. The first is a series of poems on Ireland, printed oonsecutively, and beginning with some sonnets called Colonization. They con- clude with a poem called The Last Irish Confiscation^ which, being cast in a dramatic form, as the address of one of the early and dis- possessed race to one of the conquering race, reduced in their turn, can be judged on purely poetic grounds, and with or without the aid of political sympathy. The note at the end of the volume is necessary to explain it. The second class is the series of love poems called Psyche. One of them, beginning, ^' Such beauty was not bom to die," would, I think, have a special interest for you. My poems have been said, even by indulgent readers, to be defi- cient in passion. If so, I should think that the defect exists less in those two series than elsewhere. I have sent on your remarks to my mother and sister, who will be much interested by them.'

From Sir W. R. Hamilton to Aubrey Db Verb.

* Obsebvatobt, September 10, 1855.

^ . . . I have been as happy in my own marriage as I expected, and more than I deserved to be. My three loves have been of kinds entirely different, and were felt aU along to be so. I do not think that I ever confounded the three feelings, though it might be tedious, and in some degree impertinent, or presumptuous, for me to pretend to analyse them now. In general I might perhaps be permitted to say, to you, that they sometimes suggest themselves to my mind, as having been cliaracteristically those of a lover^ a brother y and a husband: selecting, you know, what has been emi- nent in each of them.

* I ought to be packing up and otherwise preparing for Glas- gow; but must add one line to thank you for having pointed out Psyche to my notice. I had feared that the poem was a long alU^ gory J and had resolved to take my time about reading it. The thoughts and words are beautiful.

38 Life of Sir William Rowan Hamilton. [1866.

' . . . Bat as for me, I am going rather for amnBement and to see people than to do anything important at G-lasgow. Still I would go for the mere purpose of being there on Monday next during that single hour when the airangements respecting the place of meeting for next year will be decided on ; in order that^ as a Dublin man, I may put in once more a claim for a visit of the Association to Dublin in 1857.'

<

From Aubrey De Yere to Sir W. B. Hamilton.

< Momrr Tbskchard, Fotnss, September IS, 1866.

[Beferring to a letter of old date from a friend, expressing admiration of Mr. De Yere's character, which had been sent to him by Sir W. R. Hamilton.]

'. • • Tennyson's new yoliime, Maud^ contains these linea describing the feelings of a man, when, at his desire, the lady of his love, with whom he has quarrelled, gives him back his presents : —

'< As looks a father on the things Of his dead son, I looked on these."

Such are the feelings with which we are apt to look on memorials of early praise and early expectations. There are doubtless, how- ever, some who can regard the mementos of their youth with lees mingled feelings : those persons especially of whom Wordsworth says that they " have wrought upon the plan that pleased their childish thought," and whose earliest aspirations have brought forth sixty- fold or a hundredfold. The chief misfortune of my life I regard as having been the absence of the habit of Confession, owing to my not having been brought up as a Catholic — a habit which I regard as necessary in an equal degree, though for different reasons, for the most opposite characters — the weak and the strong, men of genius and the dull. Without it, sterile soils are cheated of the increase possible to them, and rich soils abound as much in weeds as flowers : our very gifts become special sources of temptation and aberration; and we are left to learn, by the experience of life, lessons which ought to have been the foundation of a manly and Christian life. Here is a little bit of condensed biography on my part in reply, or part reply, to a portion of your letter ; for I speak from observation and experience, not theologically, and with reference to

ASTAT. 60.] Thru Worlds. 39

the human aspects of the question only, as a psyohologioal problem, without discussing the question whether or not a Bite of Forgive* fiess stands to post-baptismal sin, as Baptism stands to Original sin. . • . Yet no suffering is sent in yain. All trials find their place in that great scheme of Probation which is the Reality of Liife in its present stage . . . and all that we have thought, and felt, and done, lives on in us to the end of our lives, furnishing new materials for a probation which is ever changing its character in the successive epochs of our life.'

From Sir W. B. Hamilton to Aubrey Db Ybrb.

( Obsbbvatort, Oetobm' 19, 1855.

' I found that it at times agitated me to a degree which was imprudent for health, of body and of mind, to write as I was doiog before I went to Glasgow, on subjects that are still so verj vividly remembered. My visit was an useful diversion of my thoughts . . .'

From Aubrey De Ybrb to Sir W. B. Hamilton.

'Oeto5<r 20, 1855.

' • . . I hope you will go on writing sonnets, so as to make them embody a large proportion of your views and feelings on personal, ethical, and philosophic subjects; but I have a stUl more important work* for you which you must execute some day, and for which you have such great qualifications . . . Your visit to Glasgow must have been a pleasant one — and particularly useful at the time it took place ; for there is always an agitating interest in a review of the critical passages of one's past life, as well as a deep moral interest that allays agitation. . . .

' . . . There is something very touching in what you allude to respecting your pilgrimage to the house in which you had first been greeted by the *^ beautiful Yision." But surely all such Yisions should be looked on as Anticipations and Types of the Glory and Beauty unrevealed, rather than as lights which have melted away into the sad shadow-land of the Fast. There are three Worlds— those of Senee^ of Faithj and of Olory. The first is in some measure eclipsed, or passed by, for a Christian.

* Not here indicated, but see if\fra A. De Y.'s letter of May 11, 1856.

40 Life of Sir William Rowan Hamilton. [1855.

The last is not yet revealed : but all the shapes on Earth that are shapes of Beauty and Brightness (flowers, stars, poetry, and what- ever belongs to the Ideal) seem to me to be sparkles or flashes shot down through the dim atmosphere of the region of Faith from the region of Glory. They are gleams to remind us of a higher world, just as there are intimations from the region of Faith that transpierce the darkness of the lower region of Sense, and give a vitality even to paganism. It seems to me of the essence of these things that they should be but gleams^ for the World that unites Brightness and Permanence is yet to come.'

