DCSB ItBRAKY
 
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 V 
 
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 UCSB LIBRARY 
 
 /6 
 
 / 
 
 THE 
 
 LAWS OF VEESE.
 
 LONDON: PBINTED BY 
 
 8POTIISWOODE AND CO., NEW-STREET SQUABB 
 AND PABLIAJIENT STREET
 
 THE 
 
 LAWS OF VEESE 
 
 OB 
 
 PRINCIPLES OF VERSIFICATION 
 
 in Metrical raniation : 
 
 TOGETHER WITH AN ANNOTATED BEPRINT OP 
 
 THE INAUGUKAL PRESIDENTIAL ADDRESS TO THE 
 
 MATHEMATICAL AND PHYSICAL SECTION OF THE 
 
 BRITISH ASSOCIATION AT EXETER 
 
 BY 
 
 J. J. SYLVESTER, LL.D., F.R.S. 
 
 Of the Institute of France, the Royal Academies of Science of Berlin, Gottinyen, 
 
 Naples, Milan, ttc. &c. <kc.; 
 Examiner in Mathematics to the University of London. 
 
 LONDON : 
 LONGMANS, GKEEN, AND CO. 
 
 1870.
 
 TO 
 
 MATTHEW ARNOLD, ESQ., D.C.L 
 
 EOME\YHILE PROFESSOR OF POETRY AT THE UNIVERSITY OF OXFORD, 
 
 A CONSUMMATE MASTER OF THE ART, 
 
 IN GRATEFUL RECOGNITION OF 
 
 MUCH VALUABLE CRITICISM AND GENEROUS ENCOURAGEMENT 
 
 RECEIVED AT HIS HANDS, 
 
 gebirate 
 
 THIS ATTEMPT TO DISPLAY AND EZEMPLIFY 
 
 THE LAWS OF VERSE.
 
 ' Non ante volgatas per artes 
 
 Verba loquor socianda chordis.' 
 
 HOB. Car. iv. 9. 
 
 By methods ne'er promulged before, 
 Fit speech o'er lyric chords I pour. 
 
 riaAaio irapoifua on xffl^i"a Ta Ka\d tffTiv airy ? 
 
 PLATO, Socrat. in Cratylus. 
 
 ' Untwisting all the chains that tie 
 The hidden soul of harmony.' 
 
 MILTON, L 1 Allegro.
 
 PBEEACE. 
 
 THE technical or material part of versification 
 (the art of rhythmical composition), like that of 
 any other of the fine arts, is. capable of being 
 reduced to rules and referred to fixed principles. 
 I wish the title of LAWS OF VERSE, OR 
 PRINCIPLES OP VERSIFICATION EXEMPLIFIED, 
 to be understood in the sense of an attempt to 
 illustrate this proposition by examples. This is 
 not a treatise on Prosody, neither is it a discourse 
 de arte Poeticd. Moreover I do not profess to 
 lay down a systematic body of doctrine on the 
 Art of Versification, but merely to indicate, in 
 the way of cursory comment, chiefly contained in 
 notes to the text, the existence of such a doctrine, 
 and the possibility of moulding it into a certain 
 definite organic form. In poetry we have sound, 
 thought, and words (i. e. thought clothed in 
 sound) ; accordingly the subject falls naturally 
 into three great divisions, the cogitative, the 
 expressional, and the technical ; to which we 
 may give the respective names of Pneumatic, 
 Linguistic, and Rhythmic. It is only with
 
 10 Preface. 
 
 Rhythm that I profess to deal. This again 
 branches off into three principal branches Metric, 
 Chromatic, and Synectic. 
 
 Metric is concerned with Accent, Quantity, 
 and Suspensions; the latter including the theories 
 of Pauses, Rests, and Synthesis or Syllabic 
 Groupings. I touch very briefly on this branch, 
 accepting, in regard to it, the doctrine of Edgar 
 Poe, given in his essay on the ' Rationale of Versi- 
 fication,' rendered, as I think, more complete by 
 my introduction into it of the theory of the silent 
 syllable or rest. 
 
 Metric is concerned with the discontinuous, 
 Synectic with the continuous, aspect of the Art. 
 Between the two lies Chromatic, which com- 
 prises the study of the qualities, affinities, and 
 colorific properties of sound.* Into this part of 
 the subject, except so far as occasionally glancing 
 
 * I notice that in Mr. Tom Hood's ' Kules of Ehyme ' certain 
 of the principles of Chromatic have been incidentally discussed 
 and gone into (as regards the powers of initial consonants) in 
 some detail. Chromatic may be studied with respect to Matter, 
 Mode, and Relation. Its matter may be consonantal, vocal, or 
 diphthongal ; its mode may be taken with reference to con- 
 gruity, opposition, and transition or modulation. As to relation, 
 it may be regarded as a co-ordinate factor of Synectic or of 
 Expression, or per se, i.e. with regard to the purely sensuous 
 impression ; which last, again, will bring under view the po- 
 sition as initial, terminal, or medial. This is a mere hasty 
 and superficial view of the subject : in things of the fancy a 
 little play of fancy may be permitted.
 
 Preface. 1 1 
 
 at its existence and referring to its effects, I do 
 not profess to enter.* My chief business is with 
 Synectic. 
 
 This, also, on a slight examination, will be 
 found to run into three channels Anastomosis, 
 Symptosis, and between them the main flood of 
 Phonetic Syzygy.f But it may be asked pre- 
 liminarily how can Symptosis, which deals with 
 rhymes, assonances (including alliterations, so 
 called), and clashes (this last comprising as well 
 agreeable reiterations, or congruences, as unplea- 
 sant ones, i.e. jangles or jars), how, I say, can a 
 theory dealing with discreet matter of this kind, 
 come under the head of Synectic : but the answer 
 is easy, for if the elements with which it deals, 
 its matter, is discontinuous, not so is the object to 
 
 * I cannot resist the temptation of quoting here from a daily 
 morning paper the following unconsciously chromatic passage 
 descriptive of the total eclipse of the moon, that grand spectacle 
 of nature, which I witnessed and watched yesternight from 
 Woolwich Common in front of my house, which in a few days I 
 am to quit : ' The last portion of the shadow of the earth had 
 been passed thrcmgh by the moon, which then again sailed " in 
 its full orb of glory through the dark blue depth.' " The beauty 
 of sound in this description is almost as delicious as the im- 
 pression of the sight of nature which it recalls. 
 
 t I hare heard of practical use being made by some to whom 
 the report of it has reached of this salient principle of phonetic 
 syzygy, alike for proving, correcting, and strengthening their 
 verses. A lady also has conveyed to me through a mutual friend 
 the conviction of the value and fertility of this principle, in its 
 application to musical composition, which has forced itself on her
 
 12 Preface. 
 
 which it tends (its form) ; just, for instance, as in 
 an iron shield or curtain or a trial target, the 
 bolts and screws and rivets are separate, but 
 serve to consolidate and bring into conjunction 
 the plates, and to give cohesion and unity to the 
 structure. 
 
 Anastomosis regards the junction of words, the 
 laying of them duly alongside one another (like 
 drainage pipes set end to end, or the capillary 
 terminations of the veins and arteries) so as to 
 
 notice. I conceive that the method of triadic analysis which I have 
 employed in the genesis and distribution of the principles of lyrical 
 poetry, is founded on the nature of things and not on an arbitrary 
 subjective rule of classification. I can honestly aver that I was 
 not on the look-out for any such an arithmetical law, but that 
 starting originally with phonetic syzygy alone as my distinctive 
 principle, the connexions and ramifications which grew out of 
 and around it, grouped themselves as it were spontaneously, 
 according to this law of trichotomy, each joint of the arbore- 
 scence at which I successively arrived in my analysis, throwing 
 off from itself three branches. It may be the case that a 
 similar ternary law of development would apply to music, 
 painting, sculpture, in a word, to the elucidation of the higher 
 principles of all the fine arts. Following out this clue it is 
 conceivable that we might succeed in laying the foundations of 
 a science of Comparative Aesthetic, or at least of a general 
 A esthetico-technic. Of one thing I have no doubt, which is, that 
 when the analysis of principles which I have here faintly indi- 
 cated has been carried to its full term, we shall be in possession 
 of a system of rules, by which the criticism of the technical part 
 at least of lyrical poetry may be reduced to the form of propo- 
 sitions capable of being logically argued and debated, and en- 
 tirely removed from that indefinite region of taste which, like 
 the so-called discretion of a judge, does not admit of being made 
 the subject of rational discussion.
 
 Preface. 13 
 
 provide for the easy transmission and flow of 
 breath (unless a suspension is desired for some 
 cause, or is unavoidable) from one into the other. 
 
 The great topic of Phonetic Syzygy has some- 
 thing in common with each of these flanking 
 principles. In matter it agrees with Symptosis, 
 in form (in respect of operating with distinct 
 reference to continuity of impression) it borders 
 upon Anastomosis. 
 
 We look to Metric for correctness of form, to 
 Chromatic for beauty of color ; it is to Synectic, 
 and to its main branch Syzygy, that we must 
 attend in order to secure that coherence, com- 
 pactness, and ring of true metal, without which 
 no versification deserves the name of poetry. It 
 is to Syzygy that I have called most attention 
 in my annotations, and it was with this prin- 
 ciple exclusively that at the outset I intended 
 to deal. The subject has grown upon me in 
 passing through the press ; and the book has 
 been built up in a most unforeseen and un- 
 premeditated manner, which I state in order to 
 account for the numerous dislocations, ill-fittings, 
 gaps and other irregularities of structure, as well 
 as occasional repetitions, which I must beg the 
 courteous reader to overlook or excuse. In fact 
 the work may be truly said to have been born,
 
 14 Preface. 
 
 cradled, and nurtured in the press, nay often 
 to have fallen asleep there, to awake like a baby 
 refreshed, hungry and calling for more. I began 
 with a single fly-leaf containing a translation of 
 'Tyrrhena Regum' for distribution among the 
 audience at the Penny Reading where I was to 
 recite the ode. This, doubled subsequently into 
 a half-sheet, augmented with notes, assimilating 
 to itself fresh matter, and leading me off into 
 unintended analyses and discussions, has grown 
 up by successive stages and additions into its 
 present form, the simulacrum of a full-fledged 
 book to the surprise of no one so much as that 
 of the originator of its being. 
 
 In my translations from Horace, especially in 
 the first of them, I have aimed at a high ideal of 
 fidelity to the original probably at a higher one 
 than has been achieved or even attempted in 
 Metre since the days of Milton. What success 
 has attended this effort, philologically speaking, 
 I must leave to others to determine ; but I can 
 speak with some confidence as to the agreeable 
 musical impression made on audiences illiterate 
 as well as literate by its recital, and may do 
 so without violation of modesty, as an evidence 
 of the scientific correctness of my principles of 
 versificatory construction.* The great law of 
 
 * Starting from the safe postulate, that Horace's ear was as
 
 Preface. 15 
 
 Continuity (continuity of sound and continuity 
 of mental impression) has been my guiding star 
 throughout. Some of my readers may chance to 
 remember that I laid much stress upon this 
 principle in the inaugural address delivered by 
 me as President of the Mathematical and Physical 
 Section of the British Association for the Ad- 
 vancement of Science, at Exeter. I went, on 
 that occasion, so far as to say that Mathematics 
 under its existent aspect might be defined as the 
 Science of Continuity. I have thought, then, 
 that this would be a not unsuitable occasion for 
 republishing the address in a separate form, as 
 I have received frequent applications for copies of 
 it, with which I have not had the means of com- 
 plying. 
 
 The address in an abridged form, under the title, 
 ' A Plea for the Mathematician,' was published 
 by request of the Editor of Nature in two num- 
 bers of that valuable journal, with additional notes, 
 which are here reproduced. In an appendix will 
 be found the letters of a correspondence which grew 
 out of these notes, concerning the improper de- 
 scription of Kant's doctrine of Time and Space, 
 common with Scotch and English writers on 
 
 perfect as his taste is irreproachable, I have been able to apply 
 syzygetic principles in aid of settling two disputed readings in 
 the Latin text of ' Tyrrhena Kegum,' (Od. iii. 3, 29,) lines 6 
 and 34.
 
 16 Preface. 
 
 Mental Science. This very mischievous locution, 
 which although countenanced by the practice of 
 some of our best authors, suggests a view of Kant's 
 doctrine diametrically opposed to its most charac- 
 teristic feature, and that which differentiates it 
 from all preceding systems of Philosophy, it is 
 believed has hereby received its death-blow, 
 and must henceforth disappear from the face of 
 English literature. 
 
 P.S. In the prefatory letter to the volume of 
 collected 'Lay Sermons, Addresses, and Reviews,' 
 with which Professor Huxley has recently grati- 
 fied the public, I notice some remarks which he has 
 made on the inaugural address above referred to. 
 He says, addressing himself to Dr. Tyndall : ' In 
 the same paper (On the Educational Value of 
 the Natural History Sciences) there is a state- 
 ment concerning the method of the mathematical 
 sciences, which repeated and expanded elsewhere 
 brought upon me, during the meeting of the 
 British Association at Exeter, the artillery of 
 our eminent friend Professor Sylvester. 
 
 ( No one knows better than you do, how readily 
 I should defer to the opinion of so great a mathe- 
 matician if the question at issue were really, as 
 he seems to think it is, a mathematical one. But
 
 Preface. 17 
 
 I submit, that the dictum of a mathematical 
 athlete upon a difficult problem which mathe- 
 matics offer to philosophy, has no more special 
 weight than the verdict of that great pedestrian 
 Captain Barclay would have had in settling a 
 disputed point in the physiology of locomotion.' 
 
 To this I need only reply that I am not aware 
 what reason Professor Huxley has for attributing 
 to me the opinion that it is a mathematical ques- 
 tion to determine the place of mathematics among 
 the sciences. I have only ventured to express 
 my belief that had the distinguished lay preacher 
 been better acquainted with the real aim and 
 scope of mathematics he would scarcely have 
 committed himself to saying that the teaching of 
 languages is of the same general nature as * ma- 
 thematical training.' I remain of that belief 
 still. Supposing that Professor Huxley had had 
 no acquaintance with the anatomy, physiology, and 
 habits of the human subject, would he have felt 
 himself justified in writing as he has done, * On 
 the Place of Man in Nature ;' or, supposing he 
 had done so, would what he wrote have been 
 likely to achieve the world-wide celebrity of his 
 actual work on the subject ?* 
 
 * I may possibly have misquoted the title. I remember 
 seeing a translation into German of the book I mean, lying on 
 the counter of an Italian bookseller in Florence.
 
 18 Preface. 
 
 He further adds, * The genius which sighs for 
 new worlds to conquer beyond that surprising 
 region in which " geometry, algebra, and the 
 theory of numbers melt into one another like 
 sunset tints, or the colours of a dying dolphin," 
 may be of comparatively little service in the cold 
 domain (mostly lighted by the moon, some say) 
 of philosophy. And the more I think of it, the 
 more does our friend seem to me to fall into the 
 position of one of those " verstandigeLeute," about 
 whom he makes so apt a quotation from Goethe. 
 Surely he has not duly considered two points. 
 The first, that I am in no way answerable for the 
 origination of the doctrine he criticises : and the 
 second, that if we are to employ the terms obser- 
 vation, induction, and experiment, in the sense in 
 which he uses them, logic is as much an observa- 
 tional, inductive, and experimental science as 
 mathematics ; and that, I confess, appears to me 
 to be a reductio ad absurdum of his argument.' 
 
 With regard to the first of * the two points ' 
 here raised, I would say that Professor Huxley, 
 whether or not answerable for the origination, is 
 certainly answerable for the vindication and 
 propagation, with ' repetition and expansion,' of 
 the erroneous doctrine which formed the subject 
 of my criticism. I felt no call to go into so
 
 Preface. 19 
 
 purely subjective a question as that of ascertain- 
 ing the sources from which he had drawn the 
 erroneous opinions which found in him their 
 advocate. 
 
 As regards the second of the two points I am 
 perfectly at a loss to understand how Professor 
 Huxley can suppose that the observational, in- 
 ductive, and experimental processes which I 
 have referred to and illustrated in their bearing 
 on the illimitable sphere of mathematical dis- 
 covery and invention, can be shown to have any 
 place in the confined and circumscribed area of 
 pure logic. In a word, without the slightest 
 intention of saying anything unkind or dis- 
 courteous, I cannot conceal my opinion that what 
 my estimable and eminent adversary calls a 
 reductio ad absurdum might with much greater 
 propriety be termed a deductio ex absurdo: for it 
 seems to me absurd to suppose that there exists 
 in the science of pure logic anything that bears 
 a resemblance to the infinitely developable and 
 interminable euristic processes of mathematical 
 science. 
 
 J. J. S. 
 
 ATHENAEUM CLUB, 
 July, 1870.
 
 CONTENTS. 
 
 Laws of Verse, or Principles of Versification, exemplified 
 in Metrical Translations. 
 
 PAGE 
 
 I. TBANSLATION OF HOE. OD. iii. 29. 
 Exhibition of perdualistic or dichotomous plan . 25 
 
 Original 26-28 
 
 Translation 27-31 
 
 Notes 30-41 
 
 Criticism of Conington's Version .... 42 
 Function of Kyme in Verse ..... 44 
 Laws of Anastomosis and Syzygy .... 45 
 The Alcaic Stanza formulated .... 47 
 Evidence of Horace's native Mathematical Power . 48 
 
 Poeta fit, non nascitur 49 
 
 IL SCHJLLEK ' Die Ideale ' 49 
 
 Theory of the Diphthong . . . . . 50 
 
 III. UHLAND ' Des Goldschmieds Tochterlein ' . 53 
 
 IV. SCHILLER 'Cassandra' i .... 56 
 Theory of Alliteration ib. 
 
 V. GOETHE ' Trost in Thranen ' . . .62 
 Formation of the feminine transcendental pluper- 
 fect superlative adjective 63 
 
 Synectic, the Author's right-of-way into the Realm 
 
 ofKhythm 64 
 
 ' Synectic ' explained ...... ib. 
 
 Concerning modern Metric and accentual Feet . 65 
 
 Metre in terms of Music 66
 
 22 Contents. 
 
 PAGE 
 
 Ehythmical rests 67 
 
 Metric Criticism of opening lines of 'Bride of 
 
 Abydos,' &c ib. 
 
 Imaginary Khythmical time 69 
 
 Success of experimental Eecital of Example I. . 70 
 
 VI. HOE. OD. in. 29 Earlier Version . . .71 
 
 VII. SCHILLEB ' An den Friihling ' . . . .74 
 
 VIII. BLTTMAUKB 'AndieDonau' .... 75 
 
 Spontaneous Generation of the present Version . ib. 
 
 IX. UHLAHD ' Der Wirthin Tochterlein ' . . . 76 
 
 X. KUCKEBT 'Die Locke der Begrabenen' . . 77 
 
 XL UHLAND ' Das Schloss am Meere ' ... 79 
 
 Syzygetic Key 81 
 
 ANONYMOUS POEMS. 
 
 XII. The Evening Star 81 
 
 XIII. Acrostic . . 82 
 
 XIV. Winter . . . . .' ! . .- - : . ib. 
 XV. To an Ink-spot upon a Lady's cheek ... 83 
 
 XVI. Melancholy ib. 
 
 XVII. April 30 85 
 
 XVIII. Indifference 86 
 
 XIX. Kemonstrance . . . .."*. 87 
 
 XX. Faith. .<*".'...- . 88 
 
 XXI. Kepler's Apostrophe 89 
 
 XXII. ' Occhi ! stelle immortali ' . -1 .' . k ' . . 91 
 
 XXIII. What's in a Name ? . . .:.-.-. . ib. 
 
 XXIV. Hor. Od. HI. xxvii. 25. The Story of Europa . 93 
 Notes Mediae fraudes : its twelve meanings . 95 
 
 Virginwn culpts and Professor Newman . 96 
 Nomina : transcendental significance of the 
 
 plural form . .;.'* . . . . 97
 
 Contents. 23 
 
 Inaugural Address to the Mathematical and Physical 
 Section of the British Association, at Exeter, August, 
 1869. 
 
 PAGE 
 
 Introductory Remarks . . . . . . .101 
 
 Vindication of the mathematician as man ' Homo mathe- 
 
 maticus' . 105 
 
 Professor Huxley's opinions on mathematical science his 
 
 parallel of grammatical and mathematical training 106 
 Mathematics as dependent on invention and observation 
 
 Examples of mathematical euristic . . .108 
 Contact-points of faith and knowledge in mathematics . 114 
 Mathematical discovery dependent on observation of ma- 
 thematical phenomena . . . . . .115 
 
 The theory of reducible cyclodes 117 
 
 The place of physical science relative to mathematics . 119 
 Healthful effect of mathematical meditation on mind and 
 
 body Dii majores of the mathematical Pantheon . 121 
 Mental and spiritual gratification furnished by mathe- 
 matics 123 
 
 Mathematics the science of continuity . . . .125 
 Examples of mathematical relations . . . .127 
 
 Concluding remarks 129 
 
 Postscript Letter from Dr. Jacobi ib. 
 
 APPENDIX. 
 
 On the Incorrect Description of Kant's Doctrine of 
 Space and Time common in English writers. 
 
 Correspondence on the part of: 
 
 G. H. Lewes 131 
 
 T. H. Huxley 132
 
 24 Contents. 
 
 PAGE 
 
 C. M. Ingleby" 133 
 
 J. J. Sylvester ib. 
 
 G.H.Lewes 134 
 
 G. Groom Kobertson- ... . . . 138 
 
 W. H. Stanley Monck ib. 
 
 J. J. Sylvester. 140 
 
 George Henry Lewes 143 
 
 "W. H. Stanley Monck 146 
 
 Catena of passages from the foregoing correspondence 
 
 bearing on Mr. Lewes' final letter .... 148 
 
 Illustration of author's position drawn from Mr. Herbert 
 
 Spencer's supposed refutation of Kant . . .151
 
 LAWS OF VEBSE, 
 
 ERRATA. 
 
 Page line for read 
 
 9 ... 11 ... Poeticd ... poeticd. 
 
 10 ... 2 ... principal branches ... principal sections. 
 
 21 ... 23 ... dele adjective. 
 
 23 ... 16 ... dele from Healthful to body. 
 
 37 ... 29 (end of 2nd par.) page 1 ... page 25. 
 
 47 ... 7 ... or as, say, ... or as we say. 
 
 59, note, line 6, dele the second besides. 
 
 73 ... 7 ... smoke ... smooth. 
 
 80 ... 11 ... sigh ... dirge. 
 
 98 ... 24 ... 56.] ... 26.] 
 
 150 ... 11 ... read (7) So far from averring that the former ' 
 
 (form of understanding) ' is " indefensible," it is what I declare 
 to be true.' 
 
 And in like manner each of the eight duads above may be ren- 
 dered into separate stanzas containing a single and distinct 
 subject or image. It would of course be easy, and not uninstruc- 
 tive, to arrange this paradigm under the form of a tree bearing 
 two stems, four branches, eight branchlets, and sixteen twigs or 
 terminals.
 
 24 Contents. 
 
 PAGE 
 
 C. M. Ingleby' 133 
 
 J. J. Sylvester & 
 
 G. H. Lewes 134 
 
 G Oroom Robertson 138
 
 LAWS OF VEESE, 
 
 OR, 
 
 $ rinripifs nf 
 
 EXEMPLIFIED IN METRICAL TRANSLATIONS. 
 I. TRANSLATION OF HOR. OD. III. 29. 
 
 Originally printed for Recital and Distribution at a Penny Reading held in 
 the National School Rooms, Eltham, December 22, 1869. 
 
 EXHIBITION OF THE PEBDUAXISTIC OB DICHOTOMOTTS PLAN OF 
 THE CONSTBUCTION OF HOB. CAB. III. 29, 
 
 116 The ODE. 
 
 1 8 Extroitive. 9 16 Introitive. 
 
 1 4 Invitation. 9 12 Impersonal. 
 
 5 8 Exhortation. 13 16 Personal. 
 
 1 2 Come into the country. 9 10 Life like a river. 
 
 3 4 Leave Rome. 11 12 The past indefeasible. 
 
 5 6 The season favours. 13 14 He defies fortune. 
 
 7 8 Throw aside care. 15 16 He has nothing to lose. 
 
 [The numbers refer (o the order of the stanzas.'] 
 
 And in like manner each of the eight duads above may be ren- 
 dered into separate stanzas containing a single and distinct 
 subject or image. It would of course be easy, and not uninstruc- 
 tive, to arrange this paradigm under the form of a tree bearing 
 two stems, four branches, eight branchlets, and sixteen twigs or 
 terminals.
 
 26 
 
 Q. HORATII FLACCI CARMINUM 
 
 IIL 29. 
 
 AD MAECENATEM. 
 
 TYRRHENA regum progenies, tibi 
 Non ante verso lene merum cado, 
 Cum flore, Maecenas, rosarum, et 
 Pressa tuis balanus capillis 
 
 Jamdudum apud me est. Eripe te morae : [v. 
 Ne semper udum Tibur, et Aefulae 
 Declive contempleris arvuru, et 
 Telegoni juga parricidae. 
 
 Fastidiosam desere copiani et [ix. 
 
 Mole"m propinquam nubibus arduis : 
 Omitte niirari beatae 
 
 Fumum et opes strepitumque Romae. 
 
 Plerumque gratae divitibus vices, [xiu. 
 
 Mundaeque parvo sub lare pauperum 
 Coenae, sine aulaeis et ostro, 
 Sollicitam explicuere frontem. 
 
 Jam clarus occultum Andromedae pater [xvn. 
 Ostendit ignem : jam Procyon furit 
 Et Stella vesani Leonis, 
 Sole dies referente siccos.
 
 AN ODE OF HOEACE. 
 in. 29. 
 
 To MAECENAS. 
 
 BIRTH of Tyrrhenian regal line ! 
 In unstooped cask, a mellow brew 
 Roses and myrrh those locks of thine 
 Fresh pressed Maecenas ! to bedew, 
 
 Long wait thee here ! Shake off delay, [5 
 
 Nor spray -washed Tibur still gaze on 
 Nor Aefule's slope, nor heights survey 
 Of parricidal Telegon. 
 
 Quit gorged Profusion, and the pile [9 
 
 That soars to loftiest clouds akin ; 
 Pause in admiring for awhile, 
 Thrice-happy Home's, smoke, traffic, din. 
 
 Ofttimes the rich love change ; walls bare [13 
 And trim meals lacking purple woof 
 Have smoothed their wrinkled brow of care, 
 'Neath many a poor man's lowly roof. 
 
 Now Andromede's bright Sire doth show . [17 
 Light erewhile hid : now Procyon's rays 
 Flash, and mad Leo's, as below 
 The Sun draws back dry summer days.
 
 28 Principles of Versification exemplified. 
 
 Jam pastor umbras cum grege languido [xxi. 
 Eivumque fessus quaerit, et horridi 
 Dumeta Silvani : caretque 
 Eipa vagis taciturna ventis. 
 
 Tu civitatem quis deceat status [xxv. 
 
 Curas, et Urbi sollicitus times, 
 Quid Seres et regnata Gyro 
 
 Bactra parent Tanaisque discors. 
 
 Prudens futuri temporis exitum [xxix. 
 
 Caliginosa nocte premit Dens, 
 Ridetque, si mortalis ultra 
 
 Fas trepidat. Quod adest memento 
 
 Componere aequus : cetera fluminis [xxxm. 
 
 Eitu feruntur, nunc medio alveo 
 Cum pace delabentis Etruscum 
 In mare, nunc lapides adesos, 
 
 Stirpesque raptas, et pecus et domos [xxxvu. 
 Volventis una, non sine montium 
 Claniore vicinaeque silvae, 
 Quum fera diluvies quietos 
 
 Irritat amnes. Ille potens sui [XLI. 
 
 Laetusque deget, cui licet in diem 
 Dixisse, ' Vixi : eras vel atra 
 Nube polum Pater occupato 
 
 ' Vel sole puro : non tamen irritum, [XLV. 
 
 Quodcunque retro est, efficiet : neque 
 Diffinget infectumque reddet, 
 Quod fugiens semel hora vexit.'
 
 HOT. Od. III. 29. 29 
 
 Now with spent flock tired shepherds hie [21 
 
 To shades and brook and thickets dank 
 Of Silvan hoar : and stray winds die 
 And all lies hushed, upon the bank. 
 
 Thou heed'st what form the State beseems, [25 
 And watchful fear'st for Rome from far 
 What Ind or realm of Cyrus schemes, 
 Bactria or Tanais rent with war. 
 
 Farseeing God ii murkiest night [29 
 
 Enshrouds of future years the goal, 
 And smiles if Man in fate's despite 
 Frets his brief hour : With steadfast soul 
 
 Set right the present ! all besides [33 
 
 Doth onwards like the River flow, 
 That now in smooth mid-channel glides 
 To join Etruria's sea below ; 
 
 Now when fierce floods stir its dull rills, [37 
 
 With trunks upwrenched and waveworn stone, 
 Midst roar of neighbouring Avoods and hills, 
 Flocks, herds, and houses, whirls in one. 
 
 Lord of Himself and blest shall prove. [41 
 
 He who can boast from day to day, 
 * I've lived : to-morrow let high Jove 
 Black cloud or sunshine, as he may, 
 
 ' Pour o'er the Pole ! what's come and gone [45 
 To frustrate, doth defy his power; 
 Or aught to unshape or make undone, 
 Once ravished by the flying hour.'
 
 30 Principles of Versification exemplified* 
 
 Fortuna saevo laeta negotio, et [XLIX. 
 
 Ludum insolentem ludere pertinax, 
 Transnmtat incertos honores, 
 Nunc mihi, mine alii benigna. 
 
 Laudo manentem : si celeres qnatit [LIU. 
 
 Pennas, resigno quae dedit, et mea 
 Virtute me involve,, probamque 
 Pauperiem sine dote quaero. 
 
 Non est meum, si mugiat Africis [LVII. 
 
 Mains procellis, ad miseras preces 
 Dectirrere ; et votis pacisci, 
 Ne Cypriae Tyriaeve merces 
 
 Addant avaro divitias mari. [LXI. 
 
 Turn me, biremis praesidio scaphae 
 Tutum, per Aegaeos tumultus 
 Aura feret geminusque Pollux. 
 
 NOTES. 
 
 1.] I propose as an alternative rendering -what followsbelow: 
 
 Tyrrhenian progeny of kings I 
 In unstooped cask a mellow brew 
 Roses and balm-drawn myrrh-droppings 
 Thy hair Maecenas to bedew, 
 
 I hesitated, and chopped and changed a long time, as my 
 printers can too well attest, between the two readings, ' Birth of 
 Tyrrhenian' and 'Tyrrhenian, birth of; and yet it is as certain 
 as any proposition in Euclid can be that the former is the proper 
 order of the words. The latter, it is true, has in its favour acloser 
 correspondence with the original, and the fact of the initial T 
 being a crisper and grander opening sound than the B ; but thi s
 
 HOT. Od. III. 29 Notes. 31 
 
 Fortune at work with savage glee [49 
 
 On mocking game, remorseless bent, 
 Shifts her light favors, now to me, 
 To another now, beneficent. 
 
 I greet her stay : but if anew [53 
 
 She shakes swift wings, her gifts abjure 
 And wrapped in my own virtue woo 
 Poverty, portionless but pure. 
 
 Not mine, if straining topmasts roar [57 
 
 'Neath Afric's storms, with piteous prayers 
 Or bargaining vows each God to implore, 
 Lest Cyprus' or fine Tyrian wares 
 
 Add treasure to the ravening seas ! [Gl 
 
 Me then, upborne on pair-oared craft, 
 Shall twin-lit Pollux and the breeze, 
 Safe through the tossed Aegean, waft. 
 
 cannot outweigh the double objection, 1st, of the b in ' birth' 
 following the in ' Tyrrhenian,' contrary to the laws of Anasto- 
 mosis ; and, 2nd, of the number and measure of ' Tyrrhe ' being 
 to the number and measure of ' Tyrrhenian birth of re,' as 1:3; 
 whereas, in the contrary order, the corresponding ratio is as 2 : 3, 
 which latter, by the principles of Symptosis (here applying to 
 the clash or congruence of the open e sounds) is preferable, espe- 
 cially at the opening of the piece, as being less suggestive of 
 subdivision of measure. I use the word clash here in no bad sense 
 (for which the word jar or jangle may be reserved), but to signify 
 generally the relation between two sounds strongly recalling each 
 other, which may be agreeable or offensive (scarcely ever neutral) 
 according to the circumstances in which it occurs. When agree- 
 able, for want of a better term, a clash may provisionally be styled 
 a congruence, when offensive, a jar. Thus, ex. gr., rhymes and 
 alliterations (properly employed) are of the nature of clashes. It
 
 32 Principles of Versification exemplified. 
 
 is worth noticing, that a similar struggle for survivorship of the 
 fittest occurs in the second line of my version. On synectic 
 (syzygetie) grounds, ' stirred ' (by virtue of its stirring r's) would 
 be preferable to ' stooped.' but the latter word, besides expressing 
 the precise action of bending down the cask to get the liquor out of 
 it, is chromatically preferable, by virtue of the colorific (and also 
 slightly syzygetie) value of its pure vowel sound. Moreover, 
 the p in ' stooped ' has a fair syzygetie value as corroborative of 
 the B in birth, and precursory to the p in ' pressed,' which itself 
 preconises and ushers in a well-sustained and glittering p syzygy 
 in the two succeeding stanzas. 
 
 ii.] I do not know what authority Forcellini has for interpret- 
 ing verso to mean turned or tilted up. I think I have seen 
 amphorae in a cellar to one of the houses in Pompeii, the natural 
 way of bringing which out for use would be by turning them round 
 in contact with the wall against which they lean. Conington 
 and Newman by their renderings of Nonante -verso, ' unbroached,' 
 ' unop'd,' appear to adopt Forcellini's explanation, and are of 
 course much more likely to be right than I am if they have 
 sufficiently weighed the point.* 
 
 rv.] A sly hit at Maecenas' notorious foible for hair-washes. 
 
 4.] See Suetonius, Aug. 86, referred to in Smith's ' Classical 
 Dictionary ' (art. Maecenas), aud note the word pvpofipfx^s ap- 
 plied by Augustus to Maecenas' dncinnos. 
 
 vi.] I believe the application of semper to udum or contempleris 
 to have been consciously left ambiguous by the Poet. A similar 
 remark applies to plerumque, and to the construction of the whole 
 of the first line of the 4th stanza. This kind of ambiguity or 
 amphibolism is no blemish, but, on the contrary, a source of gain 
 as giving greater fulness to the conception : the mind seizes upon 
 the same word successively in different connections without paus- 
 ing to decide upon which is intended, so that there is no interrup- 
 tion of continuity, the one irremissible sin of lyrical composition, 
 the sole purpose of which is, through the ear and the intellect, 
 twin channels of the soul, to bring the hearer into emotional sym- 
 pathy with the composer. Conington's rendering of semper-udum 
 by never dried seems to me singularly infelicitous : an undried 
 
 * Since the above was in print, Professor Key has kindly furnished me 
 with a passage from Plautus' ' Stichus,' v. 4. 39, which he reads, ' Namque 
 edepol qnam inde subito vel cadus vorti potest ! ' which serves to settle the 
 question, and proves that the common rendering of verto is correct.
 
 HOT. Od. III. 29 Notes. 33 
 
 plain, besides being an unusual form of speech, suggests rather 
 the idea of rheumatism and dampness than that of freshness and 
 coolness, which was evidently in the poet's mind. 
 
 VHI.] The three places named would be seen in succession (in a 
 sort of irregular arc of a circle) from Maecenas' Belvedere, as he 
 turned his gaze further and further away from Horace's farm : an 
 ethical and geographical refutation (if any were needed) of the 
 gratuitous substitution (adopted by Anthon, and Tate before him, 
 and mentioned without reprobation by Conington) of Ut forNe in 
 the 6th line. I abstain from referring to the cacophony of 
 this preposterous misreading, and the pernicious rupture of the 
 resumption (after the usual agreeable break in a single fourth line) 
 of the beautiful syzygy of n sounds. One mischief attending the 
 introduction of printing is the depravation of the phonetic judg- 
 ment of verse consequent upon the appeal being transferred 
 from the ear to the eye. To request a friend to turn his back 
 upon the place of one's abode would be a very Irish way of 
 inviting him to pay a visit to his (the inviter's) part of the 
 country. Any who object to the bifid rendering of CONTEM- 
 PLERIS may substitute so for still in 6 and alway for survey in 8. 
 
 ix.] The continuity of sense makes it, I think, natural to 
 understand copia as referring to some (I do not say what) form of 
 vastness, as, ex. gr., the tiresome extent of the Eue de Kivoli or the 
 interminable Champs Elyses in Paris. Plenty, abundance, or 
 luxury appears to me rather incongruous with what immediately 
 follows. I felt half inclined, upon a sort of cy-pres principle 
 (taking sound and sense into simultaneous account), to substitute 
 loathed profusion for palling plenty.* 
 
 * Since the above was in print, I became unable to resist the phonetic seduc- 
 tion of the words ' loathed profusion," which are so advantageous as regards 
 time, melody, and imitative effect, and accordingly incorporated them in 
 the text. I believe fastidiosus admits of two principal meanings that which 
 conceives disgust, i.e. nice, delicate, squeamish, fastidious ; and that which 
 produces disgust. The former meaning in this connection would imply a 
 personification of copia, which does not seem quite suited to the context ; and 
 between causing loathing and being loathed the difference is not so very 
 wide. Whilst in the act of meditating on the sound and meaning of the 
 words fastidiosam copiam, a splendid Yorkshire pie, the gift of a kind and 
 generous friend in the North, was placed upon my luncheon table, and the 
 meaning of the words in a moment became clear ; for the fulness of the 
 contents occasioned in me such a sympathetic sense of repletion, that I was 
 unable to touch a mouthful, and finally quartered it out untasted among my 
 friends and neighbours, by whom it was gratefully appreciated. I felt, too, 
 at the same time, how well the unctuous, saponaceous sound of the words
 
 34 Principles of Versification exemplified. 
 
 xii.] I have no doubt that opes is intended to conjure Tip the 
 image of piled-np war?s and waggon-loads choking up the 
 thoroughfares, and would unhesitatingly have translated it by 
 glut were it not that that word could only be carried off by 
 a change of form in the verse and translating beatae as glittering^ 
 which, although partially justified by Orelli's paraphrase opulenta 
 ac splendida, I felt would be flying off too wide from the text, 
 to venture on. Smoky, busy, noisy Rome is evidently what is 
 intended : the very identical epithets that I lately saw applied to 
 London in some penny newspaper. 
 
 12.] The common rendering of opes and beatae makes beatae 
 redundant and reduces opes to the position of a tame elephant 
 between two wild ones. It must be, I think, clear to any unpre- 
 judiced mind that beatae is simply ironical or sub- ironical, and 
 'fumumet opes strepitumque' a phrase of collective disparagement. 
 
 15.] For sound and poetical effect, I should of course prefer 
 ' the ' to ' their wrinkled brow of care,' but it seems imperative to pre- 
 serve the distinct antithesis between divitibus and pauperum, which 
 disappears in Conington's and other of the current renderings. 
 
 18.] The reciter will please pronounce the c hard like k, for the 
 sake of supporting the final sound of back in the 4th line. Notice 
 too in 1. 5, ante, how the initial word of this line, besides touch- 
 ing up the colour in off in the same line, lends a very sensible 
 support to the final word in the line following. 
 
 23.] I believe horridus in English public schools is usually 
 translated prickly, which appears rather unmeaning. I suspect 
 that in some way or another it must refer to the particular state 
 of the woods at the time of year in question. In my state of 
 ignorance as to its exact signification I have deemed it per- 
 missible to translate the word according to sound and blind 
 association (not disdainful even of that suggested by the prickly 
 hoar-frost) instead of sense. 
 
 xxiii.] Dryden, in his admirable free version, which he says 
 
 (tolerably well preserved, I think, in the translation) corresponded to the 
 sense of cloying and satedness engendered by the closely-packed and luscious 
 contents of the spacious walls of the pasty. Those who please may read palling 
 plenty, palling luxury, or cloying plenty, or dull repletion, in lieu of loathed 
 profusion. But finally I have made up my mind since the above was set up 
 in print that it is better to accept a personification of copia (for which there 
 is no lack of precedent) and to substitute gorged for loathed as having idealis- 
 tic, quantitative, chromatic, and syzygetic reasons in its favour which col- 
 lectively far outweigh a trifling inferiority to loathed in point of anastomosis.
 
 HOT. Od. III. 29 Notes. 35 
 
 ' he has taken some pains to make his masterpiece in English,' 
 and which we are told Mr. Fox declared to be superior to the 
 original (vide Lowell's Six Essays), takes a strange liberty with 
 the word Silvani, and upon the strength of it invents the line 
 
 1 The Sylvans to their shades retire.' 
 
 Who were these Sylvans, one would like to know. Oddly enough, 
 Francis, following suit, gives 
 
 ' While rustic Sylvans seek the glade ' 
 
 as the equivalent for horridi dumeta Silvani. This Dryden' s self- 
 acknowledged masterpiece is not included in the plan of Mr. 
 Christie's very clever edition of Dryden. In Scott's edition (the 
 second is the one I have seen) the editor has been careless enough 
 to refer persistently to the ode as the 29th of the FIBST book. 
 It is certainly a pity that so magnificent and Rubens-like a 
 canvas should be spoiled by occasional instances of bad taste 
 (which might so easily have been avoided or corrected), such as 
 the daub of the Sylvans just adverted to, and ' The new Lord 
 Mayor ' ! corresponding to Tu civitatcm quis deceat status, in the 
 7th stanza of the original. Imagine Milton committing such a 
 barbarism ! The higher civilization of England must for a time 
 have been submerged after the restoration of the hateful Stuarts. 
 Mr. Lowell (if I remember aright) expresses surprise that 
 Dryden should feel so strongly and so repeatedly give rent 
 to his sense of freedom and unshackledness when having ten 
 syllables in a line to deal with instead of eight. I am more 
 surprised that Mr. Lowell, who is said to write excellent poetry 
 himself, should be surprised by anything of the kind. To me 
 the difference between the two seems like that between bathing 
 in a pond or inland creek as compared with a plunge in the open 
 sea : the very embarras de choix, the sense of infinite variety 
 of combination and unlimited room for disporting the imagina- 
 tion at will has deterred me from more than timidly venturing 
 upon this form of verse, as a miniature-painter would naturally 
 shrink from trying his pencil on a historical canvas. Between 
 octosyllabic and dekasyllabic verse, the interval is as wide as 
 between playing at marbles and bowls, or as between bagatelle 
 and billiards. If we calculate on an average two syllables to a 
 word (and as the true average is less, this is much understating my 
 own argument), we have five words in a line in one case against 
 four in the other, which by the theory of permutations gives a
 
 36 Principles of Versification exemplified. 
 
 facility as 120 to 24, i.e. as 5 to 1. Or, again, let us look to the 
 variety of form (so strangely neglected by all writers on versifi- 
 cation), but so very important an element of the general effect, 
 which depends on the manner in which syllables are combined 
 into words or into word-groups, i.e. groups which read like single 
 words. According to the theory of partitions (this being a case 
 of partition whose permutations count as distinct), the number of 
 forms of groupings for x syllables is 2 X ; accordingly, the advan- 
 tage in dealing with 10 as compared with 8 syllables is as 1,024 
 to 256, i.e. as 4 to 1. Hence we see that the magnified facility 
 of dekasyllabic over octosyllabic verse is not, as at a superficial 
 glance one might suppose, as 5 to 4, but as at the very least 5 or 
 4 to 1. Writers like Conington or Newman have noticed the 
 extreme case of monosyllabic lines, but no one seems to have 
 drawn especial attention to the distinct character and aspect 
 attaching to every different form of syllable groupings in a line. 
 The working out of this theory belongs to the subject of rests, 
 there being an incalculably small but still perfectly sensible inter- 
 ruption of breathing between every two groups of syllables ; the 
 doctrine of caesura and of line-stops is the very self-same theory 
 extended to the case of compound groups. I may notice as the 
 result of a careful and tolerably extensive induction that an octo- 
 syllabic quatrain (which might, arithmetically speaking, consist 
 of 32 simple groups), if it contain more than 24 will, in general, 
 be found defective in tension: 21 or 22 maybe reckoned as high 
 concert pitch. As another useful piece of statistical information 
 I may mention here, that for the purpose of easy but not diffuse 
 rendering from Latin into English, the number of English should 
 be to the number of Latin syllables, in a ratio intermediate to 
 and |. I of course suppose that the number of lines is main- 
 tained the same in the original and translation, i.e. that the ren- 
 dering is line for line, although not necessarily line into line. 
 
 24.] The comma in this line is inserted to indicate that a slight 
 pause should be introduced to give effect to the word hush. The 
 fact is one wants a double system of punctuation in verse 
 one to indicate the grammatical construction, and another the 
 emissions of breath ; and in default of this, it becomes necessary 
 to lean, sometimes to one principle and sometimes to the other, 
 in following the actual system.* 
 
 A friend informs me that an edition of the New Testament (very hard 
 to procure) has been printed with rhetorical pauses, and I have lately seen
 
 HOY. Od. III. 29 Notes. 37 
 
 28.] Notice the tr and tn of the first and third words collected 
 in inverted order in the word rent. Contrast the effect of rent 
 with its equivalent iu sense torn, where the system of sounds 
 is left unclosed. So, too, I have taken a slight liberty with the 
 text in substituting ' Bactria ' for ' Bactra,' for the sake of the 
 opposition of the ia in the former to ai in ' Tana'is,' as well as to 
 avoid the necessity of a musical rest after the first word of the 
 line. 
 
 xxxii.] The entire Ode is constructed (consciously, I believe, 
 by the Poet) on a dualistic, or, to speak more precisely, a per- 
 dualistic principle. The catena in the text is purposely inserted 
 by Horace to ease off the transition between the superincumbent 
 and subjacent main divisions the body of the coach and the 
 carriage proper, so to say (8 stanzas to each) ; and is bound to 
 be maintained by a translator true to his author at any and every 
 cost. There are five principal species of catenae, or rivets, as 
 they might be termed : the simple, the duplex, the prolate, the 
 oblate, and the agglutinate, of each of which there are instances 
 in this Ode. By perduMistic I mean that the 16 stanzas sub- 
 divide into two natural ideological groups of 8 each, each of 
 these octads into two of 4 each, and so on until we arrive at 
 single stanzas. It has been pointed out to me by a lady of high 
 culture that in the ' Vita Nuova ' Dante explains the distribution 
 of each sonnet (according to the Ideas) into a definite number 
 of component parts ; but what is especially noticeable in this Ode 
 is the continued dichotomy or bifurcation, springing from one 
 fundamental root-idea, carried out (consistently with the poet's 
 passion for exactness) upon a principle of strict arithmetical 
 precision. A paradigm of the deduction is given at page 1. 
 
 34.] The word Etruscum in the third line demonstrates that 
 the Poet, poet-like, had a particular river in his mind's eye. My 
 friend Dr. Ingleby suggests the Tiber, in which I have no doubt 
 he is right; and to him I am indebted for the introduction of 
 the capital R in River. In Bunsen's ' Life,' by his widow, I 
 think I remember reading of a Miss Bathurst who was drowned 
 when riding by the banks of the Tiber, in consequence of a 
 sudden rise in the river. I remember too, many years ago, 
 
 advertised Charles Kemble'a readings from Shakspear on a somewhat 
 similar plan. Blank spaces left between words might be used to indicate 
 the relative durations of pauses (or in some cases mere slowness of articu- 
 lation), desiderated by the composer.
 
 38 Principles of Versification exemplified. 
 
 travelling by diligence on the coast road between Valencia (of 
 the Cid) and Barcelona, and passing, not very far from the 
 latter city, a spot as dry and seemingly as little liable to inun- 
 dation as the Ladies' Mile in the Park, where only a AVeek 
 before, the diligence, by the sudden descent of a mountain torrent, 
 had been swept into the sea. I was told that the passengers 
 (including two young Englishmen out on a vacation tour) were 
 all drowned with the exception of a Civil Guard, one of two who 
 had got up into the diligence just before the catastrophe occurred. 
 29.] Orelli's authority, and Anthon's (who, I suppose, is good 
 enough as a sounding-board for collecting and reverberating 
 opinions), justify me, I trust, in associating the idea of fate with 
 the words ultra fas, although I believe such interpretation runs 
 counter to the current English public school tradition. Mortalis, 
 I presume, is intended, or at least serves in the original to suggest 
 the notion of the brevity of life, which I indicate by ' brief hour.' 
 Trepidat, Professor Key tells me, is connected with the word 
 rplirta, and with the notion of turning one's head up and down, 
 round and about, in a state of nervous anxiety. Professor 
 Newman translates it ' strains his nerves ' (!). The English 
 school-boy or competitive-examination word funk seems to me 
 to come nearest to it in meaning, and, like trepidat, is used gene- 
 rally in an intransitive, but occasionally in an active, sense. 
 
 xxxiv.] It seems to me certain, on phonetic grounds, that 
 alveo, and not aejuore, is the true reading. 1st. Having regard 
 to the jingle of aequus with acquore. 2nd. On the score of the 
 pernicious interruption of the beautiful I syzygy if the latter 
 reading be, adopted. Since the above was in print, I am happy 
 to find this opinion sanctioned, on quite distinct grounds, by the 
 transcendent authority of my friend Professor Key : ' The story 
 is so improbable that it must be true, for no one would have 
 thought of inventing it.' This is the sole sort of argument 
 brought forward in defence of the 'aequore ' reading, which Orelli 
 does not seem to have shown his usual good judgment in retaining. 
 
 XLI.] Evidently amnes are the rills feeding the flumen. I have 
 seen somewhere a reference to the former word used in conjunc- 
 tion with lebetis. The two stanzas (9th and 10th) lie double- 
 locked and, as it were, screwed together between rivets fore and 
 aft, and are manifestly intended to be welded into a unity of 
 the closest kind. 
 
 XLTV.] Pater = Diespiter = Sky Jove = High Jove; pater is 
 precisely the right word to employ in connexion with skyey
 
 Hor. Od. III. 29 Notes. 39 
 
 influences, and 'High' (sitting up above) is its true English 
 equivalent. 
 
 45.] A very esteemed friend strongly objects to the phrase 
 ' Pour o'er the pole ! ' and informs me that he is in the habit, 
 when he recites my verses, of substituting sky for pole. This 
 may be better for distinctness of sense, but it is defective in 
 point of syzygy, and I advisedly adhere to the reading in the text, 
 the sound of which, I think, imitates the effect of sunshine 
 gradually diffusing itself over the zenith. 
 
 49.] The sounds of the concluding word in this stanza would 
 be ineffably weak were they not supported upon the principle of 
 accumulation by being struck in the preceding lines. The ear is 
 a great integrator. Sounds linger and declare their affinities in 
 the ear long after the words to which they belong have dis- 
 appeared from the memory. I was once much puzzled to account 
 for the disagreeable effect produced by the use of the word 
 ' Leave ' (now ' Quit ') for desere in the 9th line of this version, and 
 it was some time before I discovered that it was owing to the word 
 ' rose-leaves ' (now 'Roses') having been used by me in the 3rd line. 
 
 LI.] I am perfectly satisfied that honores here means marks of 
 personal regard (i. e. favors) of Fortune as a woman, in the same 
 way as decernere honores means to decree marks of public regard. 
 It is only by an accidental coincidence that honores in this place 
 includes the notion of our English word honors along with health, 
 wealth, success, etc., the value of Fortune's favors in current coin. 
 Conington, almost always judicious in interpretation, has appa- 
 rently taken the same view, and translates honores by ' caresses,' 
 which is, I think, going too far, although in the right direction. 
 Professor Newman, on the other hand, gives an unmeaning verbal 
 rendering, ' uncertain glories.' 
 
 52.] The intention of this rendering is to redintegrate the unity 
 of the original stanza, the four assertions contained in which 
 I understand as referring to the single image of Fortune cheat- 
 ing at some sort of thimble-rigging game, which has possibly 
 come down to us from prehistoric times it would sound better, 
 but be inaccurate, for me to speak of our Aryan ancestors. After 
 all the pains taken, this stanza still remains the least satisfactory 
 of the lot. I made and broke upwards of two hundred distinct 
 castings of the stanza before I could satisfy myself that the 
 requisite idealistic conditions were fairly complied with, and I 
 believe that a solution of the difficulty would have been im- 
 possible but for the artifice of carrying back to an antecedent
 
 40 Principles of Versification exemplified. 
 
 line the sense of Nunc mihi. A guinea a line, if one takes the 
 necessary pains to work up one's verses to an approximately 
 equal pitch and polish, is often poor pay enough, when breakage 
 is taken into account, as is done in estimating the cost of grinding 
 large object-glasses for telescopes. Does any stanza in this Ode 
 ever present more than a single tableau or scheme of related 
 ideas ? 
 
 tin. Lord Lytton credits Orelli with a reference to a coin 
 containing an effigy of Fortune in a sitting posture, and an 
 inscription, ' Fortunae Manenti.' The same reference is given at 
 length in the old Delphin. 
 