From the Same to the Samb.

' MouiirT TBXNCRkBJ>, December 20, 1855.

'...lam sending youacopy of a poem which has, over and above its poetic merits, an interest for us, Irish readers, being a me- morial of a most promising young Irishman, the late Lord Belfast. I want you to tell me also how you like it, especially the singular effect of the triple rhymes in the proem. The author* has pub- lished also a volume of poems, many of which are very beautiful. . . .

Talking of poetry puts me in mind of your fair friend " who Speranza bight." She certainly must be a woman of real poetio genius to have written anything so beautiful, and also so full of power and grace as the poemf you showed me. For the sake botli of poetry and old Ireland you must do all you can to make her go on writing, and publish a volume soon. Do not forget to tell her that you showed her poem to a stranger (a stranger always counts for something) who has been addicted to poetry all his life, and re- veres it more every year, and that he felt a very sincere admiration for it ; although in the matter of your proposed metrical changes, he had the impertinence to agree with you,^

From Sir W. R. Hamilton to Aubrey De Verb.

* November 14, 1855.

* I do not feel in the least afraid, for myself, of reading any- thing. I have read atheistical books, infidel books, Socinian books, Protestant evangelical books, books by the Archbishop of Dublin,^

* Denis Florence MaoCarthy. f Shadowejrom Life, % AjrchbiBhop Whately.

A«TAT. 60.] The Nichols. 4 1

Protestant High-ohurch books, Bomanist books; and remain a moderate member of (what we nsed to call) the Church of Eng- land : more nearly perhaps approaching to the Archbishop's school than when we talked most about such matters formerly, though retaining a sincere sympathy and reverence for some whom we ealled Puseyites, and indeed for Dr. Pusey himself, though I am more canscioua now than before of being farther removed from Borne than he is. But I quite distrust my own power of expressing to you, with so much of personal delicacy as you have used towards me, any of those beliefs of mine which may, or rather must, be different from yours. Indeed we should not meet on equal terms: for while I could listen to ant/thing from you (though I see no wte in listening to it), you not merely might be, but (I should almost say) ought to be, offended if I were to express at all fully my views of the Komish Church. Merely in my calling it sitch^ you have already ground for a very pretty quarrel ! though I think you will not avail yourself of it this time.'

I now give extracts from the correspondence with Dr. Nichol and his son, commencing with a letter to the son : —

li'Ofn Sir W. R. Hamilton to John Nichol.

' On board the '< Arisl," September 26, 1855.

' ... It will gratify me much if you shall sometimes send me oopies or draughts of your poems. I do not pretend to be a poet, or in any important sense an original thinker myself, but if you knew more of my (very unimportant) private history, you would be better able to understand that, without giving up any one of my own convictions, I may be able to sympathise with young men who earnestly think for themselves, even if the process lead them quite up or down to the point of Atheism, to which it does not seem to have led you — and from which I recoiled.

' Allow me to repeat, in writing, what I half said in a recent conversation, that, much as I love and honour your father, my regard for you has a distinct and independent root; and that though I may prove a very bad correspondent to you (in the case of Aubrey De Yere there was a whole host of early recollections to be called into play, if our remembrance of each other in later times had flagged), any letter with which you may at any time favour me will interest me for its own sake.

42 Life of Sir William Rowan Hamilton. [1865.

' I trust that you oannot be displeafled by my adding that if Mifls Niohol, your sister, should ever favour me with the sight of any of her manuscripts, the kindness will be appreciated, and in some slight degree repaid by a free but friendly criticism.

' With regards to Dr. and Mrs. Nichol/ &c.

A memorandum, bearing date the same month as the above letter, records in the following words Hamilton's modest estimate of his poetical faculty : —

' 1855, September. — I am just enough of a poet myself to be enabled thereby to sympathise with other poets, to enjoy habitually their successes, and sometimes to be, without unkindness, sensible to their faults, or short-comings, better than without some such exertions of my own (in the department of poetical composition) might have been possible for me.'

Urom the Sams to the Same.

< Obseetatoht, Dubuk, September 29, 1855.

* My son Archibald (the younger of my two boys) made out, this morning, the cipher on the other half of this sheet, without his having previously the slightest notion of the subject, or even the language ; but I had previously taught him my key. I shall per- haps ask him, after a day or two, to write out the same passage for you in some other form, consistent with the same keif (not alphabet), and, like the present, definitely interpretable. You would be astonished, I think, and even your father, with all his knowledge of the powers of numbers, would be so, if I were to mention in hate many distinct ways the satne extract from your poetry could be written on my plan, without the slightest ambiguity of interpretation ! A recent and hasty calculation leads to the con- clusion that the expression of the number, on the usual decimal system, would require 230 figures. And even my own initials could be written in more than 300 millions of different ways, so that my son (for instance], or anyone else who had the key — ^the plan — which can easily be carried in the memory, and is so carried by me, would decipher, in a minute (all helps being ready), any one of those 300 millions of distinct monograms, as easily as any other of them, to signify precisely '* W. B. H.", and nothing else whatever ; and this independently of any arbitrary punctuation,

▲KTiLT. 50.] HamiltofCs Cipher. 43.

or introduotion of astronomical, or mathematioaly or Greek, or Oerman, or Oriental symbols, such as might at pleasure be mingled with the characters of the English alphabet.'

From J. P. NicHOL, ll,d., to Sir W. R. Hamilton.

' OBaxBYATORY [Glasgow], September 28, 1855.

' . . . My letter to you is, as you will find, little more than a fond recalling of the most pleasant week you spent with us. I assure- you it is a week that none of us will ever forget. You taught us far more than your cipher, viz. how exquisite and lovable is^ the highest genius.'. . .

li^om Sir W. R. Hamilton to J. P. Nichol, ll.d.