 LV.] See Forcellini for examples of antithesis in one and the 
 same sentence between virtus and probitasihe fortitude and 
 courage of man, as opposed to the chastity and purity of woman. 
 It seems a work of supererogation to add that virtus can have 
 nothing to do with the Christian notion of virtue, or with the 
 use of the word in the passage cited as a parallel one by Mr. 
 Theodore Martin : 
 
 ' And evermore himself with comfort feeds 
 
 Of his own virtues and praiseworthy deeds.' 
 The parallelism, so far as I can see, consists merely in the two 
 passages not having, nor being capable of being produced on 
 either side to have, a single point in common. 
 
 56.] This stanza may, at the reader's discretion, be replaced 
 by the following one : 
 
 ' Welcome to stay ! but if she shake 
 Swift wings her bounties I resign, 
 And wrapped in my own virtue make 
 Pure Poverty unportioned mine.' 
 
 Welcome to stay ! anticipatory of Conington's ' Stays she ? 't is 
 well,' appeared in my original version, and is more idiomatic 
 and slightly more true to the sense of the original than ' I greet 
 her stay.' Resign is better than abjure, and the interpolation 
 anew is well got rid of. The objection to the new version is the 
 weakness of the ending of the third line and the substitution of 
 wedding for wooing. A learned and witty friend, it is true, has 
 sought to quiet my scruples on this last head by suggesting 
 that the consent of Pauper ies, however proba, might be assumed 
 to a reasonably good offer ; but ' a philosopher in his thin dress 
 of virtue clad' would, I trow, hardly justify such a designation.
 
 Hor. Od. III. 29 Notes. 41 
 
 The repetition of mine in the first line of the following stanza, if 
 a fault, which it is not, but rather the contrary, to my ears (and 
 is, I am told, justified by precedent in Edgar Poe, where 
 that form of repetition is used as a source of embellishment) 
 could be obviated by reading ' Not I when ' for ' Not mine if,' 
 and ' implore ' for ' to implore.' I believe the determining 
 cause in my mind for keeping the stanza as it stands in the 
 text is that the fourth line has been honoured by the approval 
 of an eminent poet, whose instructions (in such a matter, 
 commands) to me were not on any account to change it. 
 Such approval converts the line into a ' pearl of price,' which 
 it would be folly and unthrift to let go. The third line, too, 
 in the same quatrain has equally met with the approval 
 of a great Cambridge scholar distinguished for delicate taste 
 and epigrammatic felicity. In the altered stanzas the endings, 
 with the exception of make for take, are the same as in Conington's ; 
 but this would weigh very little with me against retaining it : 
 the chromatic effect of the quatrain as it stands due to the 
 mixture in more than usual abundance of the oo with the other 
 open vowel sounds is a better reason for its retention. 
 
 LXIV.] Geminus, like every other adjective (in this Ode, at 
 least, I believe, without exception, unless (which is by no means 
 certain) horridi in the 6th stanza constitutes one, is used, not 
 otiosely as an embellishment, but dramatically or dynamically, 
 to advance the action, so to say, and with special reference to 
 the matter in hand, and is therefore properly translated so as to 
 indicate that he has both his lamps (his own and his brother's) 
 lit up, a condition precedent for the augury being favorable to 
 the mariner. Twin-lit, unshape, and whirls-in-one are, I imagine, 
 additions, and faultless ones, to our current speech, and destined, 
 I venture to believe, to take rank with invariant, covariant, 
 contravariant, and (word of wonder-working, cabalistic power!) 
 sysygetic, and their train of followers, which have been struck at 
 the same mint, and have met with universal recognition and 
 acceptance. I may as well call attention to the strong prevalence 
 of the t syzygy throughout the original poem, and its undesigned 
 reproduction in the translation, and to the intenseness and con- 
 centration of thought and expression which can set in motion such 
 a mass of ideas and feelings with the aid of no more than 305 
 Latin words, and even fewer if only detached sounds be reckoned 
 as distinct words. 
 
 C
 
 42 Principles of Versification exemplified. 
 
 THE foregoing version is built upon the ruins of one 
 made some twenty- years ago, of which only 5 lines 
 (57-61) the porch of the old building are retained 
 in the present rendering. It is in the same metre as 
 the late deeply regretted Prof. Conington's, which, having 
 gone through three edition^ and received the unstinted 
 praise of English scholars and reviewers, I may have 
 less scruple in criticising, as it cannot fail to find defen- 
 ders to my cost if I am wrong, and perhaps still more 
 so if I am right. What I particularly object to in my 
 predecessor's version as an entire departure from the 
 spirit of his author, and the essence of lyrical poetry, is 
 the continual substitution of the abstract for the con- 
 crete, the general for the particular, the oblique for the 
 direct. ' Maecenas mine ! ' addressed by a poet who knew 
 his relative social position to his patron, in 3 ; the omis- 
 sion of any equivalent for beatae in XL, for incertos in 
 LI., and for Africis in LVII. ; ' reverberate to the enor- 
 mous shock,' in 39 ; ' cancel ' for ' diffinget ' in 47 ; 
 'caresses' for ' honores,' and 'fickle dame 'in 51 (an 
 interpolation not even original, being given by Scriven, 
 1843),* are examples which could be easily extended of 
 liberties which I should never have presumed to take 
 
 * So compare Conington's 
 
 ' And laughs should man's anxiety 
 Transcend the bounds of man's short sight, 
 with Scriven's 
 
 ' And smiles when mortal's anxious tear 
 Betrays too much a mortal's fear.' 
 
 Such coincidences can hardly be accidental. Professor Conington, 
 who in his preface mentions Mr. Theodore Martin's version with 
 high praise,never once alludes to Scriven's, which, though unques- 
 tionably inferior to the other as verse, is in many respects superior 
 to it as a translation. There appears to be a common consent
 
 HOT. Od. III. 29 by Conington. 43 
 
 with an author whom I respected sufficiently to trans- 
 late, but may pass as comparatively minor blemishes. 
 But how can any excuse be offered for such renderings 
 as ' luxury ' for ' divitibus,' in 13, ' Heaven ' for ' Deus,' 
 in 29, ' a river seaward borne' for ' fluminis delabentis 
 Etruscum in mare ' (stanza 9), ' stirred to madness ' for 
 ' irritat,' line 41, 'the morn may see' (1. 41), 'storms 
 around my vessel rave,' for ' mugiat Africis malus pro- 
 cellis,' 5758 ; anything less Horatian than such substi- 
 tutions and inversions it is in my judgment impossible 
 to imagine. 
 
 I believe the only way to obtain a tolerable transla- 
 tion of the English public-schoolboy's own book, which 
 Horace is (just as much as Euclid unfortunately is or 
 was in another direction), would be to parcel the work 
 out among the members of a society who should each 
 devote the labour of a year to effect the adequate ren- 
 dering of a few hundred lines at most the results to be 
 submitted to the criticism and correction of the joint 
 body to be periodically convened for the purpose.* 
 
 Another English scholar of deservedly high reputa- 
 
 among the English translators of Horace to ignore Mr. Scriven 
 in their prefaces. This gentleman probably omitted to enrol 
 himself as a member of any of the influential Societies of Mutual 
 Admiration and Assurance (Unlimited) which undertake to guide 
 the taste of the town. 
 
 * The number of existing translations and paraphrases maybe 
 reckoned by scores. Had each translator confined himself to a 
 tithe of a single book of the Odes, the work might have been 
 already accomplished. I regard the present accepted translations 
 as doing positive mischief to the public, inasmuch as they tend 
 to lower the standard of attainable correctness and degrade the 
 ideal of translation. Think, too, of the gain to language by the 
 resources to which a translator is driven who is obstinately bent 
 on a faithful reproduction of his author. 
 c2
 
 44 Principles of Versification exemplified. 
 
 tion has favoured the world with a rendering to which he 
 gives the name of verse, but which being to my ears 
 entirely without melody or rhythm, I should rather 
 designate as harsh and distorted prose. Apparently 
 unaware of the office of rhyme in marking off a line as a 
 sort of compound foot (like a bar in music), and so 
 aiding to sustain the measure, this gentleman refers to it 
 patronisingly as ' an elegant ornament.' Only versifiers 
 gifted with an ear peculiarly sensitive to time can afford 
 to dispense with its aid : I remember reading a short 
 poem of Mr. Matthew Arnold's ' On Growing Old,' half 
 through, before I became aware, or could persuade 
 myself previous to close examination, that the verse was 
 unrhymed, an illusion consequent upon the consummate 
 skill and accuracy with which the measure is sustained. 
 It does not seem to be at all understood among us in 
 England the land where, as I once heard Dr. Theodore 
 Benfey observe, Genius abounds but Method takes no 
 root that versification has a technical side quite as well 
 capable of being reduced to rules, as that of painting 
 or any other fine art. In Miss Mitford's recently pub- 
 lished correspondence, there is a letter in which she 
 wonders at a ' travelling poetess' asking her for a book of 
 rules on poetry. The wonder should rather have been at 
 no such book (as far as I am aware) existing, or at all 
 events being generally known to do so, in the English 
 language, although we maintain a Professor of Poetry 
 at one at least of our old Universities. There is quite 
 as much room for the exposition of a method of dis- 
 tributing sound as of laying on colour, and indeed the 
 analogy between the two arts of Versification and Color- 
 ing may be demonstrated to exist down to some very 
 minute technical details. I may seek some other oppor-
 
 Laws of Anastomosis and Syzygy. 45 
 
 tunity of stating the result of my speculations in this 
 direction, and especially the principle of twofold i.e. 
 respiratory and sonorific continuity in verse founded 
 (as regards the less known law of phonetic syzygy*} on 
 the physical fact of the permanence^ of the auditory 
 impressions. 
 
 * The other law, which I call that of anastomosis, although 
 little talked about, is no secret, being necessarily familiar to 
 writers of words for song music and all judicious singing- 
 masters, a great part of whose business it is to teach the art 
 of keeping back the breath. Anastomosis gives to verse its 
 cohesion, syzygy its flow and consistency. In a vague sort of 
 way, we may call them the objective and subjective factors of 
 verse harmony. Of course I am not unaware that there is a third 
 source of phonetic beauty in verse (the highest of all), which de- 
 pends on gradation of tones, on the agreeable succession of allied 
 sounds (in especial, though not exclusively, vowel sounds), where 
 the continuity is like that of the colours and tints in the solar 
 spectrum, and the pleasure like that we feel in watching a 
 sunset or seeing a peacock unfold its tail, or a rainbow glow 
 and fade away in the sky. Some of the most beautiful and 
 popular lines in Gray and Byron owe their chief charm to 
 the prevalence of this element. Metrik, again, including the 
 study of accents, pauses, and interruptions, may be referred 
 to the antagonistic principle of discontinuity ; and I need not 
 add that continuity and discontinuity exercise parallel functions 
 in the ideological province of versification to what they do in the 
 purely technical department of the subject. There is also a 
 third province of diction expression and appropriateness, which 
 lies between these two, just as in a ball-room dress, the shape and 
 cut, the colours, ornaments, and flouncings, the texture and seams, 
 all three form a separate province of study, corresponding to the 
 ideology, the expression, and the texture of verse composition. 
 
 f This permanence, by the way, is the ground of the possi- 
 bility of hypallage ; transposed without it, consecutive sounds 
 could not be shuffled back in the sensorium into their proper 
 order of succession. Its existence, too, is proved directly by 
 the bare fact of the sensuous pleasure (the so-called tickling 
 of the ear) derived from rhyme. Alliteration and rhyme, it 
 need scarcely be observed, are under one point of view only
 
 46 Principles of Versification exempli/led. 
 
 As regards metre, let us denote a spondee, the first 
 epitrite, a dactyl, and a trochee, by A, B, c, D respee- 
 
 extreme cases, or as we say in algebra, limiting forms of phonetic 
 syzygy. It is, however, I consider, more correct to refer each of 
 them to Symptosis, or the theory of clashes and beats. Anasto- 
 mosis, Syzygy, and Symptosis are the three subdivisions of 
 Synectic, as Synectic, Chromatic, and Metric are of Rhythm. So, 
 too, Symptosis trifnrcates into the theories of Beats or Jars, Asso- 
 nances, and Rhyme ; and again, Rhythm, Expression, and Idealistic 
 (corresponding to Sound, Word, and Thought) are the three main 
 divisions of Poetry as a whole. Without phonetic syzygy, rhyth- 
 mical composition is no more like verse than shoddy is like cloth : 
 it is this which gives the fibre and texture to versification, and 
 explains the success of generally-accepted quotations, proverbial 
 sayings, and happy repartees. Sounds must be regularly intro- 
 duced and carried out of the verse-canvas : suspended, prepared, 
 recalled, played with, as it were, before finally let go, concentrated, 
 diffused, crossed, perplexed, and interlaced. It is of importance 
 chiefly as a canon to the composer ; but those who have to recite 
 in public will find no small advantage to follow from a previous 
 study of the syzygies, with a view, by subtle management of the 
 voice and the introduction of almost imperceptible stresses on 
 particular sounds, to give the fullest effect to the ruling har- 
 monies of the verse. All real poets consciously or unconsciously 
 give us sounds of ' linked sweetness long drawn out ; ' but we have 
 some versifiers and highly cried up, betitled, and decorated ones 
 too of the present day, who have no notion, explicit or implicit, 
 of the law of syzygy, whose verses are accordingly utterly flabby 
 and limp, as void of backbone as a jelly-fish, and fail to make 
 any continuous or solid impression on the mind or organs of 
 the hearer. The effect on the senses of the double continuity 
 (conjunctive and objective, disjunctive and subjective), when well 
 maintained and duly brought out, is something quite sui generis 
 a sort of transcendental substance so intense in its action (if 
 I may judge from my own sensations and the reported ones of 
 the only fellow-versifier I have the advantage of knowing inti- 
 mately) as to be capable of giving a spasm to the whole nervous 
 system, like a lump of solidified carbonic acid gas placed on the 
 palm of the hand, or the charge of an electrical machine passed 
 through the arms and shoulders. Anastomosis gives a sort of 
 rectilinear fibre to the web of verse in one direction, syzygy
 
 Mathematical Harmony of Alcaic Stanza. 47 
 
 lively : then the construction of the Alcaic stanza, as 
 commonly practised by Horace (allowing for the liberty 
 of the final syllable of a line to be made long, which is 
 only stealing from the natural interval of breath between 
 two consecutive lines), will be represented by the 
 scheme (or as, say, in determinants, the square matrix) 
 
 A B c c 
 
 A B c c 
 
 A B D D 
 C C D D 
 
 which (as is apparent) has a pure algebraical or tactical 
 deep-seated harmony of its own. Denoting the lines of 
 
 curvilinear threads of connexion (or say lines of force) iii the 
 transverse direction. I have spoken above of beats and jars, 
 the former term (for which perhaps congruence would be a 
 useful substitute) may be used to denote the relation of two 
 sounds which forcibly recall each other in a legitimate or agree- 
 able, the latter in an illegitimate or disagreeable connexion, 
 clash being reserved as the generic term to include the other 
 two. The source of the illegitimacy which exists seems to lie 
 in a tendency to misdirect the ear by breaking up the rhythm. 
 Thus, ex. gr., like sounds occurring in the 4th place of two 
 tolerably contiguous lines, or in the 4th and 8th of the same or 
 neighbouring lines, are in general objectionable in octosyllabic 
 metre. Two like sounds in adjoining places, or when one of 
 the couple is in the first place, rarely produce a jar. I believe 
 it will turn out that the complete discussion of the theory of 
 beats and jars depends on a refined doctrine of numerical ratios, 
 the quantities which form the terms of the ratios being the quanti- 
 ties of time into which the line or lines in which the clashing 
 elements occur, is or are divided by those elements reckoned as 
 appertaining to the anterior portion of each such line. As a general 
 rule it may be stated that the nearer the homologous quantities 
 are to a ratio of equality without being actually equal, the better 
 (just as in music a fifth is a better interval than a twelfth), and 
 when the ratio is given, the smaller the common measure of the 
 terms the better. The case of equal ratios belongs to a special 
 theory. Also, it is obvious that on a distinct ground very strongly 
 congruent elements must not lie too close to one another.
 
 48 Principles of Versification exemplified. 
 
 symbols by single letters, and reading the square up- 
 wards, the scheme assumes the type L M N N, which is 
 homceomorphic with the upper two lines of the square. 
 And again, using a, /3, y to denote the duads AB, cc, DD 
 respectively, and counting only as one the repeated 
 uppermost horizontal line, we obtain the complete com- 
 bination system 
 
 a/3 
 
 ay 
 
 fty 
 
 Compare this remark with notes to xxxvi. and LXIV. as 
 evidence of the strong mathematical bias of Horace's 
 mind, wherein perhaps is to be sought the secret of the 
 peculiar incisive power and diamond-like glitter of his 
 verse. Had Athens been Cambridge, and Orbilius 
 Colenso (whose private pupil at the University I was long 
 before the far-famed Zulu was heard of), I have little 
 doubt that Horace might have come out the Numa 
 Hartog or Pendlebury of his year. 
 
 The annexed trifling translations from the German, 
 or most of them, were done about the same time as the 
 first and superseded form of the Horace-translation which 
 precedes. I have not cared to incur the trouble and loss 
 of time necessary to recast them according to my present 
 more severe notions of a translator's duty of fidelity to 
 his original. 
 
 Of the three first pieces, ' The Ideals ' is, I believe, the 
 most fairly open to censure on this ground. The last 
 stanza of this, if I remember right, was an afterthought, 
 and did not appear in Schiller's original edition of the 
 poem it seems to me only appended as sonorous ballast,
 
 Schiller ' Die Ideale.' 49 
 
 
 
 to give greater weight and solemnity to the close, and I 
 do not hold myself responsible, as a translator, for its 
 emptiness or little worth of meaning. I heard with 
 inexpressible rapt emotion, but yesterday, the manly 
 colloquy between Wallenstein and Max (the Temptation 
 scene), at the Harrow Speeches, and could hardly be- 
 lieve I was listening to the imitated accents of the author 
 of the mawkish personification of Endeavour in ' The 
 Ideals.' Schiller and Dryden, let me add Byron who 
 shall read your earlier and your later works, and say that 
 a Poet is born and not made ? We all know, too, 
 the story of Alfieri's self-culture. All the world over, 
 Art beats Nature. 
 
 II. THE IDEALS. Schiller. 
 
 AH 1 wilt thou faithless from me sever ! 
 
 Ah ! wilt thou thus inexorably, 
 With all thy fancies fade for ever, 
 
 With all thy pains and pleasures, fly ? * 
 
 * For a precedent (not known to me when I ventured upon 
 1 inexorably ') for the use of a final assonant tribrach, cf. 
 Byron's ' Hebrew Melodies ' : 
 
 ' But we must wander witheringly, 
 In other lands to die, 
 And where our fathers' ashes be 
 Our own may never lie.' 
 
 Any one happening to object to ' thus inexorably' may substitute 
 for it ' with averted eye.' The terminal sound in witheringly or 
 inexorably accords with the terminal sound i (in it) of the di- 
 phthong i (in fie), but not with what ought to be the pure vowel 
 in me, which only by a vice of pronunciation not uncommon in
 
 50 Principles of Versification exemplified. 
 
 Nor yet a little linger near me, 
 
 Oh ! thou my youth's fresh aureate prime, 
 In vain ! the waves still onward bear thee, 
 
 On to the boundless Sea of Time ! 
 
 Quenched now the suns serenely glowing, 
 
 Whose light, life's orient path illumed ; 
 And quelled th' inebriate heart, o'erflowing 
 
 Whilst yet its loved Ideals bloomed ! 
 For ever fled, once prized so holy, 
 
 The faith in that, my spirit dreamed, 
 By the rude Eeal turned to folly, 
 
 What once so fair, so heavenly seemed ! 
 
 England can drawl itself out to resemble the vowel sound in 
 ' it.' I am told by a great scholar (a principal ornament of 
 Owen's College in Manchester) that been in rapid colloquy in the 
 phrase ' I have been,' for example, almost invariably becomes 
 bin. Honest Italian singing-masters find it especially difficult 
 to make their English pupils maintain the purity of the vowel 
 sounds. The greater number of them give it up in despair from 
 the outset. Fashionable drawing-room Italian must be fun 
 indeed to the exquisite Italian ear, but the Italians are a grave 
 people and know how to keep their coxmtenance, which they 
 must do if they would keep their pupils. To return to the 
 ' assonance ' of ' inexorably ' with ' fly ' why is it so faint, so 
 infinitesimal ? For a reason depending on a theory which, as 
 far as I know, I have been the first to enunciate, viz. that the 
 common definition of a diphthong, ' a complexion 6r coupling of 
 vowels when the two letters send forth a joint sound, so as in 
 one syllable both sounds be heard ' (Ben Jonson), is quite defec- 
 tive, if not absolutely erroneous. Between a coupling of sounds 
 and a diphthongal sound the interval is as wide as between a 
 mechanical mixture and a chemical combination. The two marks 
 of sound which connote a diphthong are neither of them sounded : 
 they do but indicate the two limits from one of which to the
 
 Theory of the Diphthong. 51 
 
 As when, enamoured of his creature 
 
 Pygmalion Ig^gHhis statue bride, 
 Till through each pallid marble feature 
 
 Sensation poured its glowing tide ; 
 So I, in fond delirium often 
 
 Wooed nature with a lover's zest, 
 Till she to warm, to breathe, to soften, 
 
 Relented on this poet-breast ; 
 
 And all its fervid transports meeting 
 
 She who was dumb, an utterance found, 
 Gave back my lips' ecstatic greeting, 
 
 And felt my heart's impassioned sound. 
 Then lived each tree, each flower flashed feeling, 
 
 With silver fall, each fountain sang; 
 E'en soulless things, sensation stealing, 
 
 With echoes of my spirit rang. 
 
 other the voice passes continuously in uttering the diphthong ; 
 it is the filliug-up of the interval so symbolised which constitutes 
 the diphthongal sound ; and accordingly it is not every two vowel 
 symbols which can be conjoined to represent a diphthong, but only 
 such two as admit of a continuous uninterrupted passage of the 
 breath from one limit to the other. A diphthong is a sound of an 
 essentially different nature from a vowel or any combination of 
 vowels. However rapidly two vowels are made to succeed each 
 other, they will remain two vowels still, and never blend into 
 a diphthong. The nearest analogue to the diphthong is the slur 
 in vocal music. In general (I do not say always), a diphthong 
 cannot be reversed as such ; i.e. in the act of reversal it be- 
 comes a vowel syllable ; but this is not surprising, seeing that 
 we are equally unable to reverse the two initial sounds of a 
 word like praise ; if we attempt to do so, the word becomes a 
 dissyllable (repays).
 
 52 Principles of Versification exemplified. 
 
 Then strove with might unseen, unseeing, 
 
 A shapening world, this breast's, confine, 
 To burst the bands that bound its being 
 
 In word and deed, in sound and sign. 
 A shape, of what enchantment moulded, 
 
 While with closed bud, its head reclined, 
 But ah ! whose blossom now unfolded, 
 
 Flaunts weak and withered in the wind. 
 
 Upsprang, by his bold spirit speeded, 
 
 Blest in the madness of his dream, 
 By care unbridled, unimpeded, 
 
 The youth o'er life's ecstatic scene ; 
 Up to the faintest blue of heaven, 
 
 To circling orbs that pale on high, 
 On wings of dauntless venture driven, 
 
 He cleaves free passage through the sky. 
 
 How joyous then life's path appearing, 
 
 As gaily he o'erleaps each bound, 
 While near his chariot wheels careering, 
 
 Hope's airy escort dance around ; 
 Love with the sweet reward entrancing, 
 
 Fortune with gold crown dearly won, 
 Fame with her starry brow proud glancing, 
 
 And Truth irradiant as the sun. 
 
 But ere midway the goal discerning, 
 
 My treacherous guides began to stray, 
 And on their viewless steps returning, 
 
 Stole softly one by one away : 
 Away, light-footed Fortune hurried ; 
 
 Unslaked my thirst at Wisdom's tide, 
 In doubts and clouds of error buried, 
 
 Truth waned, then vanished from my side.
 
 Uhland ' Des Goldschmieds Tochterlein.' 53 
 
 I saw profaned Fame's ensigns cover 
 
 Her halo gild the Vulgar head ; 
 And ah ! too soon its springtime over, 
 
 Love's hours of soft enchantment fled. 
 Then stiller wore and stiller ever, 
 
 More steep and lonely still the way, 
 And fainter now the last gleams quiver 
 
 Of Hope's declining, dying ray. 
 
 Of all who early thronged to guide me, 
 
 Who in my hour of need stood fast, 
 Who hangs consoling still beside me, 
 
 And follows to the grave at last ? 
 'Tis thou ! who healing aid still bearest, 
 
 Friendship ! who bindest up each wound, 
 Who lovingly life's burthen sharest, 
 
 Thou, whom I earliest sought and found ! 
 
 Thou, too, who passion's storms allayest, 
 
 With Friendship freely mated ever, 
 Who laborest on, nor e'er destroyest, 
 
 Busy, unwearied, stern Endeavour ! 
 Who tho' but grains of sand thou heapest 
 
 To swell the eternal pile sublime, 
 Yet from the mouldering record sweepest, 
 
 Hours, days, and years of mortal time. 
 
 III. THE GOLDSMITH'S DAUGHTER. Uhland. 
 
 A GOLDSMITH in his workshop stands 
 
 Where pearl and ruby shine, 
 
 The brightest jewel in my hands 
 
 Thyself art still, Helena, 
 
 Thou darling daughter mine ! '
 
 54 Principles of Versification exemplified. 
 
 Steps in a knight of bravest mien 
 
 ' Good even, maiden fair ! 
 And Master goldsmith too, good e'en !- ' 
 
 A jewelled wreath, I prithee, 
 Shape for my maiden's hair.' 
 
 And when the goldsmith's work was done, 
 And sparkled bright the charm, 
 
 Helena soon as she's alone, 
 
 With heaving bosom claspeth 
 The wreath around her arm. 
 
 ' Ah ! wondrous happy lot is thine, 
 
 Who shall this chaplet wear ; 
 Ah ! what delight, what joy were mine, 
 
 Gave he me but a chaplet 
 Of roses, I might wear.' 
 
 Not long before the knight came back, 
 
 Approved the wreath and cried, 
 ' I would, Sir goldsmith ! ye would make 
 
 A wedding-ring with diamonds 
 For my enchanting bride.' 
 
 And when the -wedding-ring was made, 
 Glittering with diamond-stone, 
 
 She drew it sad and half afraid 
 
 Upon her bridal finger, 
 Soon as she was alone. 
 
 ' Ah ! wondrous happy lot is thine 
 
 Who shall this token wear ; 
 Ah ! what delight, what joy were mine, 
 
 Gave he me but a ringlet 
 Of his own golden hair.'
 
 Uhland <Des Goldschmieds Tochterlein.' 55 
 
 Nor longer now the knight delayed 
 
 "Well pleased the jewels eyed, 
 ' Eight fine, Sir goldsmith, ye have made 
 
 These precious true-love offerings 
 For my enchanting bride. 
 
 { Beseech ye ! beauteous maid, come near, 
 
 Think thou art she I woo, 
 On thee I'll test the bridal gear, 
 If well it may beseem her, 
 For she is fair like you.' 
 
 On that same morn the maiden fair, 
 
 To grace the Sabbath day, 
 Was decked with more than wonted care, 
 As she to church was wending, 
 
 Donned in her best array. 
 
 She blushing like a rose fresh blown, 
 
 Before the knight doth stand ; 
 
 He sets on her the jewelled crown, 
 
 The ring upon her finger, 
 
 Then takes her by the hand. 
 
 ' Helena sweet, Helena dear, 
 
 The jest right out is played, 
 'Tis thou the wedding wreath shalt wear, 
 
 And thus I ring thy finger, 
 My chosen, cherished maid ! 
 
 ' Here gold and pearl and precious stone 
 
 Have long encharmed thine eyes, 
 And well these tokens have foreshown 
 
 That ye with me to honour 
 Shall higher yet arise.'
 
 56 Principles of Versification exemplified; 
 
 IV. CASSANDRA. Schiller. 
 
 JOY ran high in halls of Ilion 
 
 Ere the haughty fortress fell ; 
 Song from all th' exulting million 
 
 Shook the tuneful golden shell ; 
 Wearying labor laid aside is,* 
 
 Rests each hand from tearful strife, 
 Whilst the hero-souled Pelides 
 
 Priam's daughter woos to wife. 
 
 * It is worthy of notice how by ' alliteration's artful aid ' a 
 construction which would otherwise offend the ear as forced 
 is made to appear perfectly natural. Whoever has had any 
 practice in versification knows that sounds exercise a perceptible 
 attraction upon one another in the mind, or, so to say, a strong 
 sound seeks to procreate another like unto itself: thus labor 
 appears to demand laid to be brought into apposition with it, 
 and the displacement of the copula passes unnoticed. Alliteration 
 and the tendency of crimes to repeat themselves both alike 
 belong to the wide category of habit, of which Newton's first law 
 of motion exhibits the physical image. Why the p sound in 
 particular tends to reproduce itself is a subject worthy of serious 
 consideration. It is probably a purely physiological effect 
 owing to the strength of the impression made on the sen- 
 sorium during the suspension of breathing which the production 
 of this sound demands. I have been told by my friend the 
 eminent painter and academician, Mr. Solomon Hart, of a 
 passage which he thinks he has met with in the ' Decline and 
 Fall,' where the p begins a word no less than ten or eleven times 
 in uninterrupted succession, and we have all read in Dickens of 
 the Mrs. General who recommended Little Dorrit, in order to 
 give a good form to her lips, to say sometimes to herself, 
 before entering a room, 'papa, potatos, poultry, prunes and 
 prism, prunes and prism,' and to ignore the existence of anything 
 that is not ' perfectly proper, placid and pleasant.'
 
 Theory of Alliteration. 57 
 
 Bearing laurel boughs they follow 
 
 To the temples, throng on throng, 
 To the shrine of bright Apollo, 
 
 To ThymhrEeus, God of song ; 
 Through each alley echoes waking, 
 
 Sounds of joy Bacchantic roll, 
 "Whilst her moan unheeded making 
 
 Sorrows on one mournful soul. 
 
 Joyless midst the joy prevailing 
 
 The despised Cassandra roves, 
 Stung with sorrow unavailing, 
 
 To Apollo's laurel groves ; 
 In the forest's deep recesses 
 
 Bursts into prophetic sound, 
 And the fillet from her tresses 
 
 Casts indignant on the ground. 
 
 The second half of the stanza originally ran thus : 
 
 Weary every hand abideth, 
 
 Pausing from the tearful strife, 
 Whilst the hero-souled Pelides 
 
 Priam's daughter woos to wife. 
 
 I consider the imperfect rhyme of the first and third line in the 
 above comparatively unimportant, inasmuch as the rhyming of 
 the odd lines having only occurred once previously, the habit of 
 expecting it has not had time to form in the sensorium of the 
 hearer. Moreover, the sense of dissonance is almost effaced amidst 
 the glare of the broad diphthongal consonance of the penultimate 
 syllables. The metrical office of rhyme, i.e. the marking off of a 
 bar of time, is sufficiently fulfilled, and any slight sensuous disap 
 pointruent to the ear of an imperfect craving for accordance (like 
 a duly resolved discord in music) is more than made up for by 
 its complete gratification in the sequel. 
 D
 
 58 Principles of Versification exemplified. 
 
 1 Mirth each fleeting terror chases, 
 
 Every heart beats high in cheer, 
 Hope relumes those timeworn faces 
 
 Sumptuous swells the bridal gear ; 
 Me, alone of all the million 
 
 Me, no fond illusion waits, 
 For I see on swooping pinion 
 
 Ruin hover o'er their gates. 
 
 ' I behold a torch-light glowing, 
 
 But not borne in Hymen's hand, 
 Flashes o'er the welkin throwing 
 
 All unlike to offering brand ; 
 Banquets gaily they are spreading, 
 
 But in my prophetic mind 
 I can hear the Godhead treading, 
 
 Who shall hurl them to the wind. 
 
 ' Sunk in speechless grief I languish, 
 
 Or to desert wilds repair, 
 For they chide my mortal anguish, 
 
 And they mock at my despair. 
 By the fortunate abandoned, 
 
 By the joyful held to scorn, 
 Thou too cruelly hast wantoned 
 
 Pythian 1 I too much have borne. 
 
 * Oh ! Thou God relentless-minded, 
 
 Why unseal my spirit's sight 
 Midst a people ever blinded 
 With all senses barred to light.
 
 Schiller ' Cassandra? 59 
 
 Why impart the gift of seeing 
 
 What no power may turn aside, 
 The foreshadowed must have being, 
 
 The predestined must betide ! 
 
 ' 'Tis profane the cere-cloth riving 
 
 Where a spectre lurks beneath. 
 Error is the law of living, 
 
 Knowledge but a name for death ; 
 Take, oh take thy mournful splendor, 
 
 From mine eyes, the lurid gleam, 
 Cursed the mortal thou wouldst render 
 
 Mirror to thy heaven-lit beam ! 
 
 ' Give me back my vision bounded, 
 
 And my senses' duskened sheen 
 Song nor voice of joy I've sounded 
 
 Since thy mouth-piece I have been ;* ] 
 Thou the future hast imparted, 
 
 But the present turned to pain, 
 Rifled me of youth light-hearted ; 
 
 Take thy treacherous gifts again ! 
 
 ' With the Bride's adornment never 
 
 I my dewy locks might twine, 
 Since thy Priestess vowed for ever, 
 I have served thy mournful shrine ; 
 
 * Some friendly critic regards the phrase ' thy mouthpiece ' 
 as an inadequate rendering of deine Stimme, or as a solecism in 
 language ; but I think it a fair approximation to the sense, and 
 permissible in form, in the same way as we may speak of Miss 
 Harriet Martineau being in England the mouthpiece of Comte.or 
 Professor Huxley (besides the much more besides that he is in. 
 himself) a mouthpiece of the myriad-minded Darwin. 
 
 D2
 
 60 Principles of Versification exemplified. 
 
 Grief my budding spring-time blighted, 
 Youth exhaled in Sighs unblessed ; 
 
 Every pang that near me lighted 
 Thrilled from my responsive breast. 
 
 ' Sportive joy of soul revealing, 
 
 All around me live and love 
 In the youthful tide of feeling ; 
 
 Me, but pain and sorrow move, 
 Nor for me the spring reviving 
 
 Spreads o'er earth its festive green ; 
 Who that owns to joy in living 
 
 Down its dark abyss has seen ! 
 
 ' Happy in her blind delirium, 
 
 In her hopes ecstatic blessed, 
 To enclasp the dread of Ilium 
 
 As a bridegroom to her breast ; 
 See my sister's heart proud swelling, 
 
 Vainly struggling calm to seem ; 
 Scarce yon Gods, there o'er us dwelling, 
 
 Hails she happier in her dream ! 
 
 ' I've too gazed on him entreating 
 
 Whom my yearning heart desired, 
 And have shared the blissful greeting 
 
 By the glow of love inspired. 
 But to nuptial dwelling never 
 
 With the loved one might depart, 
 For a Stygian shadow ever 
 
 Cast its baleful gloom athwart.
 
 Schiller i Cassandra.' 61 
 
 ' Spectres gaunt and shapes ungainly 
 
 Flock from Tartarus' shores to me, 
 Seeking rest or roaming vainly 
 
 From the grisly bands to flee ; 
 Through the youthful sports and babble, 
 
 Still the phantom troop would steal ; 
 Shuddering grim and hideous rabble, 
 
 Howe'er could I joyous feel ! 
 
 ' I behold the death-steel glitter, 
 
 And the murderer's visage glare, 
 Can ne'er flitting hither, thither, 
 
 'Scape that portent of despair, 
 Nor my rooted gaze unfasten : 
 
 Fixed, foreboded, fearless scanned, 
 To fulfil my doom I hasten, 
 
 Falling on the foemen's land.' 
 
 Whilst her plaintive tones thus wander, 
 
 Hark ! what deafening shouts arise ! 
 At Apollo's portal yonder, 
 
 Stretched a corpse, Achilles lies. 
 Discord's gory crest proud towers, 
 
 The protecting Gods are gone, 
 Thunder breaks and darkness lowers 
 
 O'er devoted Ilion.
 
 62 Principles of Versification exemplified. 
 
 V. COMFORT IN TEARS. Goethe. 
 
 WHENCE comes it, thou thus pensive art 
 While all else glad appears ? 
 
 Too well we see, in those sad eyes 
 The tell-tale trace of tears. 
 
 ' And tho' I lonely may have wept, 
 
 Mine only is the smart ; 
 The tears that trickle down so sweet, 
 Relieve my gushing heart.' 
 
 Thy joyous friends beseech thee come, 
 
 Oh ! come unto our breast ; 
 There safe, whatever loss has happed, 
 
 Unburthen thy unrest. 
 
 * Your mirthful fancies ill divine 
 What makes my bitter pain ; 
 Ah ! no, 'tis not what I have lost, 
 But what I cannot gain.' 
 
 Wake then, and call thy courage up, 
 Time hath not dulled thy soul ; 
 
 With thy fresh life, man has the strength 
 And will, to win the goal. 
 
 ' Ah ! no, the goal I cannot win, 
 
 It looms too distant far ; 
 It dwells so high, it shines so bright 
 As yonder dazzling star.'
 
 Miscellaneous Examples. 63 
 
 The stars one should not covet them, 
 
 But glory in their light ; 
 And with enraptured gaze look out 
 
 Into the cloudless night. 
 
 1 And with enraptured gaze I look, 
 
 So many a garish day ; 
 For weeping, leave me still the night, 
 So long as weep I may.'* 
 
 HAVING since the preceding matter was in type stumbled 
 upon the original free (I should now say, over-free) 
 rendering of Tyrrliena regum, together with a similar 
 one of a portion x>f Impios parrae (Hor. iii. 27), done at 
 about the same period, and certain other similar effusions, 
 I may as well take this opportunity of ridding my 
 hands of this lumber of unconsidered trifles, which, 
 after all, reviewing them as impartially as I (the author 
 of their being) am able to do, seem to me not vastly 
 inferior in sense and expression to many of the vamped- 
 up, far-fetched, transcendental inanities of some of the 
 third-class poetasters of the day which find a ready 
 echo in the press. If Joseph Scaliger thought himself 
 qualified in his twice-edited ' Cyclometrica Elementa ' 
 to attempt the Quadrature of the Circle, said to have 
 been ' victoriously refuted by Vieta,' by way of teaching 
 their business to the geometricians of his time, and 
 
 * As it seems to be a womanish sort of youth (possibly, even a 
 girl in boy's clothes) who is speaking, I have allowed more so's 
 to stand than might otherwise have been justifiable. It ought 
 to be expressly laid down in future editions of ' Mary's Grammar ' 
 that so is the feminine transcendental pluperfect form of super- 
 lative, as, ex. gr. lovely, lovelier, loveliest, so lovely, or such a love.
 
 64 Principles of Versification exemplified. 
 
 Thomas Hobbes, though with a better intention, laid 
 himself open, on a like ground, to refutation and cen- 
 sure, I may hope to be excused crossing over, from the 
 other side,* the border-line between scholarship and 
 science, and for submitting, with a less ambitious aim 
 and in a much more humble frame of mind, some of my 
 long-forgotten (d ' outre-tombe) transgressions in verse 
 and rhythmical speculations to the inspection of my 
 hoped-ior private-circle century of indulgent readers.f 
 
 As I shall most probably never take up pen again on 
 the subject of Verse, I may as well embrace this oppor- 
 tunity of making a brief profession of faith concerning 
 modern Metric and what are termed accentual feet. I 
 am satisfied, then, that on this subject Edgar Poe is 
 perfectly right in the principles laid down by him in 
 his ' Rationale of Versification,' J that the substratum 
 
 * Chronology, leading straight to Astronomy, I presume was 
 Vieta's crossing-point : Synectic, which leads down from the 
 Alps of Cauchy and Eiemann to the flowery plains of Milton and 
 Byron, my own. 
 
 f When the above was set up in print it was my intention 
 only to publish 100 copies for private distribution, and I might 
 have persisted in this intention had I not felt that the remarks 
 I have passed on the labours of others rendered it imperative 
 upon me to face the consequences of the public avowal of my 
 opinions. 
 
 \ He ought to have called it ' Eationale of Metre.' Rhythm, 
 used in its most general sense to signify the purely technical 
 part, one of the three main heads of versification, itself subdivides 
 again into three branches synectic, chromatic, and metric, the 
 latter including accent, quantity, and suspension ; which last 
 again subdivides into the theories of rests, stops, and pauses. 
 Metric gxiards the ear, Synectic satisfies, Chromatic charms it. 
 The first ensures correctness, the second organization, the last 
 beauty and embellishment. For the benefit of my non-mathe- 
 matical readers, I may state that ' Synectique ' is a word used,
 
 A Theoi^y of Accentual Feet. 65 
 
 of measure is time ; that an accented syllable is a long 
 syllable, and that an unaccented syllable is a short one 
 of varying degrees of duration, and that feet in modern 
 metre are of equal length. Professor Newman is of 
 an opposite opinion, and goes the length of saying, that 
 accent is so far from lengthening that it even tends 
 to shorten syllables, instancing the first syllable in 
 female as shortened by the accent, and of course imply- 
 ing that it is shorter in female than it would be in 
 female : to argue against such an assertion (which I think 
 no one who is not time-deaf will be found to concur 
 with) would be like reasoning upon colours with one 
 who is born colour-blind.* 
 
 and I believe for the first time, by Cauchy in his Theory 
 of Functions, the true and very insufficiently acknowledged 
 foundation and origin of Rieman's great doctrine of Continuity, 
 in like manner as the Triads of Kant appear to me to contain 
 the germ (impossible to have escaped ulterior development) of 
 the method of Hegel ; or, as I am told, Turner had not existed 
 but for Claude. At the opposite pole to Rhythm, as previously 
 observed, we have the Idealistic of Verse, which has its con- 
 tinuity and discontinuity branches (the analogues of Synectic and 
 Metric, to attempt to go into any analysis of which here would 
 lead me too far), intermediate to which lies Imagery, the ana- 
 logue of Chromatic. Ex. gr. Construction, Deduction, Develop- 
 ment, Action, and Invention, will belong to the continuity 
 branch ; Distribution, Transition, Contrast, Light and Shade, 
 Quantification, &c. to the discontimiity one. Between Rhythm 
 and Idealistic, as also already noticed, lies Expression (sense 
 clothed in sound). At the base of and giving nourishment to 
 our poetical plant, lies Emotion, at once the root and crown of 
 lyric verse. 
 
 * If it be true, as Professor Newman alleges, ' that an 
 English voice cannot dwell on accented syllables without seem- 
 ing to drawl,' it must be because of the difficulty of getting over 
 the accented syllable in right time, in consequence of the ten- 
 dency to be over delayed by giving effect to the accent.
 
 66 Principles of Versification exemplified. 
 
 But in reckoning the length of feet, attention must be 
 paid to the time expended in preparing and closing, as well 
 as in actually emitting the sound, and also to the silent 
 syllables or pauses, to which Poe has not paid sufficient 
 attention. I believe that his theory of substitution is 
 perfectly correct ; that, to use musical nomenclature 
 (which appears not to have been familiar to him), an 
 iambus with us is a quaver and crotchet ; a trochee, a 
 crotchet and quaver ; an anapaest, so called (when sub- 
 stitutable for an iambus, of which many examples will 
 be found in my preceding Horatian version;,* two semi- 
 
 * It may be noticed that all the anapaests therein employed 
 are convertible, by elision or contraction, into iambic feet. A 
 pretty copious sprinkling of such equivocal anapaests (as I am 
 used to call them) helps to confer lightness and dignity on octo- 
 syllabic metre, much in the same way as raised heels are said to 
 be worn by the young ladies of the period, to give spring and 
 distinction to their gait, and to add to their height. I have 
 noticed that in the two first letters in the ' Essay on Man,' Pope 
 in no single instance, as far as I can recollect, allows contraction 
 to take place by elision or by two contiguous vowels in a word 
 running into one another; every word is made to contain its 
 maximum number of syllables. Pope, I imagine, would have 
 rejected as incorrect such a line as 
 
 ' Have linked that amorous power to thy soft lay,' 
 and as downright false, 
 
 1 While the jolly Hoxirs lead in propitious May.' 
 
 The Kev. Mark Pattison has kindly informed me that in Pope's 
 Satire I., in 156 lines there are 24 commencing with -w, and only 
 two cases of accent or weak syllable in any other position. I 
 remember reading, when a child, in some common English 
 school-book, that a trochee in iambic verse was only permitted 
 at the beginning of a line. (By the way, why is it that we 
 cannot conversely substitute an initial iamb for a trochee, in 
 a trochaic line ?) I have recently been told by a high authority,
 
 Metre reduced into Terms of Music. 67 
 
 quavers followed by a crotchet, and a dactyl, substituted 
 for a trochee, a crotchet followed by two semiquavers. 
 Poe even quotes cases (very unsatisfactory ones, in my 
 opinion, borrowed from unknown American versifiers), 
 where a quaver is resolved into a triplet. Such cases, 
 however, do exist, as ex. gr. in the imaginary line, 
 'And earth the o'erpowering tones rehearse;' in [ering] 
 each syllable is a semiquaver, but in [the o'er] only 
 the third of a quaver. I think also, that there are 
 some lines which occur, chiefly in very modern poetry, 
 where the principle of apocopation must be applied to 
 the scanning, and others, where that of tempo rubato is 
 intended or necessary to give full effect to the recital. 
 
 The principle of the silent syllable, or to speak more 
 intelligibly, of the rest, removes all the anomalies or 
 supposed imperfections of metre which Edgar Poe 
 imagined to exist (and they are purely imaginary) in 
 the opening lines to the ' Bride of Abydos.' * He has 
 
 that a trochee is admissible anywhere in an English iambic line, 
 subject to the sole condition that two trochees shall not occur in 
 succession. I believe the safer rule to be that in general a trochee 
 should only occur at the beginning of a line, or after a pause or 
 close of a period, or when the second part of the foot is a 
 monosyllable or ends a word, the ground of the exception in all 
 these cases being the same, and involving the theory of the rest. 
 * ' Know ye the land where the cypress and myrtle 
 
 Are emblems of deeds that are done in their clime, 
 Where the rage of the vulture, the love of the turtle, 
 
 Now melt into sorrow, now madden to crime ? 
 Know ye the land of the cedar and vine, 
 Where the flowers ever blossom, the beams ever shine ; 
 Where the light wings of Zephyr, oppressed with perfume, 
 Wax faint o'er the gardens of Gul in her bloom ; 
 Where the citron and olive are fairest of fruit, 
 And the voice of the nightingale never is mute ;
 
 68 Principles of Versification exemplified. 
 
 made the exceedingly interesting observation, that all 
 these lines run into one another, and so read will be found 
 to consist of a succession of accentual dactyls. He 
 rightly understands (collected works, vol. ii., p. 242), 
 that crime at the end of the fourth line, and tell at the 
 end of all, are to be understood as what he calls ' ccesu- 
 ras; ' in plain English, each takes on two quaver rests. 
 ' fume, Wax ' in the seventh and eighth lines, he Tightly 
 regards asa spondee substituted for a dactyl, or,as I should 
 say, two crotchets for a crotchet and two semi-quavers. 
 But he makes a difficulty, for which there is no occa- 
 sion, about the words ' twine, And,' (11. 14, 15) which 
 he says ' is false in point of melody,' for that ' we must 
 force " And " into a length which it will not naturally 
 bear.' The fact is, that twine ending a line, very natu- 
 rally takes after it a quaver rest, a slight pause which 
 assists the effect, by enabling the reciter to take a short 
 breath, so that what Poe supposes to be a spondee is vir- 
 tually a dactyl. A similar remark applies to the words 
 ' sky, In ' belonging to a triad of lines, which for some 
 unexplained reason are dropped by Poe, and also to the 
 words ' done? Oh ! ' which he scans as a spondee, but 
 which is really a dactyl, ' Oh ! ' being a quaver pre- 
 ceded by a quaver rest. So in the seventh line of 
 
 Where the tints of the earth, and the hues of the sky, 
 
 In colour though varied, in beauty may vie, 
 
 And the purple of Ocean is deepest in dye ; 
 
 Where the virgins are soft as the roses they twine, 
 
 And all, save the spirit of Man, is divine ? 
 
 Tis the clime of the East, 'tis the land of the Sun 
 
 Can he smile on such deeds as his children have done? 
 
 Oh ! wild as the accents of lovers' farewell 
 
 Are the hearts which they bear and the tales which they tell.'
 
 Metrical Analyses. 69 
 
 ' Paradise Lost,' ' of Oreb, or of Sinai, didst inspire,' 
 I consider that eb and or are both quavers, and that 
 the comma between them represents a quaver rest. So, 
 again, I consider that the most eligible scanning upon 
 Poean principles of the admired line 56 in my version 
 of Ti/rrhena regum, ' Poverty portionless but pure,' is 
 crotchet, two semiquavers ; quaver-rest, crotchet ; two 
 semi-quavers, quaver, quaver-rest; quaver, crotchet; as 
 shown in the subjoined arithmetical scheme : 
 
 i i 
 
 (i) i I i i i (i) 
 
 Thus much for my general notions about Metric, 
 except that I ought to add, that as by force of associa- 
 tion imaginary rhymes (such as far and war, brood and 
 flood} pass muster even to the ear, so there are cases 
 of imaginary time, where the measure is rather im- 
 puted than computed, and number usurps the function 
 of, or in a Mahaffo-Kantian* sense -may be said to 
 schematise, duration.^ 
 
 I may be pardoned for adding, in conclusion, that the 
 
 * I allude hereto the sense ascribed to Kant's use of the word 
 ' schematism ' by the learned and accomplished Professor Mahaffy 
 in his most truly valuable introduction to Kunb Fischer's Com- 
 mentary on Kant. Kant is like a rainbow every man sees his 
 own. Had Kant studied versification, as (if I remember right) 
 Socrates did in his youth, he would have learned the art of using 
 words. No philosopher or savant need blush to give some time 
 to the practice of this art, if he sets any value upon the faculty 
 of rendering himself intelligible to the bulk of mankind. 
 
 t I think, too, that (as a rule) the ear, by an almost un- 
 conscious act of cerebration, attends to and takes note con- 
 currently of number and time, accent and quantity, combined in 
 metre. If we lay stress on either of these elements too exclu- 
 sively, our theories will be sure to err.
 
 70 Principles of Versification exemplified. 
 
 experiment which called these renderings and observa- 
 tions into present being, turned out eminently successful, 
 and that the recital of the Ode before an audience of 
 several hundred men and women, boys and girls, 
 with few exceptions belonging to the labouring classes, 
 was received with great applause, thereby demon- 
 strating a posteriori the justness of the musical prin- 
 ciples upon which the version was constructed. This 
 recital formed only one ingredient out of an extensive and 
 varied bill of fare, consisting of songs, glees, perform- 
 ances on the pianoforte, rehearsals from Shakespeare 
 and modern authors, in prose and verse, etc.* Of all 
 the performances that took place, it was xmiversally 
 admitted that next to ' That Rogue Kiley,' a comic 
 song sung by a gifted young lady, Horace's ' Invita- 
 tion to Maecenas to pass a Day with him in the Coun- 
 try,' called forth the greatest demonstration of public 
 favour, and as I was told by some military friends 
 who were present from the neighbouring garrison, the 
 very National School children in the front rows, who 
 
 * I think the excellent and humanising influence of Penny 
 Readings would admit of an easy and important development 
 by being turned into Penny Gatherings. Besides recitations, 
 works of art might be exhibited, and new songs or pieces of 
 music, and poems or other forms of literary composition, sub- 
 mitted to a preliminary essay, and principles of criticism be 
 introduced and discussed. How useful this would be, alike to 
 authors and their audience ! I remember dipping not long ago, 
 for want of anything better to do, into the oration ' Pro Archia,' 
 from which it seems that it was the custom in antient times 
 for eminent orators or poets to give free recitations of their 
 works to the people of the towns through which they passed. 
 My proposed Penny Gatherings (where tea and coffee also 
 might be made to circulate at a trifling expense) would serve a 
 somewhat similar purpose.
 
 Hor. Od. III. 29 Earlier Version. 71 
 
 poked their fun over Marc Anthony's Funeral Oration on 
 Julius Caesar, were too much awed to laugh, and looked 
 on and listened in rapt and solemn wonderment. The 
 meaning of the proper names had been previously ex- 
 plained to them, and the situation brought home to their 
 understandings by aid of a modern parallel. Thomas 
 Moore did duty provisionally for Horace, and the 
 Marquis of Lansdowne, Lord President of the Council, 
 for Maecenas. 
 
 VI. INVITATION TO MAECENAS. Horace* 
 
 TYRRHENIAN progeny of kings, 
 
 Wine mellowed with a jealous care 
 
 Hoses and what choice essence flings 
 Odors of Araby o'er the hair ; 
 
 Wait thee Maecenas why delay ? 
 
 Must Tibur, Aesula's steep plain, 
 And heights of Telegon alway 
 
 Thee, from our Sabine farm detain ? 
 