* Obsbrtatort, DuBLnr, October 1, 1855.

* The cipher on the other side seems to me likely to be found a difficult one to make out, so long as the kei/ is not given, or at least the plan explained : an almost xmlimitod flexibility as to the tniting in this cipher, combined with an absolutely rigorous de^ finiteness in the reading of it, seem to me to be the chief character- istics of the method ;....! claim to be able to teach the method to any sufficiently intelligent person in something like five minutes : at least if I should be allowed to use a very simple machine which I have invented for the purpose of writing and reading the cipher, but with which I can upon occasion dispense. Th» principle cannot be forgotten, and the key can be at any moment reconstructed, or the machine re-made, with ease. ... It occurred to me about ten years ago, but the war has since made it surge up into my thoughts again — for it might, perhaps, be useful on some occasion of a secret despatch. . . .'

From Sir W. R. Hamilton to John Nichol.

* Obse&tatort, DuBLnr, October 10 , 1855.

* . . . When you know me better, you will be aware that I am an abominably bad correspondent, except now and then by fits- end starts. To Aubrey de Yere I had not written for several years; but, within two or three recent months, he and I have exchanged letters, which would make (in size) a respectiAle little^ volume, though they were (and are) in no way designed for

44 Life of Sir William Rowan Hamilton. [i860.

pablioatioxiy and indeed were in many respects confidential; for we wrote much to each other about the days of long ago, being at least twenty-five years acquainted, and having, from some droum- ^tanoes of my history, become intimate almost immediately . . . You and he are pretty nearly antipodes of each other, in many important respects, yet I can most sincerely sympathise with each of you — each being earnest and sincere, and also cultivated and poetical. That neither is specially scientific may (who knows P) be another attraction; though, that I can honestly enjoy the fame of a scientific brother — ^if this last word may without presumption be used by me — ^will be seen, if I shall ever transcribe my sonnet to the deceased Fourier (author of the mathematical Theory of Heat, &c.), or one of those to the living Herschel. Still, the two names they mentioned are of men who have been much more than mathematical calculators : and your father has such a vast variety of cultivation, that one may be pardoned for sometimes forgetting that he is by profession (and of course in reality) a man of science. Professor De Morgan, of London, is again a person excessively un- like to all of you ; yet he and I have exchanged a great number •of pleasant letters, partly no doubt on mathematics, but we are not afraid to write nonsense to each other ; at least I send him nonsense at times, and he sends me back wit in return, rising •occasionally to humour. I wonder whether I shall ever venture to show you (if I can lay my hand upon it) that letter from Mrs. Flamsteed to the late Francis Baily, which De Morgan professed to find among the papers of the latter! Flamsteed, you know, was the first Astronomer Eoyal at Ghreenwich, and a quarrel between him and Newton has even recently become matter of discussion. Baily died only a few years ago, but he had taken Flamsteed's part in the controversy. Mrs. Flamsteed writing (if I remember) from 3, Paradise Kow (or perhaps it was, from 3, Astronomer's Bow, Paradise), tells BaUy that her good man is just gone out to take a social stroll with Sir Isaac, with whom he has become quite reconciled ; but that, as to that scoundrel, Halley, who had oome between them, it is lucky for him that he had not come up there, for her husband would have beaten him within an inch of his life ! (after all, Halley, whose name has been given to a comet, was in many respects a fine fellow.) I never write in that style myself, but certainly I enjoyed De Morgan's report of that celestial-

AKTAT. 60.] Estimate of yohn Nichol. 45

infernal letter — though I did not show it to my wife, who would (or at least might — I was not sure) have said it was profane. Still she has been much amused with many of De Morgan's letters, and I think would welcome him here*

*If there be any logic at all in this gossip about my correspon- dents, or some of them, it tends to show that I shall be pleased to receive at any time a letter from you, whom it is scarcely praise^ and certainly not flattery, to say that I regard as a remarkable young man. Had I only met you in a steam-boat on one of those- extemporised committees about poetry, I persuade myself that I should have long remembered you. As it is, with all the associa- tions of your father's fame, and recollections of my reception at his- Yery pleasant home, I feel certain that I shall never forget you»^ Yet I am aware that it is too late for me to hope ever to enjoy with you that hind of friendship, which mighty nay (I am sure) wouldy have resulted if it had been possible and permitted for us ta meet as two young men. On that subject, I think that I must extract for you a passage from one of my friend Aubrey's letters. Meanwhile, you will just write to me as seldom, or as often, as you shall feel inclined ; and will remember me with patience and good humour, even if I shall leave some interesting letter of yours for months, or years, unanswered, though I think that I shan't be quite so bad as all that ; but I do take fits on me, at times, of soli* tary study, during which I cannot bear to write a letter, and then I grow ashamed to write at all. . . .

* About my cipher (only one of my boys as yet knows it — a cipher and a mystery seem to be congenial) you really deserve credit for your guesses. You are, what in some chUdish game is called " hot" — close on the scent ; but have not quite caught the hare as yet. You deserve that I should enclose the translation — I do not say the key. In finding out the latter, I enjoy the thought of your having some trouble still !'

From Sir W. B. Hamilton to J. P. Nichol, ll.d.

* Obsebvatobt, Dttblin, October 17, 1855.

^ I don't know what puts it into my head, but I am in a mood to remember, and write down for you, the latter part of a sonnet

* See Professor De Morgan's Budget of Faradaxes, p. 188.