 Leave sumptuous pomp and the proud pile 
 That seeks to mount into the skies ; 
 
 Leave Rome its smoke and din awhile 
 With village scenes to cheer thine eyes. 
 
 * This looser translation, thrown off at a white heat, cost me 
 probably about as many minutes only as the preceding exact one 
 half-hours or hours, and yet an uncritical eye will probably see 
 little difference between the two. It is the last turn of the screw, 
 and the blow of the hammer which is to drive the nail home, that 
 call for the only real exertion of strength.
 
 72 Principles of Versification exemplified. 
 
 The rich love change less dainty fare 
 And walls undraped with purple woof, 
 
 Oft smoothe the wrinkled brow of care 
 Under the plain thatched peasant's roof. 
 
 Now Cepheus shows his light again, 
 Now Procyon blazes in the south, 
 
 The Lion shakes his frantic mane 
 
 And summer fields lie parched with drouth. 
 
 The weary shepherd seeks the shade, 
 Leads to the brook and thickets dank 
 
 His languid flock, nor winds invade 
 But all lies hushed upon the bank.* 
 
 Thou, what with public weal accords 
 And Rome's defence provid'st from far, 
 
 Lest Seric or Avild Bactrian hordes 
 Or Tanai's roll the tide of war. 
 
 * Poor cheery old Silvanus has got left out in the cold here. 
 It was the remonstrance (not unaccompanied with encourage- 
 ment) against this unjustifiable omission by a most learned and 
 accomplished professor (crowned with recent laureate honors by 
 an illustrious foreign Academy) at our most antient University, 
 to whom I showed these lines, that awakened in me the dormant 
 sense of a higher ideal of fidelity in translation. Just about 
 the same time, too, the newspapers of the day were full of an 
 account of an altar to the worthy old god, which had been found 
 in the bed of the river Wear, in the North of England, which 
 made his exclusion (whtn every other proper name received 
 its due share of notice) the more invidioiis. 'Twas like being 
 left out by an old friend from a dinner-party, to which all your 
 mutual acquaintance have been invited.
 
 Hor. Od. III. 29 Earlier Version. 73 
 
 O'er all, the future may impart 
 
 Wise Gods have clouds and darkness thrown, 
 And smile when feeble mortals start 
 
 At shadows of the dim unknown. 
 
 Live to the present all besides 
 Is drifted like the changeful wave 
 
 That now in smoke mid-channel glides 
 Seeking Etruscan shores to lave. 
 
 Now with uprooted tree and stone, 
 Cattle and houses swept from shore 
 
 Into an eddying torrent grown 
 
 Shakes woods arid rocks with maddening roar. 
 
 Lord of himself and blest shall prove 
 He who can boast ' I've lived to-day 
 
 ' To-morrow let dispensing Jove 
 Cast o'er the skies what tint he may 
 
 ' Sunshine or cloud ! the work begun 
 
 And ended may his power defy, 
 He cannot change nor make undone 
 
 What once swift Time has hurried by. 
 
 ' Fortune whose joy in mischief lies, 
 
 Grown hardened in her cruel game 
 
 Changes from hand to hand the prize 
 
 Smiling on each in turns the same. 
 
 ' Welcome to stay ! but if she shake 
 
 Her fickle plumes wrapped in my pride 
 I scorn her gifts and spotless make 
 Unportioned poverty my bride.
 
 74 Principles of Versification exemplified. 
 
 ' Not mine, when towering topmasts roar 
 
 'Neath Afric's storms with piteous prayers 
 Or bargaining vows each God to implore 
 Lest Cyprus' or fine Tyrian wares 
 
 ' Add treasure to the ravening seas. 
 
 Me shall my bounding pair-oared craft 
 With favouring Pollux and the breeze 
 Safe through the tossed Aegaean waft.' 
 
 VII. TO SPRING. Schiller. 
 
 WELCOME beauteous youth 
 
 Nature's darling child ! 
 
 Welcome on the verdant plain 
 
 With thy wealth of wood-flowers wild ! 
 
 Here meeting thee again 
 My heart with joy runs o'er 
 For thou art come again 
 And smiling as of yore. 
 
 Know'st thou the maiden still ? 
 Ah ! canst thou friend forget ? 
 'Twas here she loved me well, 
 That maiden loves me yet. 
 
 To deck my maiden's brow 
 Choice flowers I asked of thee ; 
 I come and ask again 
 And thou ! thou giv'st them me.
 
 Blumauer ' An die Donau.' 75 
 
 Then welcome beauteous youth ! 
 Nature's darling child ; 
 Welcome on the verdant plain 
 With thy wealth of wood-flowers wild ! 
 
 THE annexed translation was worked out between a 
 young Moravian clergyman who tenanted a contiguous 
 attic to my own in the city of New York and myself. 
 
 My friend, who was at work for the newspaper called 
 the New York World appealed to me from time to time 
 for a word or a rhyme as a poet is apt to do from any 
 bystander, when he has clenched his fists, knit his 
 brows and despairingly thrown up his eyes to the 
 ceiling in search of inspiration, which will not come, all in 
 vain. It ended in my getting warmed and interested in 
 my friend's work and after taking taking the pen out 
 of his hand pretty well dashing off in hot haste the 
 translation given below, whereby I was made conscious 
 for the first time of the possession of a traductory power 
 of the existence of which within me I was until then 
 entirely unconscious, as much so as the innocent Faublas 
 of a productive faculty of quite another kind, before his 
 first lesson after the evening of the ball. 
 
 VIII. TO THE DANUBE. Blumauer. 
 
 OH ! joy, that I, thou German stream ! 
 
 May hail thee, kinsman true, 
 Who doubts thy kin to our dear land, 
 Come and thy image view.
 
 76 Principles of Versification exemplified. 
 
 Come view the German pride of soul 
 
 Thou in thy bosom bearest, 
 When like the German heart aroused 
 
 Thy angry waves thou rearest. 
 
 The German giant-march behold 
 
 In thy majestic course, 
 And point what race more kin to thee 
 
 E'er started from its source : 
 
 Or see thee eager to the deep 
 Thy seven fond arms expand, 
 
 And say who more resemble thee 
 In friendship's sacred band. 
 
 Then viewing how beneath the wave 
 
 Thy modest bosom swells, 
 Exclaim, within thy veiled career 
 
 Germania's spirit dwells. 
 
 Joy ! then that I thou ancient flood 
 
 May still thy praise renew, 
 And still in thee my race invoke 
 
 Its imaged self to view. 
 
 IX. THE HOSTESS' DAUGHTER. Uhland. 
 
 THREE friends who were students crossed over the Rhine 
 To the house of a hostess where they went in : 
 
 ' Bring out Mother Hostess ! good cyder and wine 
 But where is that beautiful daughter of thine ? '
 
 Ruckert ' Die Locke der begrabenen. 9 77 
 
 ' My cyder and wine run sparkling and clear, 
 
 But my daughter lies there, stretched out on her bier.' 
 
 And when they went in to the fair maiden's room, 
 Lo ! she lay dead and dressed for the tomb. 
 
 The first student drew her veil on one side 
 And wistfully gazing the dead maiden eyed, 
 
 ' Oh ! wert thou but living thou beautiful maid 
 Henceforth how dearly I'd love thee,' he said. 
 
 The second one covered her face up again, 
 And turned round and wept, in piteous strain : 
 
 ' I loved thee so fondly, this many a year, 
 
 And alas ! thou now liest stretched on thy bier.' 
 
 The third one once more, her veil drew aside, 
 Then kissed her pale cheek, and passionate cried, 
 
 1 1 loved thee long fondly, I love thee yet still, 
 And love thee for ever and ever I will.' 
 
 X. THE DEATH-LOCK. RiicTcert. 
 
 ' Eh' ihr sie ins Grab miisst sinken, 
 Gebet mir die Locke nur ! ' 
 
 ERE the earth close o'er thee, 
 
 Maiden loved and fair ! 
 Leave me, I implore thee, 
 
 This one lock of hair.
 
 78 Principles of Versification exemplified. 
 
 Thou, lock ! so lately thrown 
 
 In shadow round her brow, 
 Its glory shed and flown 
 
 Thine, how lustrous now ! 
 
 Nought else of her but will 
 
 To the tomb repair ; 
 But thou ! unfaded still 
 
 Freely float in air. 
 
 Frail as thou appearest, 
 
 Tress so finely wove, 
 Thou the burthen bearest 
 
 Of a heaven of love ! 
 
 One lingering last caress 
 
 Let my fondness share, 
 Then, wind thou sacred tress 
 
 Hound this ring I wear. 
 
 Turning this magic toy 
 
 She whom I adore, 
 Radiant with love and joy, 
 
 Springs to sight once more.* 
 
 * I have taken considerable liberty with the number and 
 time elements of the metre in the above, but I do not find the 
 result offend my ear. For the intermixture of iambic and 
 trochaic lines (although upon a more exact plan) a friend re- 
 minds me that there is Horatian precedent, as also familiar 
 examples in Milton and Ben Jonson. The version is rather a 
 paraphrase than a translation.
 
 Uhland c Das Schloss am Meere.' 79 
 
 I BELIEVE in the earlier stanzas of the annexed version 
 there are some patent errors of interpretation. I re- 
 member being told so at the time when it was com- 
 posed, at which period I was even less conversant with 
 German than at present, and had no dictionary at hand, 
 but only my inward consciousness, to appeal to. We have 
 not Uhland at the Athenaeum Club, and I do not possess 
 a copy of my own to enable me to correct my errors. 
 So I let the piece pass forth as it originally came out 
 of my hands. I cannot read it without some emotion 
 myself, and therefore presume that it must possess a 
 certain synthetic fidelity of tone and feeling, albeit de- 
 fective in verbal conformity to, or even correct perception 
 in some passages, of the meaning of the original. The 
 third stanza always brings back to my mind St. Mary's 
 at Cambridge, as I used to see it, when an undergraduate, 
 by moonlight. 
 
 XL THE CASTLE BY THE SHOEE.* Uhland. 
 
 HAST thou the castle beholden 
 
 The castle by the shore, 
 Where roseate hues and golden 
 
 Over the turrets soar ; 
 
 Beetling as though it might fall 
 
 Into the mirror-bright stream 
 Or rise like a giant tall 
 
 And melt in the evening beam. 
 
 * Mr. Longfellow, I am informed, has translated this poem, 
 but to the best of my recollection I have not seen his translation.
 
 80 Principles of Versification exemplified. 
 
 Oh ! yes, the castle I've seen 
 
 Lifting its spectral head, 
 When above the moon hath been 
 
 And around dim clouds were spread. 
 
 Beating against the sea-wall, 
 
 Made the winds music gay ? 
 Sounded from the castle-hall 
 
 The lute and festive lay ? 
 
 The winds and the waves hushed all, 
 Like, an infant asleep were lying, 
 
 But a^^&om the castle-hall 
 
 Came blent with a piteous sighing. 
 
 Saw'st thou the bride with the king, 
 
 A joyous measure tread, 
 The sheen of the golden ring 
 
 And their mantles dyed with red ? 
 
 Welcomed they not with delight] 
 
 Nuptials of one so fair, 
 More beauteous than morning light, 
 
 Streaming with golden hair ? 
 
 The father and mother I saw, 
 
 Their garments with black were dyed, 
 
 The crowns from their heads withdraw, 
 But never saw more the bride.
 
 Anonymous Poems. 81 
 
 THE annexed and subsequent trifling pieces marked 
 Anonymous come from obscure sources as, long ago, a 
 roving fancy may have dictated, and it would not be 
 worth while to affect to ascertain and afficlier the original 
 authorship of rhymes here reproduced, as a better sort 
 of nonsense-verses, for the sake of exemplifying syzygetic 
 principles. In the Acrostic following the piece below 
 any practised ear will at once notice the prevalence of 
 a ruling N sound, the character imparted by which is 
 a certain mildness and serenity, as in the T sound we 
 may detect a sort of vitreous quality of strength. The 
 compound key N T, as we may call it, is one of frequent 
 occurrence, and forms a peculiarly natural and agreeable 
 combination. Cf. the opening stanzas of the version of 
 Europa, the last piece of the collection. I imagine it 
 would not be difficult, on examination, to ascertain the 
 favorite syzygetic key of any of our more finished poets. 
 
 XII. THE EVENING STAR. Anon. 
 
 WHY ask me, fair and gentle maid, 
 
 Friend to my soul and song ! 
 Who chief in elegance arrayed 
 
 Adorned the festive throng ? 
 
 When Venus seated in the sky 
 
 Amidst the starry choir, 
 Turns on the rapt uplifted eye 
 
 Her gracious orb of fire, 
 
 And looks from out night's vaulted brow 
 
 A queen above the rest, 
 How canst thou fail untaught to know 
 
 The loveliest, brightest, best?
 
 82 Principles of Versification exempli/led. 
 
 XIII. ACKOSTIC. Anon. 
 
 JOY ! happy mother, that indulgent Heaven 
 Unto thy love, so dear a child hath given. 
 Serenely bright, like yon pure starry way 
 That shines with lustre lovelier than the day ; 
 Innocent joy be still her treasured dower, 
 Nor ever evil, staining that sweet flower, 
 Alloy the golden gleam of life's fair opening hour ! 
 
 XIV. WINTEE. Anon. 
 
 WHEN winter treads his dreary round 
 
 And cold congeals the air 
 And snows lie deep upon the ground 
 
 And woods wave bleak and bare, 
 
 When winds in angry warfare meet 
 
 And clouds obscure the sun 
 And pining for their vital heat 
 
 The streams forget to run, 
 
 Say ! were it best my constant friend 
 
 Of heart unfeigned, and pure ! 
 Cowering beneath the blast to bend 
 
 Or manfully endure: 
 
 And still through winter's dreariest gloom 
 
 A cheerful trust maintain 
 That Heaven will smile, the woodlands bloom 
 
 And spring come round again.
 
 Anonymous Poems. 83 
 
 XV. TO AN INK-SPOT UPON A LADY'S CHEEK. 
 
 Anon. 
 
 WHERE tender-hued emotion's tide 
 
 Mirrors the soul within, 
 Why seek, dull spot ! the bloom to hide 
 
 Or veil the lustrous skin ? 
 
 Why on .that rose with envious spite 
 
 Pillow thy ebon head. 
 Shadowing the soft and sunny light, 
 
 Those orbs of feeling shed ? 
 
 Pencilled with clouds, the azure vault 
 
 But beams more heavenly pure, 
 And spots upon the sun exalt 
 
 The brightness they obscure. 
 
 Presumptuous spot ! some elsewhere aeek 
 
 A meaner flower to stain, 
 Nor hope to mar this matchless cheek 
 
 Where youth and beauty reign. 
 
 Here dwells a secret sacred charm, 
 
 All ill intents to foil ; 
 No touch of malice, here can harm 
 
 No spot of envy soil. 
 
 XVI. MELANCHOLY. Anon. 
 
 OH, why my fair and only love 
 Thus heaves thy gentle breast ? 
 
 That tender bosom where the dove 
 Of peace should build her nest.
 
 84 Principles of Versification exemplified. 
 
 Like one whom inward thoughts oppress 
 
 Thou smotherest oft a sigh, 
 And at the name of happiness 
 
 A tear starts to thine eye. 
 
 As if there lay within the word 
 Some secret power to wound, 
 
 You shudder like a startled bird 
 Whene'er I breathe the sound. 
 
 No more the joyous sunbeams dance 
 
 In those once playful eyes ; 
 They flame but with a fitful glance 
 
 Lighting Hope's obsequies. 
 
 Upon thy uncomplaining brow 
 
 Sits melancholy throned, 
 And every feature tells of woe 
 
 Those lips have never owned. 
 
 Some nourished pain thou shunn'st to speak 
 
 Shadows thy rising years, 
 And spreads a paleness o'er thy cheek 
 
 More pitiful than tears. 
 
 So young, so lovely, and caressed 
 Whence can thy sorrow spring, 
 
 What scorpion touch of grief has pressed 
 To those soft veins its sting ? 
 
 Oh ! but to feel thy heart beat sound 
 Washed clear from every stain, 
 
 My lips would suck the venomed wound 
 And all its poison drain ;
 
 Anonymous Poems. 85 
 
 The mortal anguish I'd endure 
 
 And triumph 'midst my pain, 
 Could I but so thy sorrows cure 
 
 And see thee smile again ! 
 
 XVH. APEIL 30. Anon. 
 
 ONCE more the breath of spring 
 With fragrance fills the air, 
 
 And birds on happy wing 
 Trill forth their paeans clear. 
 
 The swelling buds disclose 
 Their treasures garnered long, 
 
 The balmy west wind blows 
 The trembling boughs among. 
 
 And gaily through the mist 
 The cheerful sun doth break, 
 
 Like lover who has kissed 
 The tears off beauty's cheek. 
 
 In vain for me the while 
 The rustling zephyrs play, 
 
 Or opening blossoms smile 
 To welcome back the May: 
 
 In vain the sun doth slant 
 
 Down the green sward his beam, 
 And the winged choir descant 
 
 Their gaily carolled theme.
 
 86 Principles of Versification exemplified. 
 
 Banished from looks which fell 
 Like dews from heaven on me, 
 
 And lips whose tones could swell 
 My soul to ecstasy, 
 
 The pomp of vernal skies 
 
 Is powerless to win 
 This heart where feeling dies 
 
 And winter dwells within. 
 
 XVIII. INDIFFERENCE. Anon. 
 
 OR give me praise or give me blame 
 
 Each I would learn to bear, 
 But teach me not that hateful name 
 
 Indifference to hear. 
 
 Indifference wars against the plan 
 
 Decreed by powers above, 
 When God in love created man 
 
 And bade him live by love. 
 
 Spread o'er the earth its soft attire 
 With song inspired the groves 
 
 Lent to the orbs of eve their fire, 
 And blessed each thing that moves. 
 
 By no indifferent hand designed, 
 Such joys to man were given, 
 
 But from a free and bounteous mind, 
 Spontaneous grace of Heaven.
 
 Anonymous Poems. 87 
 
 His love was with thee at thy birth 
 
 And formed thee what thou art ; 
 His love still walks with thee on earth 
 
 And glows within thy heart ; 
 
 Sheds on thy cheek its varying hue 
 
 Soft lustre on thine eye ; 
 Smiles on those lips more soft to view 
 
 Than sunset in the sky ; 
 
 Bids Nature teach thee skill to know 
 
 The beautiful and true, 
 And Art her magic mantle throw 
 
 On all within thy view. 
 
 When Chaos was, ere yet the light 
 
 Had dawned upon the day, 
 Indifference sat o'er cloud and night 
 
 In solitary sway. 
 
 But when Night fled as one ashamed, 
 
 And Chaos' rule was o'er, 
 The voice of Heaven itself proclaimed 
 
 Indifference rules no more. 
 
 Then give me praise or give me blame 
 
 Each I will learn to bear, 
 But force me not that hateful name 
 
 Indifference to hear. 
 
 XIX. REMONSTRANCE. Anon. 
 
 OH ! why those narrow rules extol ? 
 
 These but restrain from ill, 
 True virtue lies in strength of soul 
 
 And energy of will.
 
 88 Principles of Versification exemplified. 
 
 To all that's great and high aspires, 
 
 Prompts to the path of fame 
 From Heaven draws down Promethean fires 
 
 And wraps the soul in flame. 
 
 With brow erect, eye undismayed 
 
 Confronts the midday sun, 
 Nor sleeps inglorious in the shade 
 
 Of praises cheaply won ; 
 
 Scans not too curiously the chance 
 
 Of good or evil fate, 
 But with a free and fearless glance 
 
 Knocks at Hope's golden gate ; 
 
 The truthful course pursues and knows 
 
 By Heaven-imparted light, 
 And scorns to shape to outward shows 
 
 Its conscious sense of right. 
 
 Still, while it renders Reason's name 
 
 The meed of honour due 
 Forgets not sacred instincts claim. 
 
 Their share of reverence too. 
 
 The frown of unjust censure braves, 
 
 Retreats not with the tide, 
 But nobly stems and stills the waves 
 
 Of prejudice and pride. 
 
 XX. FAITH. Anon. 
 
 NOR earth, nor air, nor seas, nor fire, 
 Nor aught that fate can interpose 
 Nor open scorn nor secret foes 
 
 Shall tear me from my heart's desire.
 
 Anonymous Poems. 89 
 
 Like those antique imperial dyes 
 
 Which age nor use can e'er efface, 
 
 But win from Time a nobler grace, 
 Stamped on my soul, thy image lies. 
 
 While Faith still vivifies this frame, 
 Or Memory prompts one soul-felt sigh 
 And Hope looks upward to the sky, 
 
 This heart shall beat, for thee the same. 
 
 No mortal strength nor skill can sever 
 The link which kindred atoms binds, 
 Nor less, congenial kindred minds, 
 
 United once, are one for ever. 
 
 XXI. KEPLER'S APOSTROPHE. Anon. 
 
 YES ! on the annals of my race, 
 
 In characters of flame, 
 Which time shall dim not nor deface, 
 
 I'll stamp my deathless name. 
 
 The fire which on my vitals preys, 
 
 And inly smouldering lies, 
 Shall flash out to a meteor's blaze 
 
 And stream along the skies. 
 
 Chafed as the angry ocean's swell 
 
 My soul within me boils, 
 Like a chained monarch in his cell, 
 
 Or lion in the toils. 
 F
 
 90 Principles of Versification exemplified. 
 
 To wealth, to pride, to lofty state, 
 
 No more I'll bend the knee, 
 But Fortune's minions, meanly great, 
 
 Shall stoop their necks to me. 
 
 The God which formed me for command, 
 And gave me strength to rise, 
 
 Shall plant His sceptre in my hand, 
 His lightning in my eyes ; 
 
 Shall with the thorny crown of fame 
 
 My aching temples bind, 
 And hail me by a mighty name 
 
 A monarch of the mind. 
 
 Me, heaven's bright galaxy shall greet 
 
 Theirs by primordial choice, 
 And earth the eternal tones repeat 
 
 Of my prophetic voice. 
 
 Stung in her turn, the heartless fair 
 
 Who proudly eyes me now, 
 Shall weep to see some other share 
 
 The godhead of my brow ; 
 
 Shall weep to see some lovelier star 
 Snatched to my soul's embrace, 
 
 Ascend with me Fame's fiery car 
 And claim celestial place. 
 
 Tune oh ! my soul thy loftiest strain, 
 
 Exult in song and glee, 
 For scorn has snapped each earthlier chain 
 
 And set the immortal free.
 
 Anonymous Poems. 91 
 
 Minds destined to a glorious shape 
 
 Must first affliction feel ; 
 Wine oozes from the trodden grape, 
 
 Iron's blistered into steel ; 
 
 So gushes from affection bruised 
 Ambition's purple tide, 
 
 And steadfast faith unkindly used 
 Hardens to stubborn pride. 
 
 XXII. FROM THE ITALIAN. 
 
 OCCHI ! stelle immortali, 
 Cagione de' miei mali ! 
 Se chiusi m' ammazate, 
 Aperti che farete ! 
 
 EYES, like stars in heaven that glow, 
 Eyes, creators of my woe ! 
 If e'en closed, my soul ye slew, 
 What, wide open, would ye do ! 
 
 XXIH. WHAT'S IN A NAME ? Anon. 
 
 IN names a mystic virtue lies 
 Concealed but clear to loving eyes, 
 And sounds have influence to control 
 The inmost workings of the soul.
 
 92 Anonymous Poems. 
 
 The voice which breathes thy name in air, 
 Speaks thou art gentle, good, and fair, 
 Mild as the fragrant breeze in May, 
 Or earliest blushes of the day. 
 
 The guardian angel at thy birth, 
 When first he welcomed thee on earth 
 Rapt in the wonder of thine eyes 
 Murmured a Ha ! of pleased surprise. 
 
 But grieved that one like angels fair 
 The mortal soil of earth must share, 
 And e'en thy star of beauty set 
 Sighed out an ah ! of fond regret. 
 
 Attendant spirits hovering nigh 
 Caught up the murmur and the sigh, 
 With two dull links the sounds brought near 
 And stamped the name, each loves to hear. 
 
 Whichever way we turn that name 
 It speaks to eye and soul the same ; 
 It tells of honesty and truth, 
 Unaltering innocence of youth.
 
 Hor. Od. III. xxvii. 25. 93 
 
 XXIV. THE STORY OF EUROPA.* 
 HOB. OD. IIL xxvii. 25. 
 
 SNOW-WHITE midst Ocean's monster-brood, 
 
 Set sidelong on the crafty steer, 
 At mantling perils of the flood, 
 
 The bold Europa paled with fear. 
 
 She who but now culled meadow-flowers, [5 
 
 And for the Nymphs, vowed garlands wove, 
 
 Sees nought in twilight's dusky hours, 
 Save billows round and stars above ! 
 
 So when to mighty Crete she came, [9 
 
 The hundred-citied, ' Father !' cries, 
 ' Oh ! forfeit filial tie and name,' 
 
 Whilst fury flashes from her eyes. 
 
 * I quote the subjoined argument from honest old Lem- 
 priere : ' Europa, a daughter of Agenor, King of Phoenicia and 
 Telephassa. She was so beautiful that Jupiter became enamoured 
 of her, and the better to engage her affections, he assumed the 
 shape of a bull, and mingled with the herds of Agenor, while 
 Europa and her female attendants were gathering flowers in the 
 meadows. Europa caressed the beautiful animal, and at last 
 had the courage to mount upon his back. The god took ad- 
 vantage of her situation, and retiring towards the shore, crossed 
 the sea, with Europa on his back, and arrived safe in Crete. 
 Here he assumed his original shape, and declared his love. The 
 nymph, a stranger on an unknown shore, consented (although 
 she had once made vows of perpetual celibacy), and became the 
 mother of Minos, Sarpedon, and Khadamanthus.' Could any- 
 thing be more regular and satisfactory ?
 
 94 Principles of Versification exemplified. 
 
 1 Whence come and where ? One death were gain [13 
 
 Lost maiden honour to redeem ; 
 Weep I awake, a suffered stain, 
 
 Or mocks me guiltless, a vain dream, 
 
 ' Flit through the ivory porch of sleep ? [17 
 
 Which were the happier choice to prove, 
 
 To crop the freshly flowering heap, 
 Or o'er long wastes of sea to rove ? 
 
 ' Oh ! that the monster near me stood, [21 
 
 Too fondly loved now loathed again ! 
 This steel I'd crimson with his blood, 
 
 And rend his milk-white horns in twain. 
 
 ' Shameless I fled my father's home, [25 
 
 Shameless 'scape death oh ! hear my prayer, 
 
 And grant, some God ! that I may roam 
 Naked where lions make their lair ; 
 
 ' Ere from my form the juices drain, [29 
 
 Or foul decay my fair cheeks soil, 
 Let tigers hunt me o'er the plain, 
 
 But beauteous still, devour their spoil.' 
 
 Cries, ' vile Europa ! Why delay ? ' [33 
 
 My far-off Sire { on yon ash nigh 
 In virgin zone, well fetched away, 
 
 Go wrench thy neck and pendent die : 
 
 ' Or trusting to the whirlwind's breath, [37 
 
 If rocks and reefs more charm thy soul, 
 
 Fall on these ledges lined with death ; 
 Else, take the shame of carding wool,
 
 Hor. Od. III. xxvii. 25 Notes. 95 
 
 V 
 
 ' Handmaid to some barbarian dame, [41 
 
 And harlot of a royal line ; ' 
 With loosened bow, young Love now came, 
 
 And Venus with a laugh malign. ;w 
 
 Who, when enough she had mocked the fair : [45 
 Said ' Hush thy wrath, no more complain ; 
 
 The hateful bull, since such thy prayer, 
 Yields thee his horns to rend in twain : 
 
 ' Of mighty and all-conquering Jove [49 
 
 Know thou art consort, sobs forswear ; 
 
 Learn worthy thy proud state to prove, 
 
 Earth's fractioned orb, thy names shall bear.' 
 
 NOTES. 
 
 2. Medias fraudes.'] Very difficult to interpret, for there are four 
 different meanings attributed to medias, viz. ' intervening,' ' en- 
 veloping,' ' midway,' ' laid open ; ' and three to fraudes, viz.' frauds,' 
 ' damages,' 'dangers ; ' making twelve combinations in all to choose 
 from. The commentators at my command give no help (as I find 
 is usual with them in any case of real difficulty) ; and Forcellini 
 fails me. Some people tell me that medias means peripheral that 
 the frauds in the middle of Europa, or Europa in the middle of 
 the frauds, is, by poetical licence, all one. I once thought medias 
 must mean ' intermediate,' in the sense of referring to the frauds 
 which intervened between her playing with the bull and her 
 finding herself where she was ; but then, I asked myself, was she 
 in a position to turn pale at thoughts of anything that had hap- 
 pened? were not all her thoughts and emotions concentrated 
 on the present? Professor Key tells me that the old meaning 
 of fraus is ' damage,' and that the word is employed here in 
 that sense. I should have thought this was rebutted, by doloso 
 preceding ; but I bow to so great an authority, which also is 
 supported by Newman's ' midway mischiefs,' and to some extent
 
 96 Pi^mciples of Versification exemplified. 
 
 also by Professor Conington's, who, as not unusual -with him, goes 
 off, not at a tangent, but at an asymptote, and gives as the equiva- 
 lent for medias fraudes, ' the yawning grave.' What if the old 
 Delphin version of apertas for inedlas, and Scriven's frauds 
 displayed (the very heart of the fraud, as one might say, ' the 
 very heart of the machine'), were the true conception, after all ? 
 Yielding (although entirely unvisited by a single ray of con- 
 viction from ' the illative sense ') to my a priori faith in the cor- 
 rect judgment, in such a matter, of Key, Newman, and Conington, 
 i. e. accepting their interpretation of fraudes, I take fraudes 
 medias to mean dangers ahead, perils on her path midway 
 between where she is and (not where she was, but) wherever 
 she may unconsciously be drifting to. I can understand how 
 medias X's may come to mean surrounding X's, in the manner 
 following : If an X is intermediate between me and anywhere 
 I may be going to, then (like the case of differentiating a function, 
 a la Cauchy, all round a point) I am enveloped by X's, and so 
 medias fraudes may come to mean enveloping 'fraudes,' a medium, 
 a net- work of ' fraudes,' ' fraudes ' encompassing me all round 
 about. 
 
 14.] Virginum culpa I understand to refer to loss of character 
 consequent upon Europa being thrown an unprotected female on 
 an island with its hundred cities swarming with the dangerous 
 sex. I maintain fearlessly in opposition to the dark and unwar- 
 rantable imputations cast by Professor Newman on the conduct 
 of the heroine, and still more on the taste of the elegant recounter 
 of the story, that it contains no reference to any worse conduct on 
 the part of Europa than, Clarissa-like, allowing herself to be 
 thoughtlessly carried off from her father's house by the back door. 
 The words ' Credidit tauro latus,' ' Nuper in pratis,' ' quae simul 
 tetigit,' ' unde quo veni,' not unsupported also by the sneering 
 words 'zona bene te secuta,' give a complete account of her 
 actions and establish an irrefragable alibi as regards the locus 
 in quo for any improper purpose, from the time of her sidling 
 on the bull's back to the moment of her being landed on shore, 
 and momentarily abandoned by the instrument of her abduction. 
 At the end of her burst of rage, after she has had a good cry, 
 Jupiter reappears (in his own character) like a prince restored 
 to his proper form and throwing off his disguise in the retrans- 
 fonnation or denouement scene of a pantomime, and Venus with 
 her boy is the good fairy, all in white with crown on head and
 
 HOT. Od. III. xxvii. 25 Notes. 97 
 
 sceptre in hand, who smiles on the reunited lovers and assures 
 and consecrates their mutual happiness. With the odious view 
 Professor Newman has chosen to take of Horace's treatment of 
 the subject, why did he trouble himself to introduce any part of it 
 into his translation ; why not have left it alone altogether ? 
 
 Professor Newman in his preface vindicatory of his peculiar 
 mode of translation says, ' some approximation may be attained 
 which gives to the reader not only a knowledge of the substance 
 but a feeling of the form of thought and a right conception of 
 the antient tone of mind.' Has he favored the world with this 
 torso of the beautiful original in order that the rising age might 
 not lose the benefit of the form of thought and antique tone con- 
 veyed by his interpolated, ' heavenly Venus stood at her side, and 
 soft words whispered of MYSTIC COMFORT, which dream not thou 
 to hear ' ? What moral right had Mr. Newman to put such words 
 into the mouth of his author, and to substitute his own pedantic 
 mode of ri vetting the story to its procemium, the jewel to his 
 setting, for the graceful and poetical abandon of his inimitable 
 original? Was this just to Horace, or fair to his readers? It 
 reminds one of the King of Portugal, who would have taught 
 God a simpler and a better plan of constructing the Universe 
 had he stood by and been consulted on the day of creation. 
 
 47.] ' Dolose ac maligne,' sed juncta ironia, non enim irata 
 advenit Venus,' says the excellent Orelli a propos of ' perfidum 
 ridens.' This then we see is the exact counterpart of the French 
 sourire matin, and offers a good occasion of introducing the 
 idiom into our own language. 
 
 52.] Why nomina in the plural ? Once I thought it might be 
 simply idiomatic, as we say ' style and title ; ' again, I thought 
 it was possibly poetical amplification, or magnification a sort 
 of reflected ascription of plurality an attempt to stretch out a 
 name, to make it fit to clothe so vast a subject as the Orbs terra. 
 Then, again, I thought it was possibly a logical consequence of 
 the partibility of a name of the fact that every syllable of a 
 name is itself a name a thing by which the bearer of the name 
 may be known ' and airy tongues that syllable men's names.' 
 Nay, I found some were of opinion that the plural was contrary 
 to sense and introduced only for the sake of euphony and metre. 
 But I think now that the true solution is neither idiomatical nor 
 poetical nor logical, nor metrical, but transcendental intended 
 as a gratification of that sense of the manifold in unity (equally
 
 98 Principles of Versification exemplified. 
 
 the delight of Mariolater and Methodist) which is the chief source 
 of religious ecstasy, as the converse principle that of unity in 
 the manifold is of philosophic exaltation. The phrase sectus 
 orbis raises the conception of division of a frontier line between 
 Europe and the rest of the world. Wherever, on one side, along 
 this frontier line, or within it, one might ask the general name 
 of the place, ' Europa ' we should hear in reply : a painted map 
 would be starred all over with ' Europas ' as many ' Europas ' 
 as kingdoms or subdivisions of the Continent, the name swarm- 
 ing everywhere, like the Bourbon fleur-de-lys or the ' T. M.' of 
 the Catholic sovereigns. The passages from Horace and Ovid 
 quoted by Orelli, both referring to Icarus, corroborate this 
 manner of interpretation, as each island in the sea belonging 
 to him would, as it were separately, assert his name. This 
 view justifies me, I think, in preserving the plural form of the 
 word in the translation, and so getting a soft s into the line. 
 The much-abused sibilants the hard and soft s or s sounds 
 are for English verse what his glazes, or I believe I ought to say 
 his varnish, are for the painter (is there not a sort of analogy 
 between sibilance and glare, or tendency to crackle ?) : they are 
 the indispensable menstruum for giving unity and continuity to 
 the surface of the canvas ; but of course care must be taken, in 
 the one case as in the other, not to overvarnish. 
 
 56.] I join with Orelli and Macleane in applauding this honest 
 burst of feminine feeling, the heroic and martyr-like regard to 
 the conservation of her good looks, which is a woman's first 
 duty to her sex, and to her prerogative of upholding in herself 
 and others the type of physical perfection, which in the long 
 run brings moral and intellectual perfection too, in its train. I 
 well remember hearing the late agreeable and clever octogenarian 
 
 Madame , a connection by marriage of the Bonaparte family 
 
 (whom she strikingly resembled in feature), express herself to me 
 with some disdain of her American countrywomen, who, as she 
 said, marry a man ' because they like him and admire his good 
 looks, whereas in Europe girls marry for rank and social position.' 
 This lady, who had imbibed European notions, evidently thought 
 it was rather a vulgar taste in women to admire beauty, strength, 
 and stature in a man, or, at all events, to act on such a feeling. 
 She was, in my opinion, quite wrong ; and her countrywomen, 
 in taking heed of their natural instincts in the matter, are per- 
 forming a high moral duty, of which society reaps the benefit.
 
 INAUGUEAL PRESIDENTIAL ADDRESS 
 
 TO THE 
 
 MATHEMATICAL AND PHYSICAL SECTION 
 
 OF THE 
 
 BEITISH ASSOCIATION AT EXETER, 
 August, 1869.
 
 101 
 
 INAUGURAL PRESIDENTIAL ADDRESS, 
 
 &c. &c. 
 
 LADIES AND GENTLEMEN, 
 
 A few days ago I noticed in a shop window the 
 photograph of a Royal mother and child, which seemed 
 to me a very beautiful group; on scanning it more 
 closely, I discovered that the faces were ordinary, or, at 
 all events, not much above the average, and that the 
 charm arose entirely from the natural action and 
 expression of the mother stooping over and kissing her 
 child which she held in her lap; and I remarked to 
 myself that the homeliest features would become 
 beautiful when lit up by the rays of the soul like the 
 sun ' gilding pale streams with heavenly alchemy.' 
 By analogy, the thought struck me that if a man would 
 speak naturally and as he felt on any subject of his 
 predilection, he might hope to awaken a sympathetic 
 interest in the minds of his hearers ; and, in corrobora- 
 tion of this I remembered witnessing how the writer of a 
 well-known article in the ' Quarterly Review ' so mag- 
 netised his audience at the Royal Institution by his 
 evident enthusiasm that, when the lecture was over 
 and the applause had subsided, some ladies came up to 
 me and implored me to tell them what they should do 
 to get up the Talmud ; for that was what the lecture 
 had been about.
 
 102 Inaugural Presidential Address. 
 
 Now, as I believe that even Mathematics are not 
 much more repugnant than the Talmud to the common 
 apprehension of mankind, and I really love my subject, 
 I shall not quite despair of rousing and retaining your 
 attention for a short time if I proceed to read (as, for 
 greater assurance against breaking down, I shall beg 
 your permission to do) from the pages I hold in my 
 hand. 
 
 It is not without a feeling of surprise and trepidation 
 at my own temerity that I find myself in the position of 
 one about to address this numerous and distinguished 
 assembly. When informed that the Council of the 
 British Association had it hi contemplation to recom- 
 mend me to the General Committee to fill the office of 
 President to the Mathematical and Physical Section, 
 the intimation was accompanied with the tranquillizing 
 assurance that it would rest with myself to deliver or 
 withhold an address as I might think fit, and that 
 I should be only following in the footsteps of many of 
 the most distinguished of my predecessors were I to 
 resolve on the latter course. 
 
 Until the last few days I had made up my mind to 
 avail myself of this option, by proceeding at once to the 
 business before us without troubling you to listen to 
 any address, SAvayed thereto partly by a consciousness 
 of the very limited extent of my oratorical powers, partly 
 by a disinclination, in the midst of various pressing 
 private and official occupations, to undertake a kind of 
 work new to one more used to thinking than to speak- 
 ing (to making mathematics than to talking about 
 them), and partly and more especially by a feeling of 
 my inadequacy to satisfy the expectations that would
 
 Introductory Remarks. 103 
 
 be raised in the minds of those who had enjoyed 
 the privilege of hearing or reading the allocution 
 (which fills me with admiration and dismay) of 
 my gifted predecessor, Dr. Tyndall, a man in whom 
 eloquence and philosophy seem to be inborn, whom 
 Science and Poetry woo with an equal spell, and 
 whose ideas have a faculty of arranging themselves 
 in forms of order and beauty as spontaneously and 
 unfailingly as those crystalline solutions from which, in 
 a striking passage of his address, he drew so vivid and 
 instructive an illustration. 
 
 From this lotos-eater's dream of fancied security and 
 repose I was rudely awakened by receiving from the 
 editor of an old-established journal in this city, a note 
 containing a polite but peremptory request that I 
 should, at my earliest convenience, favour him with a 
 ' copy of the address I proposed to deliver at the 
 forthcoming meeting.' To this invitation, my first 
 impulse was to respond very much in the same way as 
 did the ' Needy knife-grinder ' of the ' Antijacobin,' 
 when summoned to recount the story of his wrongs to 
 his republican sympathiser ' Story, God bless you, 
 I have none to tell, Sir ! ' ' Address, Mr. Editor, I 
 have none to deliver.' 
 
 I have found, however, that increase of appetite still 
 grows with what it feeds on, that those who were 
 present at the opening of the Section last year, and 
 enjoyed my friend Dr. Tyndall's melodious utterances, 
 would consider themselves somewhat ill-treated if they 
 were sent away quite empty on the present occasion, 
 and that, failing an address, the members would feel 
 very much like the guests at a wedding-breakfast
 
 104 Inaugural Presidential Address. 
 
 where no one was willing or able to propose the health 
 of the bride and bridegroom. 
 
 Yielding, therefore, to these considerations and to 
 the advice of some officially connected with the Asso- 
 ciation, to whose opinions I feel bound to defer, and 
 unwilling also to countenance by my example the 
 too prevailing opinion that mathematical pursuits unfit 
 a person for the discharge of the common duties of life 
 and cut him off from the exercise of Man's highest 
 prerogative, ' discourse of reason and faculty of speech 
 divine,' rather, I say than favour the notion that we 
 Algebraists (who are wont to regard each other as 
 the flower and salt of the earth) are a set of mere 
 calculating-machines endowed with organs of locomo- 
 tion, or, at best, a sort of poor visionary dumb creatures 
 only capable of communicating by signs and symbols 
 with the outer world, I have resolved to take heart of 
 grace and to say a few words, which I hope to render, 
 if not interesting, at least intelligible, on a subject to 
 which the larger part of my life has been devoted. 
 
 The President of the Association, Prof. Stokes, is so 
 eminent alike as a mathematician and physicist, and so 
 distinguished for accuracy and extent of erudition and 
 research, that I felt assured I might safely assume 
 he would, in his Address to the Association at large, 
 take an exhaustive survey, and render a complete 
 account, of the recent progress and present condition 
 and prospects of Mathematical and Physical Science 
 at home and abroad. This consideration narrowed 
 very much and brought almost to a point the ground 
 available for me to occupy in this Section ; and as I 
 cannot but be aware that it is as a cultivator of pure 
 mathematics (the subject in which my own researches
 
 'Homo mathematicus.'' 105 
 
 have chiefly, though by no means exclusively, lain*) 
 that I have been placed in this Chair, I hope the Section 
 will patiently bear with me in the observations I shall 
 venture to make on the nature of that province of the 
 human reason and its title to the esteem and veneration 
 with which through countless ages it has been, and, 
 so long as Man respects the intellectual part of his 
 nature, must ever continue to be, regarded. f 
 
 It is said of a great party leader and orator in the 
 
 * My first printed paper was on Fresnel's Optical Theory, 
 published in the Philosophical Magazine ; my latest contribution 
 to the Philosophical Transactions is a memoir on the ' Rotation 
 of a Free Rigid Body.' There is an old adage, ' purus mathe- 
 maticus, purus asinus.' On the other hand, I once heard the 
 great Richard Owen say, when we were opposite neighbours in 
 Lincoln's Inn Fields (doves nestling among hawks), that he 
 would like to see Homo mathematicus constituted into a distinct 
 subclass, thereby suggesting to my mind sensation, perception, 
 reflection, abstraction, as the successive stages or phases of pro- 
 toplasm on its way to being made perfect in Mathematicised 
 Man. Would it sound too extravagant to speak of perception 
 as a quintessence of sensation, language (i.e. communicable 
 thought) of perception, mathematic of language? We should 
 then have four terms differentiating from inorganic matter and 
 from each other the Vegetable, Animal, Rational, and Super- 
 sensual modes of existence. 
 
 f Mr. Spottiswoode favoured the Section, in his opening ad- 
 dress, with a combined history of the progress of Mathematics 
 and Physics ; Dr. Tyndall's address was virtually on the limits 
 of Physical Philosophy ; the one here in print is an attempted 
 faint adumbration of the nature of Mathematical Science in the 
 abstract. What is wanting (like a fourth sphere resting on three 
 others in contact) to build up the ideal pyramid is a discourse 
 on the Relation of the two branches (Mathematics and Physics) 
 to, their action and reaction upon, one another, a magnificent 
 theme with which it is to be hoped some future President of 
 Section A will crown the edifice, and make the tetralogy 
 (symbolizable by A + A', A', A, A.A') complete. 
 G
 
 106 Inaugural Presidential Address. 
 
 House of Lords that, when lately requested to make a 
 speech at some religious or charitable (at all events 
 a non-political) meeting, he declined to do so on the 
 ground that he could not speak unless he saw an 
 adversary before him somebody to attack or reply 
 to. In obedience to a somewhat similar combative 
 instinct, I set to myself the task of considering certain 
 recent utterances of a most distinguished member of 
 this Association, one whom I no less respect for his 
 honesty and public spirit than I admire for his genius 
 and eloquence,* but from whose opinions on a subject 
 which he has not studied I feel constrained to differ. 
 Goethe has said 
 
 ' Verstandige Leute kannst du irren sehn : 
 In Sachen, namlich, die sie nicht verstehn.' 
 
 Understanding people you may see erring in those 
 things, to wit, which they do not understand. 
 
 I have no doubt that had my distinguished friend, 
 the probable President-elect of the next Meeting of the 
 Association, applied his uncommon powers of reasoning, 
 induction, comparison, observation, and invention to 
 the study of mathematical science, he would have 
 become as great a mathematician as he is now a 
 biologist ; indeed he has given public evidence of his 
 ability to grapple with the practical side of certain 
 mathematical questions; but he has not made a study 
 of mathematical science as such, and the eminence 
 of his position and the weight justly attaching to his 
 name render it only the more imperative that any 
 assertions proceeding from such a quarter, which may 
 
 * Although no great lecture-goer, I have heard three lectures 
 in my life which have left a lasting impression as master-pieces 
 on my memory Clifford on Mind, Huxley on Chalk, Dumas on 
 Faraday.
 
 Huxley's Opinions on Mathematical Science. 107 
 
 appear to me erroneous, or so expressed as to he 
 conducive to error, should not remain unchallenged or 
 be passed over in silence.* 
 
 He says ' mathematical training is almost purely 
 deductive. The mathematician starts with a few 
 simple propositions, the proof of which is so obvious 
 that they are called self-evident, and the rest of 
 his work consists of subtle deductions from them. The 
 teaching of languages, at any rate as ordinarily 
 practised, is of the same general nature authority and 
 tradition furnish the data, and the mental operations 
 are deductive.' It would seem from the above some- 
 what singularly juxtaposed paragraphs that, according to 
 Prof. Huxley, the business of the mathematical student 
 is from a limited number of propositions (bottled up and 
 labelled ready for future use) to deduce any required 
 result by a process of the same general nature as 
 a student of language employs in declining and conju- 
 gating his nouns and verbs that to make out a 
 mathematical proposition and to construe or parse 
 a sentence are equivalent or identical mental opera- 
 tions. Such an opinion scarcely seems to need serious 
 refutation. The passage is taken from an article in 
 ' Macmillan's Magazine ' for June last, entitled ' Scien- 
 tific Education Notes of an After-dinner Speech,' and 
 I cannot but think would have been coiiched in more 
 guarded terms by my distinguished friend had his 
 speech been made before dinner instead of after. 
 
 The notion that mathematical truth rests on the 
 
 * In his eloge of Daubenton, Cuvier remarks, ' Les savants 
 jugent toujours comme le vulgaire les ouvrages qui ne sent pas 
 de leur genre.' 
 
 e2
 
 108 Inaugural Presidential Address. 
 
 narrow basis of a limited number of elementary 
 propositions from which all others are to be derived by 
 a process of logical inference and verbal deduction, has 
 been stated still more strongly and explicitly by the 
 same eminent writer in an article of even date with the 
 preceding in the ' Fortnightly Review,' where we are 
 told that ' Mathematics is that study which knows 
 nothing of observation, nothing of experiment, nothing 
 of induction, nothing of causation.' I think no state- 
 ment could have been made more opposite to the 
 undoubted facts of the case ; that mathematical analysis 
 is constantly invoking the aid of new principles, new 
 ideas, and new methods, not capable of being denned 
 by any form of words, but springing direct from the 
 inherent powers and activity of the human mind, and 
 from continually renewed introspection of that inner 
 world of thought of which the phenomena are as 
 varied and require as close attention to discern as 
 those of the outer physical world (to which the inner 
 one in each individual man may, I think, be conceived 
 to stand in somewhat the same general relation of 
 correspondence as a shadow to the object from 
 which it is projected, or as the hollow palm of 
 one hand to the closed fist which it grasps of the 
 other), that it is unceasingly calling forth the faculties 
 of observation and comparison, that one of its principal 
 weapons is induction, that it has frequent recourse to 
 experimental trial and verification, and that it affords a 
 boundless scope for the exercise of the highest efforts of 
 imagination and invention.* 
 
 * The annexed instance of Mathematical euristic is, I think, 
 from its intrinsic interest, worthy of being put on record. The 
 so-called canonical representation of a binary quartic of the
 
 Example of Mathematical Euristic. 109 
 
 Lagrange, than whom no greater authority could be 
 quoted, has expressed emphatically his belief in the 
 importance to the mathematician of the faculty of 
 
 eighth degree I found to be a quartic multiplied by itself, toge 
 ther with a sum of powers of its linear factors, just as for the 
 fourth degree it was known to be a quadric into itself, together 
 with a sum of powers of its factors ; but for a sextic a cubic 
 multiplied into itself, with a tail of powers as before, was not 
 found to answer. To find the true representation was like 
 looking out into universal space for a planet desiderated according 
 to Bode's or any other empirical law. I found my desideratum 
 as follows : I invented a catena of morphological processes which, 
 applied to a quadric or to a quartic, causes each to reproduce 
 itself: I then considered the two quadrics and two quartics to be 
 noumenally distinguishable (one as an automorphic derivative 
 of the other) although phenomenally identical. The same catena 
 of processes applied to the cubic gave no longer an identical but 
 a distinct derivative, and the product of the two I regarded as 
 the analogue of the before-mentioned square of the quadric or 
 of the quartic. This product of a cubic by its derivative so ob- 
 tained together with a sum of powers of linear factors of the 
 original cubic, I found by actual trial to my great satisfaction 
 satisfied the conditions of canonicity, and it was thus I was led 
 up to the desired representation, which will be found reproduced 
 in one of Prof. Cayley's memoirs on Quantics, and in Dr. Salmon's 
 lectures on Modern Algebra. Here certainly induction, obser- 
 vation, invention, and experimental verification all played their 
 part in contributing to the solution of the problem. I discovered 
 and developed the whole theory of canonical binary forms for 
 odd degrees, and, as far as yet made out, for even degrees too, 
 at one evening sitting, with a decanter of port wine to sustain 
 nature's flagging energies, in a back office in Lincoln's Inn 
 Fields. The work was done, and well done, but at the usual 
 cost of racking thought a brain on fire, and feet feeling, or 
 feelingless, as if plunged in an ice-pail. That night we slept no 
 more. The canonisant of the quartic (its cubic covariant) was 
 the first thing to offer itself in the inquiry. I had but to think 
 the words ' Resultant of Quintic and its Canonisant,' and the 
 octoderadic skew invariant would have fallen spontaneously into
 
 110 Inaugural Presidential Address. 
 
 observation ;* Gauss has called mathematics a science of 
 the eye, and in conformity with this view always paid 
 the most punctilious attention to preserve his text free 
 
 my lap. By quite another mode of consideration, M. Hermite 
 subsequently was led to the discovery of this, the key to the 
 innermost sanctuary of invariants so hard is it in Euristic to 
 see what lies immediately before one's eyes. The disappointment 
 weighed deeply, far too deeply, on my mind, and caused me to 
 relinquish for long years a cherished field of meditation; but 
 the whirligig of time brings about its revenges. Ten years later 
 this same Canonisant gave me the upper hand of my honoured 
 predecessor and guide, M. Hermite, in the inquiry (referred to at 
 the end of this address) concerning the invariantive criteria of 
 the constitution of a Quintic with regard to the real and imagi- 
 nary. By its aid I discovered the essential character of the 
 famous amphigenous surface of the ninth order, and its bicus- 
 pidal unicur&al section of the fourth order (otherwise termed the 
 bicorn), as may be seen in the third part of my Trilogy, printed 
 in the Philosophical Transactions. 
 