46 Life of Sir William Rowan Hamilton. [1865.

which I oomposed by starlight about seven years ago, in the high {gallery of the great telescope at Parsonstown.* The former part of that sonnet has happily escaped my recollection^ but I know that it was execrable. Certainly I did not intend to flatter Lord Roese, to whom I had the honour of being introduced by his father -a great many years before ; but there was something of compli- ment, or at least of politeness, in my mood, at first, which ought not to be, or rather cannot be, the inspiring spirit of any true and genuine poetry. Yet I own that I rather like, on recollection, the last six lines, expressive of an astronomical enthusiasm, including also a feeling for natural beauty, into which my tone gradually -deepened, and in which I know that you can sympathise. I re- member that I was standing alone at midnight, on a sort of little bridge somewhat like sixty feet above the ground, while Airy, with Lord Bosse, was seeing, at a lower altitude, some newly-dis- oovered spiral nebula.'

* Pursuing still his old Homerio march, Northward beneath the Pole slow wheeled the Bear : Rose over head the great Galactic Arch ; Eastward the Pleiads, with their tangled hair : Gleamed to the west, far seen, the lake below, And through the trees was heard the river's flow.'

Froni the Same to the Same.

[from a copy.]

* Obsebyatort, Dublin, October 31, 1855. 'All JBallowa' Eve.

* . . .1 really must write again to Agnes [Nichol] to tell her a little more about the budding '* authorship " of my Helen. It takes me quite by surprise, though it may never ripen to anything important for the world. She poured upon me, a few days ago, quite a stream of questions about your daughter: what sort of authorship she was engaged upon, and soforth ; but all that may better be told to your Agnes herself. I assure you that a thought •of my daughter's about the Sea and its " Despair/' which (with

• Vol. ii., p. 620.

AKTAT. 50.] The Seds Despair. 47

glowing cheek pressed to my own) she oonfeased to me last night, appeared to me to be perfectly original ! It was at least entirely new to m€ ; and yet it seemed so deep, hut true, that if I had ever met with it in reading, I could not have forgotten it.'

In a later letter to Dr. Niohol, referring to this idea of his daughter's, he writes — ' I know that there is a Latin motto '^ Co- nantia frangere frango": but still the thought of the sea's despair seemed to me new.'

JFV-OW J. P. NiCHOL, LL.D., to SiR W. E. HAMILTON.

< Obsebyatort, Glasgow, November 6, 1855.

' Would that I could adequately tell you how much I value your confidences, and how gladly I welcome— even at this com- paratively late date in life — ^the approaches of a new friendship — to say nothing of such a friendship as yours ! I have outlived much, far more than I can estimate in value of any kind ; and it is something to find, when one is growing almost weary, and in« dined to think oftenest of the future, and a final rest, that new companions may still be found to take place on benches that have been vacated, and wilUng to pull with one at the oar. But this is only the selfish view of the case. I look with still profounder interest on the events of which you have so kindly told me, because I would fain learn what those things are that have torn, tried, and educated a mind like yours. Is it not possible that when summer returns I may induce you to cross over to us again, and that we two shall talk of such things and much else, during a ramble through £annock Moor, or by the margin of vast and soli- tary Loch AweP It is in such places, I always think, that it is best for the mind to look into its own depths, and to hear of the sorrows and triumphs of another. Do keep this in memory* I shall do my best to induce Lady Hamilton to spare you for awhile then.

* I never heard of your daughter's rare idea, the " Despair of the Sea," but how many images it brings up. Tell her from me that she has added a new note to that grand music — a music which generally gives me a deeper sense of infinitude than even

48 Life of Sir William Rowan Hamilton. [1866.

the midnight deeps. Depend on it that the mind which could suggest or find that eonoeption will find many more rare ones. Agnes sits opposite me just now, writing a chapter of Hermione. We are alone together in the green room. It is veiy late, and the docks seem to tick loudly. . . .

^ Mrs. Nichol — who has heen a guardian angel to Agnes — is not quite well to-night, and has retired. But you are sure that her affection and respect always extend to you.'

H'otn Sir W. E. Hamilton to John Nichol.

'Ob8£KTATobt, Dubldt, Nov. 12, 1866.

*. . . Any criticism on the " Maud " will interest me much, hut especially any notes on that poem by one whom I do so strongly associate with it as I do yourself. Will you believe that it is only within the last few days I have read the poem here ! or indeed properly speaking anywhere ; but within those days I have read it several times ; and think that it was not indolence which prevented me from procuring and reading it sooner, but rather the wish not soon to disturb the associations with my having heard you read it (or most of it) at your father's Observatory. Perhaps I might have reposed on that recollection for some weeks longer, if it had not been for the shock received on Monday last (November 5th) by the perusal of a clever but uncandid article on Tennyson's poetry in general, which appeared in the first number (for Novem- ber 3rd) of a new London publication, the Saturday Review^ a specimen whereof was sent to me. I had recently been reading^ throughy and more than once, the "In Memoriam": you conceive, from the connexion, that I do not speak here of your lines so en- titled, though I have lately perused them also with much interest, but of Tennyson's, whose Princess^ and several shorter poems, I had also not long since read again. Consequently, I was the more prepared to form my own opinion, as I went along, about the justice and candour of the reviewer's criticLBms ; and if you wish to lash yourself up to some degree of indignation, I recommend you to expend sixpence on procuring the article .... One artifice of the critic is to treat Tennyson as speaking in his cum person throughout — for instance, in Locksley Hall^ and Maud: as if Shake- speare were to be identified with lago I . . .'

AETAT. 60.] Despatches from Russia. Logic. 49

Fi'oni the Samb to the Same.

< Obseetatort, DuBLiKy November 24, 1855.

* ... I am glad that you liked the sonnet to Fourier. Fourier was (as your father will tell you) a true poet in Mathematics, and in the applications of mathematical science to nature (especially to the theory of heat). So was (though not Laplace) Lagrange, to whose memory I consider myself as having inscribed those essays on a general method in dynamics, for which I received long ago a diploma, with an enormous double eagle engraved, and the names of Nicholas and of Hamilton stretching about equally across the sheet, from the Imperial Academy of Sciences at St. Fetersburgh, which body has sent me a large packet during the war. There is something inspiring and consoling to humanity in the friendly and appreciating hand thus stretched through battle across Europe! I astounded a Viceregal party by telling them that I had just received despatches from St. Fetersburgh, and high people spoke, half seriously, of arresting me; but I appealed to Lord Carlisle, who was so polite as to take charge of, and after- wards return, a specimen of my Bussian bulletins. When we next met, the Lord Lieutenant asked me whether I had since been en- gaged in an animated correspondence with St Fetersburgh P '^No, my Lord,'' I replied, ^' my last despatches have been from Bome.'' "And your next," said His Excellency, "will be, I suppose, from China.*' I bowed, and had the grace not to answer, that "I should not be excessively surprised ! " America noticed me very early.

* Egotistical all this, is it not P To be sure it is ; and do t/ou, in revenge, make your reply as egotistical as you can find it in your heart to do. You will write to a safe and not an inquisitive person, who likes to know something of the inner history of any one whom he thinks of with regard, but is quite satisfied with the suppression of names. . . . Affectionately yours.'

H'om the Same to the Samb.

* Obsbbyatobt, Ntwetnber 26, 1865.

* I hoped to write more fully on the logical question, but have only been able to give it a comer of my thoughts. The spirit of a remark made at the end of a recent note is that we can't go on

YOL. UI. E

50 Life of Sir William Rowan Hamilton. [1855.

proving for eyer ; we must, it seems, assume some principles ; and indeed in each single syllogism the premises of that syllogism are given, not proved. It is not bt/ syllogism, but by insight and sagacity, that the general rules of syllogism itself have been estab- lished; though I am not prepared to deny that any argument whatever may be staled in the syllogistic form. That " domino " can, I suppose, in the masquerade of thought, be slipped over any one of the intellectual characters which figure at the ball ; whether usefully or not is a diflEerent question. Whenever we reason^ we are conscious that we generalise; some principle or a^-sumption (the major) is, or at least mat be extricated, as we feel sure, from the perhaps individual instance which we have first in view : we regard that case (if it be one) as a mere illustration or exemplification, of a principle: and then comes in the «n6-sumption (the minor), whereby we apply what had been formerly generalised, and so arrive at a conclusion. But it does not seem to me natural^ even for a long-trained thinker, to throw arguments into the Aristotelian form ; which yet I would advise you to study very diligently, as I once did myself. My first science honour in Dublin was won in logic.

*I have just now noticed in that wonderful Almagest of Ptolemy— the world's astronomical Bible for almost 2000 years — the word tjvWoyia^o^, applied to mathematical calculation. Hobbes, as perhaps you are aware, regarded all reasoning as a calculation. But I must have forgotten a whole Library I '

▲BTAT. 60.] Vtsti to Cheltenham. 5 1

CHAPTER XU.

VISIT TO CHBLTBNHAM. lOOSIAN CALCULUS. COBBBSPOKBENCE WITH AUBREY DB VBBB. LBTTERS ON MATHEMATICAL SUBJECTS.

(l856.)

DuBiNG the first half of 1856 Lady Hamilton was seriously indisposed with illness of a nervous oharaoter, similar to that by which she was affected in 1840-41, and letters of her husband prove not only his natural anxiety on the subject, but his affec- tionate devotion to her of personal care and detailed consideration. He encouurages her pastor, Dr. Sadleir of Castleknock, to enter into religious conversation with her, urging with truth and wisdom, * I have known even the body benefited by a courageous reference to things of a higher life' : he mentions incidentally, 'I have been walking nearly the whole of this morning with Lady Hamilton in the garden': and he remains in doubt till the very last day, whether he shall allow himself the anticipated pleasure of at- tending the Meeting of the British Association and being a guest of his old friend John Graves at Cheltenham, telling his ex- pectant host (August 8) that 'Lady Hamilton has been really very ill for a good while past. She has often parted with me before, but for the last six months or nearly so, I have been a sort of nune to her, and it is a great effort to her to part with me, at present, even for a few days.' This illness of Lady Hamilton, and the confinement to which it doomed himself, had undoubtedly an injurious effect upon Hamilton's own health and spirits. There are indications of this in his journals and letters, prompting in the mind of the reader uneasiness and expectation of some break-down > Happily he was able at the last moment, on the 10 th of August,

E2

52 Life of Sir William Rowan Hamilton. [1856.

to obtain a release from Lome duties, and arrive at Cheltenham before the olose of the Meeting. He was thus enabled to gratify his desire publiclj to manifest his feeling towards Dr. Lloyd by seconding Whewell's proposal that at the succeeding Meeting of the Association in Dublin his old friend should have the honour of being its President.

Mr. Ghrove, the eminent author of The Correlation of Physical Forces^ was his fellow-guest in the house of his friend; and familiar intercourse with these brothers in science, and more cursory meet- ings with other distinguished men, had the happiest effect upon his spirits, affording him the enjoyment and stimulus of intellectual companionship; but the physical effects of the disadvantageous circumstances I have referred to were not to be escaped from, and showed themselves in a severe fit of gout, by which he was ren- dered unable to walk, and obliged to remain for a fortnight longer than he had intended a recipient of his friend's hospitality. By both host and guest this was considered to be the reverse of a penalty. Letters given below show how he feasted upon the contents of the rich scientific library of Mr. Graves, and, as in earlier times, received from his friend intelligent sympathy in his most recent researches, and hints for prosecuting them iu new directions.

Very soon after his return home he forwarded to Mr. Gh*aveB two valuable scientific Papers: the first a criticism on Scheffler's book, Der Situations Kalkul (a work on the Geometry of Space), in which the author arrives, after long discussion, at a conclusion which in 1832 had been rejected by Hamilton as insufficient founda- tion for the required calculus ; the second, an extension by means of quaternions of some propositions laid down by Oauss in his Diaquisitiones Arithmetieae* Their general nature is set forth in letters to Mr. Ghraves, which are, however, too mathematical for insertion in this volume: the papers themselves will probably appear in an early number of Hermathena.