 * I was under the conviction that a passage to that effect 
 from Lagrange had been cited to me some years ago by M. 
 Hermite of the Institute of France ; on applying to him on the 
 subject, I received the following reply: 
 
 ' Relativement a 1' opinion que suivant vous j'aurais attribute a 
 Lagrange, je m'empresse de vous informer qii'il ne faut aucune- 
 ment, a ma connaissance, Ten rendre responsable. Nous nous 
 sommes entretenus du role de la faculte d 'observation dans les 
 etudes que nous avons poursuivies de concert pendant bien des 
 annees, et c'est alors, sans doute, que je vous aurai conte une 
 anecdote que je tiens de M. Chevreul. M. Chevreul, allant a 
 1'Institut dans la voiture de Lagrange, a etc vivemeut frappe du 
 sentiment de plaisir avec lequel ce grand geometre lui faisait 
 voir, dans un travail manuscrit, la beaute exterieure et artistique, 
 si je peux dire, des nombreuses formules qui y figuraient. Ce 
 sentiment nous 1' avons tous eprouve en faisant, avec sincerite, 
 abstraction de 1'idee analytique dont les formules sont 1'expres- 
 sion ecrite. II y a la, n'est-il point vrai, un imperceptible lien 
 qui rattache au monde de 1'art le monde abstrait de 1'algebre et 
 de 1'analyse, et j'oserai nieme vous dire que je crois a des sym-
 
 Dependence of mathematics on observation. Ill 
 
 from typographical errors ; the ever to be lamented 
 Riemann has written a thesis to show that the basis of 
 our conception of space is purely empirical, and our 
 knowledge of its laws the result of observation, that 
 other kinds of space might be conceived to exist subject 
 to laws different from those which govern the actual 
 space in which we are immersed, and that there 
 is no evidence of these laws extending to the ultimate 
 infinitesimal elements of which space is composed. 
 Like his master Gauss, Riemann refuses to accept 
 Kant's doctrine of space and time being forms of 
 intuition,* and regards them as possessed of physical and 
 
 pathies reelles, qui vous font trouver un charme dans les nota- 
 tions d'un auteur et des repulsions qui eloignent d'un autre, 
 par 1'apparence seule des formules.' 
 
 I am, however, none the less persuaded that on one or more 
 than one occasion, M. Hermite, speaking of Lagrange, expressed 
 to me, if not as I supposed on Lagrange's, then certainly on his 
 own high authority, ' that the faculty of observation was no less 
 necessary for the successful cultivation of the pure mathematical 
 than of the natural sciences.' I am glad also to notice that 
 Lagrange was able to accommodate a friend dans sa voiture. 
 England has much to learn from France and Eussia as to the 
 proper mode of treating its greatest men. 
 
 * It is very common, not to say universal, with English 
 writers, even such authorised ones as Whewell, Lewes, or Her- 
 bert Spencer, to refer to Kant's doctrine as affirming space ' to 
 be a form of thought,' or ' of the understanding.' This is putting 
 into Kant's mouth (as pointed out to me by Dr. C. M. Ingleby), 
 words which he would have been the first to disclaim, and is as 
 inaccurate a form of expression as to speak of ' the plane of a 
 sphere,' meaning its surface or a superficial layer, as not long 
 ago I heard a famous naturalist do at a meeting of the Royal 
 Society. Whoever wishes to gain a notion of Kant's leading 
 doctrines in a succinct form, weighty with thought, and free 
 from all impertinent comment, should study Schwegler's Hand- 
 book of Philosophy, translated by Stirling. He will find in the
 
 112 Inaugural Presidential Address. 
 
 objective reality. I may mention that Baron Sartorius 
 von "Waltershausen (a member of this Association) in 
 his biography of Gauss (' Gauss zu Gedachtniss '), 
 published shortly after his death, relates that this great 
 man was used to say that he had laid aside several 
 questions which he had treated analytically, and hoped 
 
 same book a most lucid account of Aristotle's doctrine of matter 
 and form, showing how matter passes unceasingly upwards into 
 form, and form downwards into matter ; which will remind 
 many of the readers of Nature of the chain of depolarisations 
 and repolarisations which are supposed to explain the decompo- 
 sition of water under galvanic action, eventuating in oxygen 
 being thrown off at one pole and hydrogen at the other (it 
 recalls also the high algebraical theories in which the same 
 symbols play the part of operands to their antecedents and 
 operators to their consequents): at one end of the Aristotelian 
 chain comes out irpdiTT) v\ri, at the other ttpSnov elSos. We have, 
 then, only to accept and apply the familiar mathematical principle 
 of the two ends of infinity being one and the same point (like the 
 extremities of a divided and extended ring), and the otherwise 
 immovable stumbling-block of duality is done away with, and 
 the universe reintegrated in the wished-for unity. For this 
 corollary, which to many will appear fanciful, neither Aristotle 
 nor Schwegler is responsible. We perfectly understand how in 
 perspective the latent polarities of any point in a closed curve 
 (taken as the object) may be developed into and displayed in the 
 form of a duad of quasi points or half-points at an infinite distance 
 from each other in the picture. In like manner we conceive how 
 actuality and potentiality which exist indistinguishably as one 
 in the absolute may be projected into seemingly separate elements 
 or moments on the plane of the human understanding. What- 
 ever may be the merits of the theory in itself, this view seems to 
 me to give it a completeness which its author coiild not have 
 anticipated, and to accomplish what Aristotle attempted but 
 avowedly failed to effect, viz. the complete subversion of the 
 ' Platonic Duality,' and the reintegration of matter and mind 
 into one.
 
 Higher Views of Space. 113 
 
 to apply to them geometrical methods in a future state 
 of existence, when his conceptions of space should have 
 become amplified and extended ; for as we can 
 conceive beings (like infinitely attenuated bookworms* 
 in an infinitely thin sheet of paper) which possess only 
 the notion of space of two dimensions, so we may 
 imagine beings capable of realising space of ftmr or 
 a greater number of dimensions.-]- Our Cayley, the 
 
 * I have read or been told (I believe erroneously) that eye of 
 observer has never lighted on these depredators, living or dead. 
 Nature has gifted me with eyes of exceptional microscopic power, 
 and I can speak with some assurance of having repeatedly seen 
 the creature wriggling on the learned page. On approaching it 
 with breath or finger-nail it stiffens out into the semblance of a 
 streak of dirt, and so eludes detection. 
 
 t It is well known to those who have gone into these views 
 that the laws of motion accepted as a fact suffice to prove in a 
 general way that the space we live in is a flat or level space (a 
 ' homaloid '), our existence therein being assimilable to the life 
 of the bookworm in a flat page ; but what if the page should 
 be undergoing a process of gradual bending into a curved 
 form ? Mr. W. K. Clifford has indulged in some remarkable 
 speculations as to the possibility of our being able to infer, 
 from certain unexplained phenomena of light and magnetism, 
 the fact of our level space of three dimensions being in the 
 act of undergoing in space of four dimensions (space as incon- 
 ceivable to us as our space to the supposititious bookworm) 
 a distortion analogous to the rumpling of the page. I know 
 there are many, who, like my honoured and deeply lamented 
 friend the late eminent Prof. Donkin, regard the alleged notion 
 of generalised space as only a disguised form of algebraical 
 formulisation ; but the same might be said with equal truth 
 of our notion of infinity in algebra, or of impossible lines, or 
 lines making a zero angle in geometry, the utility of dealing 
 with which as positive substantiated notions no one will be 
 found to dispute. Dr. Salmon, in his extension of Chasles' 
 theory of characteristics to surfaces, Mr. Clifford, in a question
 
 1 1 4 Inaugural Presidential Address. 
 
 central luminary, the Darwin of the English school 
 of mathematicians, started and elaborated at an early 
 
 of probability (published in the Educational Times'), and myself 
 in my theory of partitions, and also in my paper on Barycentric 
 Projection in the Philosophical Magazine, have all felt and 
 given evidence of the practical utility of handling space of four 
 dimensions, as if it were conceivable space. Moreover, it should 
 be borne in mind that every perspective representation of figured 
 space of four dimensions is a figure in real space, and that the 
 properties of figures admit of being studied to a great extent, if 
 not completely, in their perspective representations. In philo- 
 sophy, as in aesthetic, the highest knowledge comes by faith. I 
 know (from personal experience of the fact) that Mr. Linnell or 
 Madame Bodichon can distinguish purple tints in clouds where 
 my untutored eye and unpurged vision can perceive only confused 
 grey. If an Aristotle, or Descartes, or Kant, assures me that he 
 recognises God in the conscience, I accuse my own blindness if I 
 fail to see with him. If Gauss, Cayley, Riemann, Schalfli, Salmon, 
 Clifford, Kronecker, have an inner assurance of the reality of tran- 
 scendental space, I strive to bring my faculties of mental vision into 
 accordance with theirs. The positive evidence in such cases is 
 more worthy than the negative, and actuality is not cancelled or 
 balanced by privation, as matter plus space is none the less matter. 
 I acknowledge two separate sources of authority the collective 
 sense of mankind, and the illumination of privileged intellects. 
 As a parallel case, I would ask whether it is by demonstrative 
 processes that the doctrine of limits and of infinitely greats 
 and smalls, has found its way to the ready acceptance of the 
 multitude; or whether, after deducting whatever may be due 
 to modified hereditary cerebral organisation, it is not a conse- 
 quence rather of the insensible moulding of the ideas under the 
 influence of language which has become permeated with the 
 notions originating in the minds of a few great thinkers ? I am 
 assured that Germans, even of the non-literary class, such as 
 ladies of fashion and novel readers, are often appalled by the 
 hebetude of their English friends in muddling up together, as 
 if they were nearly or quite the same thing, the reason and the 
 understanding, in doing into English the words Vernunft and 
 Verstand, thereby confounding distinctions now become familiar
 
 Examples of Observation. 115 
 
 age, and with happy consequences, the same bold 
 hypothesis. 
 
 Most, if not all, of the great ideas of modern mathe- 
 matics have had their origin in observation. Take, for 
 instance, the arithmetical theory of forms, of which the 
 foundation was laid in the diophantine theorems of 
 Fermat, left without proof by their author, which 
 resisted all the efforts of the myriad-minded Euler to 
 reduce to demonstration, and only yielded up their cause 
 of being when turned over in the blowpipe flame of 
 Gauss's transcendent genius ; or the doctrine of double 
 periodicity, which resulted from the observation by 
 Jacobi of a purely analytical fact of transformation ; or 
 Legendre's law of reciprocity ; or Sturm's theorem 
 about the roots of equations, which, as he informed me 
 with his own lips, stared him in the face in the midst 
 of some mechanical investigations connected with the 
 motion of compound pendulums ; or Huyghen's method 
 of continued fractions, characterized by Lagrange as one 
 of the principal discoveries of 'that great mathematician, 
 and to which he appears to have been led by the con- 
 
 (such is the force of language) to the very milkmaids of 
 Fatherland. 
 
 As a public teacher of mere striplings, I am often amazed by 
 the facility and absence of resistance with which the principles 
 of the infinitesimal calculus are accepted and assimilated by the 
 present race of learners. When I was young, a- boy of sixteen 
 or seventeen who knew his infinitesimal calculus would have 
 been almost pointed at in the streets as a prodigy, like Dante, 
 as a man who had seen hell. Now-a-days, our Woolwich cadets 
 at the same age, talk with glee of tangents and asymptotes and 
 points of contrary flexure and discuss questions of double maxima 
 and minima, or ballistic pendulums, or motion in a resisting 
 medium, under the familiar and ignoble name of sums.
 
 116 Inaugural Presidential Address. 
 
 struction of his Planetary Automaton ; ' or the New 
 Algebra, speaking of which one of my predecessors 
 (Mr. Spottiswoode) has said, not without just reason 
 and authority, from this chair, ' that it reaches out and 
 indissolubly connects itself each year with fresh branches 
 of mathematics, that the theory of equations has almost 
 become new through it, algebraic geometry transfigured 
 in its light, that the calculus of variations, molecular 
 physics, and mechanics ' (he might, if speaking at the 
 present moment, go on to add the theory of elasticity 
 and the highest developments of the integral calculus) 
 ' have all felt its influence.' 
 
 Now, this gigantic outcome of modern analytical 
 thought, itself, too, only the precursor and progenitor 
 of a future still more heaven-reaching theory, which 
 will comprise a complete study of the interoperation, the 
 actions and reactions, of algebraic forms (Analytical 
 Morphology in its absolute sense), how did this origi- 
 nate ? In the accidental observation by Eisenstein, 
 some score or more years ago, of a single invariant (the 
 Quadrinvariant of a Binary Quartic) which he met with 
 in the course of certain researches just as accidentally 
 and unexpectedly as M. Du Chaillu might meet a 
 gorilla in the country of the Fantees, or any one of us 
 in London a white polar bear escaped from the Zoolo- 
 gical Gardens. Fortunately he pounced down upon his 
 prey and preserved it for the contemplation and study 
 of future mathematicians. It occupies only part of a 
 page in his collected posthumous works. This single 
 result of observation (as well entitled to be so called as 
 the discovery of Globigerinae in chalk or of the confoco- 
 ellipsoidal structure of the shells of the Foraminifera),
 
 The Theory of Reducible Cydodes. 117 
 
 which remained unproductive in the hands of its distin- 
 guished author, has served to set in motion a train of 
 thought and to propagate an impulse which have led to 
 a complete revolution in the whole aspect of modern 
 analysis, and whose consequences will continue to be 
 felt until Mathematics are forgotten and British Associa- 
 tions meet no more. 
 
 I might go on, were it necessary, piling instance upon 
 instance, to prove the paramount importance of the 
 faculty of observation to the progress of mathematical 
 discovery.* Were it not unbecoming to dilate en one's 
 personal experience, I could tell a story of almost roman- 
 tic interest about my own latest researches in a field 
 where Geometry, Algebra, and the Theory of Numbers 
 melt in a surprising manner into one another, like sun- 
 set tints or the colours of the dying dolphin, ' the last 
 still loveliest,' a sketch of which has just appeared in 
 the Proceedings of the London Mathematical Society!), 
 which would very strikingly illustrate how much obser r 
 vation, divination, induction, experimental trial, and 
 verification, causation, too (if that means, as I suppose 
 
 * Newton's Rule (subsequently and for the first time reduced 
 by myself to demonstration in No. 2 of the London Mathematical 
 Society's Proceedings) was to all appearance, and according to 
 the more received opinion, obtained inductively by its author. 
 So also my reduction of Euler's problem of the Virgins (or 
 rather one slightly more general than this) to the form of a 
 question (or, to speak more exactly, a set of questions) in simple 
 partitions was (strangely enough) first obtained by myself in- 
 ductively, the result communicated to Prof. Cayley, and proved 
 subsequently by each of us independently, and by perfectly 
 distinct methods. 
 
 f Under the title of Outline Trace of the Theory of Reducible 
 Cydodes.
 
 118 Inaugural Presidential Address. 
 
 it must, mounting from phenomena to their reasons or 
 causes of being), have to do with the work of the 
 mathematician. In the face of these facts, which every 
 analyst in this room or out of it can vouch for out of 
 his own knowledge and personal experience, how can it 
 be maintained, in the words of Professor Huxley, who, 
 in this instance, is speaking of the sciences as they are 
 in themselves and without any reference to scholastic 
 discipline, that Mathematics ' is that study which knows 
 nothing of observation, nothing of induction, nothing of 
 experiment, nothing of causation.'* 
 
 * Induction and analogy are the special characteristics of 
 modern mathematics, in which theorems have given place to 
 theories, and no truth is regarded otherwise than as a link in an 
 infinite chain. ' Omne exit in infinitum ' is their favourite motto 
 and accepted axiom. No mathematician now-a-days sets any 
 store on the discovery of isolated theorems, except as affording 
 hints of an unsuspected new sphere of thought, like meteorites 
 detached from some undiscovered planetary orb of speculation. 
 The form, as well as matter, of mathematical science, as must 
 be the case in any true living organic science, is in a constant 
 state of flux, and the position of its centre of gravity is liable to 
 continual change. At different periods in its history defined, 
 with more or less accuracy, as the science of number or quantity, 
 or extension or operation or arrangement, it appears at present 
 to be passing through a phase in which the development of the 
 notion of Continuity plays the leading part. In exemplification 
 of the generalising tendency of modern mathematics, take so 
 simple a fact as that of two straight lines or two planes being 
 incapable of including ' a space.' When analysed this statement 
 will be found to resolve itself into the assertion that if two out 
 of the four triads that can be formed with four points lie. 
 respectively in directo, the same must be true of the remaining 
 two triads ; and that if two of the five tetrads that can be 
 formed with five points lie respectively in piano, the remaining 
 three tetrads (subject to a certain obvious exception) must each 
 do the same. This, at least, is one way of arriving at the notion
 
 Space-conceptions embodied in Algebra. 119 
 
 I, of course, am not so absurd as to maintain that the 
 habit of observation of external nature* will be best or 
 in any degree cultivated by the study of mathematics, 
 at all events as that study is at present conducted, and 
 no one can desire more earnestly than myself to 
 see natural and experimental science introduced into 
 our schools as a primary and indispensable branch of 
 
 of an unlimited rectilinear and planar schema of points. The 
 two statements above made, translated into the language of 
 determinants, immediately suggest as their generalised expression 
 my great ' Homaloidal Law,' which affirms that the vanishing of 
 a certain specifiable number of minor determinants of a given 
 order of any matrix (i.e. rectangular array of quantities) implies 
 the simultaneous evanescence of all the rest of that order. I 
 made (inter alia) a beautiful application of this law (which is, I 
 believe, recorded in Mr. Spottiswoode's valuable treatise on 
 Determinants, but where besides I know not) to the establish- 
 ment of the well-known relations, wrung out with so much 
 difficulty by Euler, between the cosines of the nine angles, which 
 two sets of rectangular axes in space make with one another. 
 This is done by contriving and constructing a matrix such that 
 the six known equations connecting the nine cosines taken both 
 ways in sets of threes shall be expressed by the evanescence of 
 six of its minors ; the simultaneous evanescence of the remaining 
 minors given by the Homaloidal Law will then be found to 
 express the relations in question (which Euler has put on 
 record, it drove him almost to despair to obtain), but which 
 are thus obtained by a simple process of inspection and reading 
 off, without any labour whatever. The fact that such a law, 
 containing in a latent form so much refined algebra, and capable 
 of such interesting immediate applications, should present itself 
 to the observation merely as the extended expression of the 
 ground of the possibility of our most elementary and seemingly 
 intuitive conceptions concerning the right line and plane, has 
 often filled me with amazement to reflect upon. 
 
 * As the prerogative of Natural Science is to cultivate a taste 
 for observation, so that of Mathematics is, almost from the 
 starting-point, to stimulate the faculty of invention.
 
 120 Inaugural Presidential Address. 
 
 education : I think that that study and mathematical 
 culture should go on hand in hand together, and that 
 they would greatly influence each other for their mutual 
 good. I should rejoice to see mathematics taught with 
 that life and animation which the presence and example 
 of her young and buoyant sister could not fail to im- 
 part, short roads preferred to long ones, Euclid honour- 
 ably shelved or buried ' deeper than e'er plummet 
 sounded' out of the schoolboy's reach, morphology 
 introduced into the elements of Algebra projection, 
 correlation, and motion accepted as aids to geometry 
 the mind of the student quickened and elevated and 
 his faith awakened by early initiation into the ruling 
 ideas of polarity, continuity, infinity, and familiariza- 
 tion with the doctrine of the imaginary and incon- 
 ceivable. 
 
 It is this living interest in the subject which is so 
 wanting in our traditional and mediaeval modes of 
 teaching. In France, Germany, and Italy, everywhere 
 where I have been on the Continent, mind acts direct 
 on mind in a manner unknown to the frozen formality 
 of our academic institutions; schools of thought and 
 centres of real intellectual co-operation exist ; the 
 relation of master and pupil is acknowledged as a 
 spiritual and a lifelong tie, connecting successive 
 generations of great thinkers with each other in an 
 unbroken chain, just in the same way as we read in the 
 catalogue of our French Exhibition, or of the Salon at 
 Paris, of this man or that being the pupil of one great 
 painter or sculptor and the master of another. When 
 followed out in this spirit, there is no study in the 
 world which brings into more harmonious action all the
 
 The D ii Majores of the Mathematical Pantheon. 121 
 
 faculties of the mind than the one of which I stand here 
 as the humble representative, there is none other which 
 prepares so many agreeable surprises for its followers, 
 more wonderful than the changes in the transformation- 
 scene of a pantomime, or, like this, seems to raise them, 
 by successive steps of initiation, to higher and higher 
 states of conscious intellectual being. 
 
 This accounts, I believe, for the extraordinary longe- 
 vity of all the greatest masters of the analytical art, 
 the dii majores of the mathematical Pantheon. 
 Leibnitz lived to the age of 70 ; Euler to 76 ; La- 
 grange to 77 ; Laplace to 78 ; Gauss to 78 ; Plato, the 
 supposed inventor of the conic sections, who made 
 mathematics his study and delight, who called them the 
 handles (or aids) to philosophy, the medicine of the soul, 
 and is said never to have let a day go by without 
 inventing some new theorems, lived to 82 ; Newton, 
 the crown and glory of his race, to 85 ; Archimedes, 
 the nearest akin, probably, to Newton in genius, was 
 75, and might have lived on to be 100, for aught we 
 can guess to the contrary, when he was slain by 
 the impatient and ill-mannered sergeant, sent to bring 
 him before the Roman general, in the full vigour of his 
 faculties, and in the very act of working out a problem ; 
 Pythagoras, in whose school, I believe, the word mathe- 
 matician (used, however, in a somewhat wider than its 
 present sense) originated, the second founder of 
 geometry, the inventor of the matchless theorem which 
 goes by his name, the precognizer of the undoubtedly 
 mis-called Copernican theory, the discoverer of the 
 regular solids and the musical canon, who stands at the 
 very apex of this pyramid of flame (if we may credit 
 H
 
 1 22 Inaugural Presidential Address. 
 
 the tradition), after spending 22 years studying in 
 Egypt, and 12 in Babylon, opened school when 56 
 or 57 years old in Magna Graecia, married a young 
 wife when past 60, and died, carrying on his work with 
 energy unspent to the last, at the age of 99. The 
 mathematician lives long and lives young ; the wings 
 of his soul do not early drop off, nor do. its pores 
 become clogged with the earthy particles blown from 
 the dusty highways of vulgar life. 
 
 Some people have been found to regard all mathe- 
 matics, after the 47th proposition of the first book of 
 Euclid, as a sort of morbid secretion, to be compared 
 only with the pearl said to be generated in the diseased 
 oyster, or, as I have heard it described, ' une excroissance 
 maladive de 1'esprit humain.' Others find its justifica- 
 tion, its ' raison d'etre,' in its being either the torch- 
 bearer leading the way, or the handmaiden holding up 
 the train of Physical Science ; and a very clever writer 
 in a recent magazine article, expresses his doubts whether 
 it is, in itself, a more serious pursuit, or more worthy ol 
 interesting an intellectual human being, than the study 
 of chess problems or Chinese puzzles.* What is it to 
 us, they say, if the three angles of a triangle are equal 
 to two right angles, or if every even number is, or may 
 be, the sum of two primes, f or if every equation of an 
 
 * Is it not the same disregard of principles, the same in- 
 difference to truth for its own sake which prompts the question, 
 ' Where's the good of it?' in reference to speculative science, 
 und ' Where's the harm of it ? ' in reference to white lies and 
 pious frauds? In my own experience I have found that the 
 very same class of people who delight to put the first question 
 are in the habit of acting upon the denial implied in the second. 
 Abit in mores incuria. 
 
 t This theorem still awaits proof; it is stated, I believe, in
 
 Sources of satisfaction stated. 123 
 
 odd degree must have a real root ? How dull, stale, 
 flat, and unprofitable are such and such like announce- 
 ments ! Much more interesting to read an account of a 
 marriage in high life, or the details of an international 
 boat-race. But this is like judging of architecture 
 from being shown some of the brick and mortar, or 
 even a quarried stone, of a public building, or of paint- 
 ing from the colours mixed on the palette, or of music 
 by listening to the thin and screechy sounds produced 
 by a bow passed haphazard over the strings of a violin. 
 The world of ideas which it discloses or illuminates, 
 the contemplation of divine beauty and order which it 
 induces, the harmonious connection of its parts, the 
 infinite hierarchy and absolute evidence of the truths 
 with which it is concerned, these, and such like, are 
 
 Eulei's correspondence with Goldbach: I re-discovered it in 
 ignorance of Euler's having mentioned it, in connection with a 
 theory of my own concerning cubic forms. The evidence in its 
 favour is induction of the undemonstrative or purely accumu- 
 lative kind, and it may or may not turn out eventually to be 
 true. As a most learned scholar who heard this address given 
 at Exeter remarked to me, not many days ago, it is certainly by 
 no process of deduction that we make out that five times six is 
 thirty. I mention this, because I know some, who agree, or did 
 agree, with Professor Huxley's published opinions about mathe- 
 matics, are under the impression that the higher processes of 
 mind in mathematics only concern ' the aristocracy of mathe- 
 maticians : ' on the contrary, they lie at the very foundations of 
 the subject. There are besides, and in abundance, mathematical 
 processes which only by a forced interpretation can be brought 
 under the head of demonstration, whether deductive or inductive, 
 and really belong to a sort of artistic and constructive faculty, 
 such for example as evaluating definite integrals, or making out 
 the best way one can the number of distinct branches and the 
 general character of each branch of a curve from its algebraical 
 equation. 
 
 H2
 
 124 Inaugural Presidential Address. 
 
 the surest grounds of the title of mathematics to human 
 regard, and would remain unimpeached and unimpaired 
 were the plan of the universe unrolled like a map at 
 our feet, and the mind of man qualified to take in the 
 whole scheme of creation at a glance. 
 