In the following month of October — the happy birth-month of both Conical Befraction and Qruatemions — Hamilton imparts to

ACTAT. 50.] The Icosian Calculus. 53

the same friend his disooveiy of a new Caloulus, to which he gave the name of Eioosian (afterwards changed to loosian), because speciallj exemplified in the case of the Icosahedron, though applicable to other polyhedra. This oflFspring of his genius was not indeed of equal note with those which have been named, but it IB not unworthy of its parentage. Professor Tait says of it — < Hamilton has published but a page or two with reference to them [the systems embraced by this discovery], yet that little is enough to show the probability of their becoming, at some future time, of great importance in the study of crystals and polyhedra in general.' It was Mr. Graves who, during Hamilton's visit to Cheltenham, had re-excited in him an interest, long dormant, in the mathematical properties of these solids, and to Mr. Oraves accordingly Hamilton first made known his discovery, in letters dated October 7 and October 17, of which the latter extended to fifty pages. A summaiy view of it was communicated by him, under date October 29, to the Philosophical Magazine iov December, 1856, with the title Memorandum respecting a New System of Roots of Unity ^ and a fuller statement of the discovery was made by him to the Boyal Irish Academy on the 10th of November, and is re- ported in the Proceedings. From these communications I extract the following passages, which will give the reader a general idea of the Calculus : —

' I have lately been led to the conception of a new system, or rather family of systems^ of non-commutative roots of unity y which are entirely distinct from the i, y, A;, of the quaternions, though having some general analogy thereto; and which admit, even more easily than the quaternion symbols do, of geometrical inteipretation. In the system which seems at present to be the most interesting one [that dealing with the icosahedron and the dodecahedron] among those included in this new family, I assume three symbols, f, K, A, such that

£» - 1, ic' = 1, X» = 1, A « IK ; (a)

where ik must be distinguished from ki, since otherwise we should have A* = 1,A = 1. Asa very simple specimen of the symbolical

54 Life of Sir William Rowan Hamilton. [18«6.

oonolusioiis deduoed from theoe fundamental assumptions^ I may mention that if we make

	/u = oe' " AiX,
we shall have also
	M* "= i» ^ = A«*M ;

SO that ft is a new fifth root of unitj, oonneoted with the former fifth root X by relations of perfect reciprocity. A long train of such symbolical deductions is found to follow ; and every one of the results may be interpreted as having reference to the passage from /<!(?« to face (or from comer to corner) of the icosahedron (or of the dodecahedron) ; on which account I am at present disposed to give the name of the ** Icosian Calculus " to this new system of symbols, and of rules for their operation.' — Philosophical Magazine. * This Calculus agrees with that of the Quaternions in three importcmt respects — ^namely, 1st, that its chief symbols, i, jc, X, are roots of unity ^ as t,y, A;, are certain fourth roots thereof; 2nd, that these new roots obey the associative law of multiplication; and, 3rd, that they are not subject to the commutative law, or that their places as factors must not in general be altered in a product. And it differs from the Quaternion Calculus — 1st, by involving roots with different exponents; and, 2ndly, by not requiring (so far as yet appears) the distributive property of multiplication. In fact + and -, in these new calculations, enter only as connect- ing exponentSy and not as connecting terms: indeed, no terms, or, in other words, no polynomes, nor even binomes, have hitherto presented themselves in these late researches of the author. As regards the exponents of the new roots, it may be mentioned that in the principal system — for the new Calculus involves a family of systems — there are adopted the equations,

I

% _

= K* = XS X « £ic ; (a)

so that we deal in it with a new square root, cube root, and fifth root J of positive unity ; the latter root being the product of the two f ormer^ when taken in an order assigned, but not in the oppo- site order. From these simple assumptions (a), a long train of consistent calculations opens itself out, for every result of which there is found a corresponding geometrical interpretation, in the theory of two of the celebrated solids of antiquity, alluded to with interest by Plato in the Timosus — namely, the Icosahedron and

ABTAT. 50.] The Icosian Game. 55

the Dodecahedron ; whereof the angleB may now be unequaL By making A^ « 1 the author obtains other symbolioal results, which are interpreted by the Octahedron and the Hexahedron. The Pyramid is, in thU theory, ahnost too simple to be interesting, but it is dealt with by the assumption A' •- 1, the other equations (a) being untouched. . . .* — Proceedings of B. I. A.

The inyestigation by this calculus of the properties of the loosahedron led Hamilton to devise a mathematical game, which he called the Icosian Game. A diagram was formed by the pro- jection of this exemplar solid upon a flat surface : and the passing continuously by the connecting lines from one comer in this dia- gram to another became in the hands of the designer a suggester of possible sequences, cyclical and non*cyclical, which, amounting in number to 62,400 (33,600 being cyclical), were included in 520 f ormulsB, all by him set forth in tabular form. The game founded upon the basis of this idea was to be played upon a board, on which the figure was cut in grooved lines with holes at the comers. In these holes, marked by the twenty consonants of the alphabet, were to be inserted consecutively, according to named conditions, movable pieces numbered from 1 to 20. The practical objection to this game was that, while some of the problems which might be set to the player required for their solution considerable thought and ingenuity, the majority were too easy to be interesting.* He corresponded at great length on the subject with Mr. Graves, by whom he was put in the way of selling the copyright of the game to Mr. Jaques of Piccadilly, who paid for it the sum of £25, the only pecuniary reward ever accruing to Hamilton directly from any discovery or publication of his. It is to be feared that Mr. Jaques did not find the bargain to be a profitable one.

The calculus itself, and the problems of the Icosian Game,

* In a note to Dr. Luby, F.T.C.D., dated July 6, I860, Hamilton writes^ < I cannot resist the temptation of telling you that you and Dr. Hart did fiot solve my little problem of the Icosian Board yesterday,' and adds, that having had the intention of presenting a copy of his Board to the Common Room of the Coll^;e, he was diBOOuraged by its reputation of being too easy.

56 Life of Sir William Rowan Hamilton, [1866.

afforded scope to their author for an amount of labour well-nigh exhaustive in its extent, whioh fills many thiok manusoript-books, and is calculated to excite a feeling of wonder in all who are capable of estimating it. The letters to Mr. Qraves forming the original oonmiunication ought, perhaps, to see the light, particularly as the writer was prevented by the preparation of his Elements of Quaierniona from fulfilling his expressed intention of sending to the PhiloBophical Magazine further oonmiunications on the subject. Professor Tait concludes his notice of the Icosian Calculus and the Icosian Qame by the comment — ' the analysis employed, though very simple, is more startingly novel than even that of the quaternions. The t,y, A;, of quaternions can, as we have seen, be represented by three definite unit-lines at right angles to each other. How can we represent geometrically the X or the /u of this new calculus, either of which produces precisely the same effect, whatever edge of whatever face of the dodecahedron it be applied toP'»

By what has been now sketched of the incidents of the year, the reader will have been prepared for the correspondence refer- ring to them ; but I give their proper precedence to letters which passed in January and February between Hamilton and Mr. DeYere. The interest of these letters is literary and personal, and the frankness, the open-heartedness of both writers, will, I think, be felt by every reader to afford the best proofs of the mutual trust, the reality and depth, of their very beautiful friend- ship. The reader will be best pleased by taking note of these proofs himself : I abstain, therefore, from forestalling his pleasure by anticipatory indication or comment.

From Sir W. R. Hamilton to Aubrey De Verb.

< OBSBavA.TOST, January 1, 1856.

^ . . . I have read the Essays [J?«sa^s, mostly Theological^ by A. De y .] quite through more than once, and many parts of them

* North British Review^ September, 1886.

AEXA.T. 50.] Speranza. Sir Aubrey De Vere* 57

with admiration ; but the chief feeling which they excite in me, or the prevailing impression that thej leave, is the old '^ Talis oum sisy ntinam noster esses," which, perhaps, you at times recip- rocate. Your present views seem to suit you at least, and you write a capital style. But this must sound to you irrelevant, perhaps irreverent.

* Many thanks for returning my manuscripts. Your last con- versation almost tempted me into writing again on the potentialitiea of the past — an idle, if not a dangerous theme — yet one to which the mind will recur.'

H-om AuBRBY Db Verb to Sir W. E. Hamilton.

' CuRRAGH Ghass, January 4, 1856.

' . . . I send you back Speranza's most amiable letter. It is indeed pleasant to meet that rare thing, poetic genius, in union with a rarer one — the magnanimity (in which genius is so often deficient, and without which it almost ceases to be respectable) which can take censure with gratitude, praise with simplicity, and both with equal grace. I am much pleased at the terms in which she speaks of my father's poetrj^ because I think them deserved. Wordsworth, a critic hard to please, thought his sonnets among the best in the language, both as to matter and composition. Notwithstanding, he remains almost as unknown in this country, to which he was deeply and loyally attached (in spite of his love of England, and dislike of popular agitation and such patriotism as is only Pat-^toAsm), as if Ireland boasted poets as numerous as blackberries.'

Fi'oni Sir W. E. Hamilton to Aubrey De Verb.

' Obsbryatoby, January 15, 1856.

' I am in your debt at least two letters, and have at this mo- ment to thank you for sending to me the newspaper containing a sketch of your very interesting lecture on Gheneral Literature, which, on the whole, appears to have been ably reported, though slight typographical faults occur : for instance . . . These things, you know, will force themselves upon a practised eye. Your own published volumes (and / may be excused for reckoning that you

58 Life of Sir William Rowan Hamilton. [1856.

have laid more than a grain or two upon the hills of gold) are singularly free from such faults ; and I too have, or think myself to have, oontributed a smaller proportion of typographical errors to my work on quaternions than is confessed by any equally oonsoientious mathematical author: for example, by Professor De Morgan.

* To turn for a moment to something higher. You know that I am not a flatterer ; but I must say that I regard your character as nobler than my own. I might easily expand upon this topic, which the slight praise given to you publicly of lat« has so little suggested, that it seems to me painfully inadequate. But with the same sincerity I must say, that the modem Boman system appears to me so corrupt that the inevitable tendency of any other system, such as Fuseyism, to it is, with me, a ^^reductio ad absurdum."

' I do not admit that I am a " touchy " person ; the pain, and often the meanness, of such a character I count myself to have, through life, escaped. Yet I am glad that you have not tried my temper, by offering to send me stamps for the prepayment of your volume of collected Essays through the post.'

From Aubrey De Verb io Sir W. E. Hamilton.

' CuRBAGH Chasa, January 24, 1856.

* The volume of my Essays reached me quite safely ; and I can assure you that, notwithstanding my joke about the stamps, nothing was ever further from my intention than to send them to you. There are, however, persons to whom I would have sent them — regular " nineteenth century " persons, as I should call them. When I was in Greece, I chanced to be acquainted with two people of good position at Athens — one an American clergy- man, the other a Scotch lawyer. They were brothers-in-law. The Scotchman, of course, was " canny " in his way, but much more for others than himself ; and while devoting all his energies to the cause of Ghreece (he had fought for that country, as well as laboured for the education of its youth at a later period), remained always as poor, not only as a field-mouse, but as a field-mouse on a Scotch heath. The American was also an excellent man, well- to-do in the world, with a fine house, comely wife, high position

▲STAT. 60.] Character of the Scotchman. 59

in a little world of fashion, large reputation, &o. &o. Well, fancy this man confiding to me one day that his brother-in-law was not quite the right thing I " Would you believe," said he, *^ it is now two months since I had to pay a penny for him one day, as we were out riding together, and he has never repaid it yet!''

* When I was in Scotland, I perceived at once, even in the Lowlands, that Scotch worldliness is not like American or Eng- lish. A Scotchman has warm and deep feelings; and if he is selfish, it is, in part, because out of the abundance of his love- power he has a great deal to spend on himself as well a« on his friends. There are those who care nothing for themselves, and care as little for their neighboiurs. Moreover, the Scotchman, however thrifty he may be, has large sympathies, and a strong imagination too. He has reverence for antiquity ; loves old kings and ohiefs even more than modem lords and ladies ; preserves old legends ; imagines a something venerable even in that shrill- voiced demagogue, John £nox ; sings the songs of Bums on moor and heather ; really loves his country, and remembers its ancient fame when he looks on Edinburgh Castle, if not, alas I when he looks on Melrose Abbey ; is capable of being profoundly attached to a cattse, as well as to a person, and in defence of either bears the beating of the worldly storm, as the northern side of his native pines bears the sleet-blast and the clinging ice. In short, in the midst of his coarser nature there is a finer one also, the grain of which is delicate as that of those woods of which musical in- stroments are made. In many of these gentler qualities he is excelled by the Irishman : but then he has — ^what we lack — a robustness like that of the canvas used for storm-sails.

* I should like to know why I am writing you a disquisition on Scotchmen. I suppose it is because I intended to say a few words on theology, in answer to your remark on a tendency to modem Bomanism being a '^ reductio ad absurdum," just as once before I wrote a theological letter to you when I meant to write one about literature and poetry.

* Friday^ January 25. P.S. — My letter was late for the post. . . . My vindication of Scotland was, I suppose, a vindication of her from an imaginary charge — that of her being implicated in the ordinary '* nineteenth century '' character, with which she is

6o Life of Sir William Ravcafi Hamilton. [1856.

commonlyy but most unjustly associated, even more than England. I might have remembered, however, that I had done what I could in this way in writing my Highland Mary^ to which you had done so much more than justice. In a large part of my poetry, indeed, my purpose has ever been to vindicate some just cause, or to write the epitaph of one unjustly trampled down, and scrape the moss from neglected tombstones.

' Now one word as to the ^'reductio ad absurdum " implied in a tendency to modem Eomanism, i.e. Eomanism seen through the mist of modem associations, party impressions, social antago- nisms, &c. I will only say that nothing of thi^ kind can be taken by a philosophic mind like yours for more than, at most, an im^ pression as distinguished from opinion, and must even be contrasted with conviction.*

Mr. DeVere then fills fourteen closely- written pages with a very ably-argued contention, that the charges brought against the Boman Church were necessarily incurred by a spiritual body, composed of sinful human beings, acting through many successive centuries upon a sinful world, and that they were of the same kind as the member of the Church of England felt to be unjust when brought against his Church by deserters. He concludes his letter by turning from the general argument to the following personal application of it : —

' I do not want to urge a new set of d priori impressions on you, in place of those so common among us, and to which I was once myself servile indeed, though I suspected it not. That would not be fair. I only want to point out the absolute necessity of shaking off all such vague impremons, and all that is not really and truly theological and philosophical in our method of thought, if we would reach truth on the most important of aU points, and discriminate between the authentic and the spurious forms of God's Bevelation. I have observed that those sorts of impressions and social traditions have often even more influence on the thoughtful than the thoughtless, if they be not on their guard against them, or if they fight the battle of theology with the left hand, while more earnestly interested in political or philosophic avocations. Once more, adieu. Yours affectionately.'

ABTAT. 50.] Non- Version. Henry Taylor. 6i

It oottld not reasonably be ezpeoted that Hamilton, with such work on his hands as the writing of his Elements of Quaternions^ and with his thoughts absorbed in it, could find time or freedom of mind sufficient to enable him to grapple with so accomplished and earnest a controversialist as his friend. In his reply, accord- ingly, he is content with intimating that his previous convictions remained unshaken, while candidly admitting the fact that he was conscious of having his share of bias and prepossession.

From Sir W. E. Hamilton to Aubrey De Vbre.

' Obsertatobt, January j 31, 1866.

S . . I like what you say about Scotland, and am not offended by your remarks on Theology — though not at all afraid of your succeeding in con- or per- verting me. In my Lectures on Quater^ nions there occur all sorts of '* Versions '' ; such as iZeversions, Proversions, and TVan^versions, with reference to rotations in geometry ; but one of them is a iVon- version I Even mathematics, you see, may supply a joke sometimes — such as Pope somewhere says, does he not P that *' gentle dulness loves."

* Of course I' admit that early impressions must in my case, as in most others, leave a very lasting trace — and that I do not pre- tend to be unbiassed — as indeed who can be P . . .'

In rejoinder to the above, Aubrey De Yere discharges a few Parthian shots, to be met with towards the conclusion of the following letter, the preceding part of which I insert on account of its interesting reference to his own poetry, and his, as it appears to me, admirable characterisation of the poetiy of Sir Henry Taylor.

From Aubrey De Vere to Sir W. R. Hamilton.

* CiTBRAOH Chabb, February 1, 1856.

*. . . There is no quality I should be better pleased to see attributed to my poetry than Passion — partly perhaps because some not unfriendly critics have thought that its chief defect was

62 Life of Sir William Rowan Hamilton. [1856.

a JMk of Passion. Henry Taylor suggests this in the form of a query ^ in a letter which assuredly is oomplimentaiy enough^ and which, if I can find it, I will send to you (but you must let me have it again), though you are not to suppose I believe in all the kind things he says also of my verse. I was so ungracious as to answer his question by saying that I doubted very much whether it was in Passion that