 In conformity with general usage, I have employed the 
 word mathematics in the plural ; but I think it would 
 be desirable that this form of word should be reserved 
 for the applications of the science, and that we should 
 use Mathematic in the singular number to denote the 
 science itself, in the same way as we speak of logic, 
 rhetoric, or (own sister to algebra *) music. Time was 
 when all parts of the subject were dissevered, when 
 algebra, geometry, and arithmetic either lived apart 
 or kept up cold relations of acquaintance confined to 
 occasional calls upon one another ; but that state of 
 things is now happily at an end ; they are drawn 
 together and are constantly becoming more and more 
 intimately related and connected by a thousand fresh 
 ties, and we may confidently look forward to a time 
 when they shall form but one body with one soul. 
 Geometry formerly was the chief borrower from arith- 
 metic and algebra, but it has since repaid its obligations 
 with abundant usury ; and if I were asked to name, 
 in one word, the pole-star round which the mathe- 
 
 * I have elsewhere (in my Trilogy, published in the Philo- 
 sophical Transactions) referred to the close connection between 
 these two cultures, not merely as having Arithmetic for their 
 common parent, but as similar in their habits and affections. I 
 have called ' Music the Algebra of sense, Algebra the Music of 
 the reason ; Music the dream, Algebra the waking life the soul 
 of each the same ! '
 
 Mathematic, the Science of Continuity. 125 
 
 matical firmament revolves, the central idea which 
 pervades as a hidden spirit the whole corpus of mathe- 
 matical doctrine, I should point to Continuity as con- 
 tained in our notions of space, and say, it is this, it is 
 this ! Space is the Grand Continuum from which, 
 as from an inexhaustible reservoir, all the fertilizing 
 ideas of modern analysis are derived ; and as Brindley, 
 the engineer, once allowed before a parliamentary com- 
 mittee that, in his opinion, rivers were made to feed 
 navigable canals, I feel almost tempted to say that one 
 principal reason for the existence of space, or at least 
 one principal function which it discharges, is that of 
 feeding mathematical invention. Everybody knows 
 what a wonderful influence geometry has exercised in 
 the hands of Cauchy, Puiseux, Kiemann, and his fol- 
 lowers Clebsch, Gordan, and others, over the very form 
 and presentment of the modern calculus, and how it has 
 come to pass that the tracing of curves, which was at one 
 time to be regarded as a puerile amusement, or at best 
 useful only to the architect or decorator, is now entitled 
 to take rank as a high philosophical exercise, inasmuch 
 as every new curve or surface, or other circumscription 
 of space, is capable of being regarded as the embodi- 
 ment of some specific organised system of Continuity.* 
 
 * M. Camille Jordan's application of Dr. Salmon's Eikosi- 
 heptagram to Abelian functions is one of the most recent 
 instances of this reverse action of geometry on analysis. Mr. 
 Crofton's admirable apparatus of a reticulation with infinitely 
 fine meshes rotated successively through indefinitely small 
 angles, which he applies to obtaining whole families of definite 
 integrals, is another equally striking example of the same phe- 
 nomenon. I am happy to be able to add that this gentleman 
 who, when the above lines were printed, was at the bottom of
 
 126 Inaugural Presidential Address. 
 
 The early study of Euclid made me a hater of geo- 
 metry, which I hope may plead my excuse if I have 
 shocked the opinions of any in this room (and I know 
 there are some who rank Euclid as second in sacredness 
 to the Bible alone, and as one of the advanced outposts 
 of the British Constitution) by the tone in which I have 
 previously alluded to it as a school-book ; and yet, in 
 spite of this repugnance, which had become a second 
 nature in me, whenever I went far enough into any 
 mathematical question, I found I touched, at last, a 
 geometrical bottom ; so it was, I may instance, in the 
 purely arithmetical theory of partitions ; so, again, in 
 one of my more recent studies, the purely algebraical 
 question of the invariantive criteria of the nature of 
 the roots of an equation of the fifth degree : the first 
 inquiry landed me in a new theory of polyhedra ; the 
 latter found its perfect and only possible complete * solu- 
 
 the Staff of the Mathematical Instructors at "Woolwich, has been 
 since appointed, with the full concurrence of his colleagues, on 
 the nomination of the Governor, Sir John Lintorn Simmons, 
 K.C.B., to succeed me as Professor of Mathematics at the Eoyal 
 Military Academy. 
 
 * Complete in the sense of universal, more than perfect or 
 complete in the ordinary sense. Two criteria are absolutely fixed ; 
 but in addition to these two an additional criterion or set of 
 criteria must be introduced to make the system of conditions 
 sufficient. The number of such set may be either one or what- 
 ever number we please, and into such one or into each of the set 
 (if more than one) an indefinite number of arbitrary parameters 
 (limited) may be introduced. Now the geometrical construction 
 I arrive at contains implicitly the totality of all these infinitely 
 varied forms of criteria, or sets of criteria, and without it the 
 existence and possibility of such variety in the shape of the 
 solution could never have been anticipated or understood. My 
 truly eminent friend M. Charles Hermite (Membre de 1'Institut), 
 with all the efforts of his extraordinary analytical power, and
 
 Examples of inter-dependence. 127 
 
 tion in the construction of a surface of the ninth order, 
 and the sub-division of its infinite contents into three 
 distinct natural regions.* 
 
 Having thus expressed myself at much greater length 
 than I originally intended on the subject, which, as 
 
 with the knowledge of my results to guide him, has only been 
 able by the non-geometrical method to arrive at one form of 
 solution consisting of a third criterion absolutely definite and 
 destitute of a single variable parameter. As is well known, I 
 have made a very important use of a criterion of the same form 
 as M. Hermite's, but containing one arbitrary parameter (limited). 
 . The subject will be found resumed from the point where I left it, 
 and pursued in considerable detail by Prof. Cayley, in one of his 
 more recent memoirs on Quartics in the ' Philosophical Trans- 
 actions.' M. Hermite it was who first surprised Invariantists 
 (1'Eglise Invariantive, as we are sometimes styled) by an a priori 
 demonstration that the nature of the roots or factors of quartics 
 could in general be found by means of invariantive criteria. 
 This was known to be possible up to the fourth order of binary 
 quartics, and impossible for the fourth. M. Hermite showed 
 that this negation which seemed to stop the way to further pro- 
 gress was an exceptional case ; that whereas for the second, 
 third, fifth, sixth, and all higher degrees the thing could be 
 done, for the fourth alone it was impossible : as regards linear 
 Qnantics, the question does not arise. I look upon this failure 
 of a law for one term in the middle of an infinite progression as 
 an unparalleled miracle of arithmetic, far more real and deeper 
 seated than the one alluded to by Mr. Babbage in connection 
 with the discontinuous action of a supposed machine in his ninth 
 Bridgwater Treatise. 
 
 * So I found, as a pure matter of observation, that allineation 
 (cdignemeni) in ornamental gardening i.e. the method of putting 
 trees in positions to form a very great number or the greatest 
 number possible of straight rows, of which a few special cases 
 only had been previously considered as detached porismatie 
 problems, forms part of a great connected theory of the plu- 
 perfect points on a cubic curve, those points, of which the nine 
 points of inflection and Plucker's twenty-seven points may serve 
 as the lowest instances.
 
 128 Inaugural Presidential Address. 
 
 standing first on the muster-roll of the Association, and 
 as having been so recently and repeatedly arraigned 
 before the bar of public opinion, is entitled to be heard 
 in its defence (if anywhere) in this place, having en- 
 deavoured to show what it is not, what it is, and what 
 it is probably destined to become, I feel that I must 
 enough and "more than enough, have trespassed on your 
 forbearance, and shall proceed with the regular business 
 of the meeting. 
 
 Before calling upon the authors of the papers con- 
 tained in the varied bill of intellectual fare which I 
 see before me, I hope to be pardoned if I direct atten- 
 tion to the importance of practising brevity and con- 
 densation in the delivery of communications to the 
 Section, not merely as a saving of valuable time, biit in 
 order that what is said may be more easily followed 
 and listened to with greater pleasure and advantage. I 
 believe that immense good may be done by the oral 
 interchange and discussion of ideas which takes place 
 in the Sections ; but for this to be possible, details and 
 long descriptions should be reserved for printing and 
 reading, and only the general outlines and broad state- 
 ments of facts, methods, observations, or inventions 
 brought before us here, such as can be easily followed 
 by persons having a fair average acquaintance with the 
 several subjects treated upon. I understand the rule to 
 be that, with the exception of the author of any paper 
 who may answer questions and reply at the end of the 
 discussion, no member is to address the Section more 
 than once on the same subject, or occupy more than a 
 quarter of an hour in speaking. 
 
 In order to get through the business set down in 
 each day's paper, it may sometimes be necessary for
 
 Concluding Remarks. 129 
 
 me to bring a discussion to an earlier close than might 
 otherwise be desirable, and for that purpose to request 
 the authors of papers, and those who speak upon them, 
 to be brief in their addresses. I have known most able 
 investigators, at these meetings, and especially in this 
 section, gradually part company with their audience, 
 and at last become so involved in digressions as to lose 
 entirely the thread of their discourse, and seem to for- 
 get, like men waking out of sleep, where they were or 
 what they were talking about. In such cases I shall 
 venture to give a gentle pull to the string of the kite 
 before it soars right away out of sight into the region 
 of the clouds. I now call upon Dr. Magnus to read 
 his paper and recount to the Section his wondrous story 
 on the Emission, Absorption, and Reflection of Obscure 
 Heat.* 
 
 POSTSCRIPT. The remarks on the use of experimental 
 methods in mathematical investigation led to Dr. 
 Jacobi, the eminent physicist of St. Petersburg, who 
 was present at the delivery of the address, favouring 
 me with the annexed anecdote relative to his illustrious 
 brother C. G. J. Jacobi. j 
 
 * Curiously enough, and as if symptomatic of the genial 
 warmth of the proceedings in which seven sages from distant 
 lands (Jacobi, Magnus, Newton, Janssen, Morren, Lyman, 
 Neumayer) took frequent part, the opening and concluding 
 papers (each of surpassing interest, and a letting-out of mighty 
 waters) were on Obscure Heat, by Prof. Magnus, and on Stellar 
 Heat, by Mr. Huggins. 
 
 t It is said of Jacobi, that he attracted the particular attention 
 and friendship of Bockh, the director of the philological semi- 
 nary at Berlin, by the zeal and talent he displayed for philology, 
 and only at the end of two years' study at the University, and
 
 1 30 Inaugural Presidential Address. 
 
 'En causant un jour avec mon frere defunt sur la 
 necessite de controler par des experiences reiterees toute 
 observation, meme si elle confirme 1'hypothese, il me 
 raconta avoir decouvert un jourune loi tres-remarquable 
 de la theorie des nombres, dont il ne douta guere qu'elle 
 fut generate. Cependant par un exces de precaution 
 ou plutot pour faire le superflu, il voulut substituer un 
 chiffre quelconque reel aux termes generaux, chiffre 
 qu'il choisit au hasard ou, peut-etre, par une espece de 
 divination, car en effet ce chiiFre mit sa formule en 
 defaut ; tout autre chiffre qu'il essaya en confirma la 
 generalite. Plus tard il reussit a prouver que le chiffre 
 choisi par lui par hasard, appartenait a un systeme de 
 chiffres qui faisait la seule exception a la regie. 
 
 ' Ce fait curieux m'est reste dans la memoire, mais 
 comme il s'est passe il y a plus d'une trentaine d'annees, 
 je ne rappelle plus des details. 
 
 < M. H. JACOBI.' 
 
 ' Exeter, 24 aout, 1869.' 
 
 after a severe mental struggle, was able to make his final choice 
 in favour of mathematics. The relation between these two 
 sciences is not perhaps so remote as may at first sight appear ; 
 and indeed it has often struck me that metamorphosis runs like 
 a golden thread through the most diverse branches of modern 
 intellectual culture, and forms a natural link of connection be- 
 tween subjects in their aims so remote as grammar, philology, 
 ethnology, rational mythology, chemistry, botany, comparative 
 anatomy, physiology, physics, algebra, versification, music, all of 
 which, under the modern point of view, may be regarded as 
 having morphology for their common centre. Even singing, I 
 have been told, the advanced German theorists regard as being 
 strictly a development of recitative, and infer therefrom that no 
 essentially new melodic themes can be invented until a social 
 cataclysm, or the civilisation of some at present barbaric races, 
 shall have created fresh necessities of expression, and called into 
 activity new forms of impassioned declamation.
 
 131 
 
 APPENDIX. 
 
 ON THE INCOEKECT DESCRIPTION OF KANT'S 
 DOCTRINE OF SPACE AND TIME COMMON IN 
 ENGLISH WRITERS.* 
 
 IN the very remarkable contribution by Professor Sylvester 
 (Nature, No. 9) this sentence occurs : ' It is very common, not 
 to say universal, with English writers, even such authorised ones 
 as Whewell, Lewes, or Herbert Spencer, to refer to Kant's 
 doctrine as affirming space to be a "form of thought " " or of the 
 understanding." This is putting into Kant's mouth (as pointed 
 out to me by Dr. C. M. Ingleby) words which he would have 
 been the first to disclaim.' 
 
 It is not on personal grounds that I wish to rectify the mis- 
 conception into which Dr. Ingleby has betrayed Professor 
 Sylvester. When objections are made to what I have written, 
 it is my habit either silently to correct my error, or silently to 
 disregard the criticism. In the present case I might be perfectly 
 contented to disregard a criticism which any one who even 
 glanced at my exposition of Kant would see to be altogether 
 inexact ; but as misapprehensions of Kant are painfully abun- 
 dant, readers of Kant being few, and those who take his 
 name in vain being many, it may be worth while to stop 
 this error from getting into circulation through the channel of 
 Nature. Kant assuredly did teach, as Professor Sylvester says, 
 and as I have repeatedly stated, that space is a form of in- 
 tuition. But there is no discrepancy at all in also saying 
 that he taught space to be a ' form of thought,' since every 
 student of Kant knows that intuition without thought is mere 
 sensuous impression. Kant considered the mind under three 
 
 * From Nature. See note *, p. 109.
 
 1 32 Appendix. 
 
 aspects, Sensibility, Understanding, and Keason. The a priori 
 forms of Sensibility, which rendered Experience possible, were 
 Space and Time : these were forms of thought, conditions of 
 cognition. It was by such forms of thought that he reoccupied 
 the position taken by Leibnitz in defending and amending the 
 doctrine of innate ideas, namely, that knowledge has another 
 source besides sensible experience the intellectus ipse. 
 
 While, therefore, any one who spoke of space as a ' form of 
 
 the understanding ' would certainly use language which Kant 
 
 would have disclaimed, Kant himself would have been surprised 
 
 to hear that space was not held by him as a ' form of thought.' 
 
 January 3. GEOBGE HENEY LEWES. 
 
 THE following paragraphs, I believe, faithfully render sundry 
 passages of Kant's writings : 
 
 ' Objects are given to us by means of sense (Sinnlichkeit), 
 which is the sole source of intuitions (Anschauungen) ; but they 
 are thought by the understanding, from which arise conceptions 
 (Begriffe).' (' Kritik,' p. 55, Hartenstein's edition.) 
 
 ' The understanding is the faculty of thought. Thought is 
 knowledge by means of conception.' (Ibid. p. 93.) 
 
 ' The original consciousness of space is an intuition a priori, 
 and not a conception (Begriff).' (Ibid. p. 60.) 
 
 ' Space is nothing else than the form of all the phenomena of 
 the external senses ; that is, it is the subjective condition of 
 sense, under which alone external intuition is possible for us.' 
 (Ibid. p. 61.) 
 
 ' Our nature is such, that intuition can never be otherwise 
 than sensual (sinnlich) ; that is, it only contains the modes in 
 which we are affected by objects. On the other hand, the power 
 of thinking the object of sensual intuition, is the understanding. 
 Neither of these faculties is superior to the other. Without 
 sense, no object would be given us, and without understanding 
 none would be thought. Thoughts without contents are empty, 
 intuitions without conceptions (Begriffe) are blind.' (Ibid. 
 p. 82.)
 
 Kanfs Doctrine of Space and Time. 1 33 
 
 ' Time and space are " mere forms of sense " ' (Formen unserer 
 Sinnlichkeit, 'Prolegomena,' p. 33) and 'mere forms of intuition.' 
 ('Kritik,' p. 76.) 
 
 With these passages before one, there can be no doubt that 
 that thorough and acute student of Kant, Dr. Ingleby, was 
 perfectly right when he said that Kant would have repudiated 
 the affirmation that ' space is a form of thought.' For in these 
 sentences, and in many others which might be cited, Kant 
 expressly lays down the doctrine that thought is the work of the 
 understanding, intuition of the sense; and that space, like time, 
 is an intuition. The only ' forms of thought ' in Kant's sense, 
 are the categories. T. H. HUXLEY. 
 
 January 14. 
 
 I DO not believe Professor Sylvester has been betrayed, as 
 Mr. Gr. H. Lewes asserts, into any misconception of this matter 
 by me. 
 
 When Kant, at the outset, says, 'Alles Denken aber muss 
 sich, es sei geradezu oder im Umschweife, vermittelst gewisser 
 Merkmale, zuletzt auf Anschauungen...beziehen,' it would take 
 the veriest dunderhead not to see that all forms of intuition must 
 be, indirectly at least, forms of th< Tight. I never dreamed of 
 disputing so obvious a position. But I object to the phrase, 
 ' forms of thought,' as designating Space and Time, on the ground 
 of precision. They are peculiarly forms of general Sense, and not 
 forms of Thought as Tliought. Kant, I believe, eschewed the 
 phrase in that sense, and, for all I see, might for the same reason 
 have disclaimed it. C. M. INGLEBY. 
 
 Ilford, Jan. H. 
 
 IT is not my habit ' when objections are made to what I have 
 written, silently to correct my error or silently disregard the 
 criticism.' If the objections are well founded, I think it due to 
 the cause of truth to make a frank confession of error, and in 
 the opposite case to reply to the objections. 
 
 With reference, then, to Mr. Lewes's strictures in Nature's
 
 134 Appendix. 
 
 last number, I beg to say that Dr. Ingleby has ' betrayed ' me 
 into no error. If I have fallen into error, it is with my eyes open, 
 and after satisfying myself by study of Kant, that to speak of 
 Space and Time, whether as forms of understanding, or as forms 
 of thought, is an unauthorised and misleading mode of expression. 
 Space and Time are forms of sensitivity or intuition. The 
 categories of Kant (so essentially in this point differing from 
 those of Aristotle) do not contain Space and Time among 
 them, and are properly called forms of understanding or 
 thought. 
 
 To the existence of thought the operation of the understanding 
 is a necessary preliminary. 
 
 Sensibility and intuition are antecedent to any such operation. 
 
 Can Mr. Lewes point to any passage in Kant where Space and 
 Time are designated forms of thought ? I shall indeed be sur- 
 prised if he can do so as much surprised as if Mr. Todhuuter or 
 Mr. Routh, in their Mechanical Treatises, were to treat energy 
 and force as convertible terms. To such a misuse of the word 
 energy it would be little to the point to urge that force without 
 energy is a mere potential tendency. It is just as little to 
 the point in the matter at issue, for Mr. Lewes to inform the 
 readers of Nature that intuition without thought is mere sensuous 
 impression. 
 
 Dr. Ingleby has rendered, in my opinion, a very great service 
 to the English reading public, by drawing attention to so serious 
 and prevalent an error as that of confounding the categories (the 
 proper forms of thought as thought) with Space and Time, the 
 forms of intuition, the sentinels, so to say, who keep watch and 
 ward outside the gates of the Understanding. 
 
 Athenaeum Club, Jan. 15. J. J. SYLVESTER. 
 
 ALTHOUGH I do not feel myself called upon to modify in the 
 least what was said in my former letter on this subject, the three 
 letters which appear to-day in answer to it are too important to 
 be left unnoticed. 
 
 The case is briefly this : In the ' History of Philosophy ' I had
 
 Kant's Doctrine of Space and Time. 135 
 
 to expound Kant's doctrine, and to criticise it, not only in itself, 
 but in reference to the great question of the origin of knowledge. 
 In the pages of exposition I uniformly speak of Space and Time 
 as forms of Intuition ; no language can be plainer. I also mark 
 the distinction between Sensibility and Understanding, as that 
 of Intuition and Thought. After enumerating the Categories, I 
 add, ' In those Categories Kant finds the pure forms of the 
 Understanding. They render Thought possible.' 
 
 But when, ceasing to expound the system, I had to criticise it, 
 and especially to consider it in reference to the great question ; 
 there was no longer any need to adhere to a mode of expression 
 which would have been obscure and misleading. I therefore 
 uniformly class Space and Time among the forms of Thought, 
 connecting them with the doctrine of Necessary Truths and 
 Fundamental Ideas, which, according to the a priori school, are 
 furnished ready-made brought by the Mind as its native dowry, 
 not evolved in it through Experience. 
 
 Now the question is, Have I put language into Kant's mouth 
 which he would disclaim, or is such language misleading ? That 
 Kant would have said the language was not what he had em- 
 ployed, I freely admit ; but that he would have disclaimed it as 
 misrepresenting his meaning, I deny. I was not bound to follow 
 his language when the task of exposition was at an end ; but 
 only bound not to translate his opinions into language which 
 would distort them. 
 
 In classing Space and Time among the Forms of Thought, I 
 classed them beside the Categories of the Understanding and the 
 Ideas of Eeason, i.e. the purely intellectual conditions existing 
 a priori in the Mind. The Mind is said by Kant to be endowed 
 with three faculties Sensibility, Understanding, and Eeason. 
 The activity of the Mind is threefold Intuitive Thought, Con- 
 ceptive or Discursive Thought, and Regulative Thought. There 
 could not be an equivoque in my using the word Thought in its 
 ordinary philosophical acceptation as expressive of all mental 
 activity whatever, exclusive of mere sensation ; although Kant 
 assigns a more restricted meaning in his technical use of the 
 word, i.e. what we call Logic. And that Kant meant nothing
 
 1 36 Appendix. 
 
 opposed to the ordinary interpretation is obvious. It is obvious 
 because, as I said in my former letter, Intuition without Thought 
 is mere sensuous impression. Mr. Sylvester demurs to this, so 
 I will show it in a single citation : ' In the transcendental 
 Aesthetic,' says Kant, ' we will first isolate Sensibility by sepa- 
 rating from it all that the Understanding through its concepts 
 thinks therewith, so that nothing but empirical Intuition remains. 
 Secondly, we will lop off from this empirical Intuition every- 
 thing relating to sensation (Empfindting) ; so that thereby 
 nothing will remain but pure Intuition and the mere form of 
 phenomena, which is the one thing that Sensibility can furnish 
 a priori. By this investigation it will appear that there are two 
 pure forms of sensuous Intuition which are a priori principles of 
 Cognition.' ('Kritik,' 1, ed. Hartenstein, p. 61.) 
 
 Mr. Sylvester correctly says, that Intuition and Thought are 
 not convertible terms. But he is incorrect in assuming that 
 they differ as potential and actual ; they differ as species and 
 genus ; therefore, whatever is a form of Intuition, though not a 
 form of Logic, must be a form of Thought ; unless intuitive 
 Thought be denied altogether. How little Kant denied it is 
 evident in every section of his work. In asserting that Space 
 and Time as Intuitions belong to the subjective constitution of 
 the Mind subjectiven Beschaffenheit unseres Gemiiths (p. 62) 
 he expresses this ; but it is unequivocally expressed in the 
 following definition : ' A perception, when it refers solely to 
 the subject, as a modification of its states, is sensation, an 
 objective perception is cognition : this is either Intuition or 
 Concept, " intuitus vel conceptus." ' (' Kritik,' p. 294.) Is not 
 thought implied in cognition? Again: 'The proposition "I 
 think " is an undetermined empirical Intuition, i.e. Perception 
 consequently, it proves that Sensation, which belongs to Sensi- 
 bility, must lie at the basis of this proposition. ... I do not 
 mean thereby that the "I" in the "I think" is an empirical 
 representation ( Vorstellung), on the contrary, it is purely intel- 
 lectual, because it belongs to thought in general. But without 
 some empirical representation which would give Thought its 
 material there could be no such act of Thought as the "I 
 think"' (p. 324,
 
 Kant's Doctrine of Space and Time. 137 
 
 'Man is always thinking,' says Hegel, 'even when he has 
 nothing but intuitions' denktnd ist der Mensch immer auch wenn 
 er nur anschaut' (Encyclop. 24.) 
 
 If, because Kant has a restricted use of the term Thought, all 
 who venture on the more ordinary use are said to misrepresent 
 his philosophical meaning, I must call upon those who criticise 
 this laxity to refrain henceforth from speaking of Reason as 
 Thought, since Kant no less excluded Reason from the province 
 of the Understanding. If ' the only forms of thought, in Kant's 
 sense, are the Categories,' this sweeps away Reason on the one 
 side, as it sweeps away Sensibility on the other ; and Ideas are 
 not more correctly named Thoughts than Intuitions are. Kant, 
 it is true, speaks of the concepts of Reason, and defines an Idea 
 to be a ' Vernunftbegriff' (page 294); but Kant, equally and in 
 a hundred places, speaks of the ' concept of Space ' (Begriff des 
 Raumes). The truth is, as already intimated, that in spite of 
 his technical restriction of Thought to the formation of concepts, 
 he recognised intuitive and regulative Thought no less than dis- 
 cursive Thought ; nor would his system have had any coherence 
 without such a recognition. Why does he call his work the 
 ' Critik of Pure Reason,' unless he intended to display the 
 common intellectual ground of Sensibility, Understanding, and 
 Reason? and does not the word Thought, in ordinary philo- 
 sophical language mean this activity of the Intellect ? When, by 
 Sir W. Hamilton, Dr. Whewell, Mr. Spencer, and myself, the 
 phrase Forms of Thought is used, does not every reader under- 
 stand it as meaning Forms of intellectual activity ? 
 
 In conclusion, I affirm that in the ordinary acceptation of the 
 term Thought the activity of the Mind Space and Time as 
 forms of Intuition are forms of Thought, conditions of mental 
 action ; and to suppose that because Kant's language is different, 
 his meaning is misrepresented by classing forms of Intuition 
 among the forms of Thought is to misunderstand Kant's doctrine 
 and its purpose. GEOEGE HENEY LEWES. 
 
 January 22.
 
 1 38 Appendix. 
 
 Dr. INGLEBY, I should think, is quite entitled to say not only 
 that Kant might, but that he would, have disclaimed the phrase 
 Form of Thought as applied to Space or Time taken simply. 
 The remark of Mr. Lewes, that ' intuition without thought is 
 mere sensuous impression,' or, as it might have been put, that 
 phenomena of sense (constituted such in the forms of Space and 
 Time) must further be thought under Categories of Under- 
 standing, before they can be said to be known or to become 
 intellectual experience cannot be a sufficient reason for making 
 a Form of Thought proper out of a Form of Intuition. 
 
 There is, nevertheless (and Mr. Lewes does not fail to suggest 
 it), a sense in which, when taken along with the Categories of 
 the Understanding, and with or without the Ideas of the Keason, 
 the Forms of Intuition may be spoken of as Forms of Thought : 
 Thought being understood, with the same extension that Kant 
 himself gives to Eeason in the title (not the body) of his work, 
 as equivalent to faculty of Knowledge in general. It is in this 
 sense that Kant calls all the forms alike, a priori principles of 
 Knowledge ; and the ambiguity of the word Thought is so well 
 recognised that the English writers arraigned by Prof. Sylvester 
 take no great liberty, when for their purpose, which commonly 
 is the discussion of the general question as to the origin of 
 Knowledge, they talk generally of Kant's ' Forms of Thought.' 
 If, indeed, any of them ever speaks of Space as a ' form of the 
 Understanding,' which was part of the original charge, the case 
 is very different ; Kant being so careful with his Verstand. 
 But Mr. Lewes, at least, would never be caught speaking thus, 
 even though his main reason for merging Intuition in Thotight 
 might seem to justify this also. G-. CEOOM KOBEETSON. 
 
 University College, January 22. 
 
 You will perhaps permit me to make a remark on a con- 
 troversy at present going on in your columns. There has seldom, 
 I believe, been a grosser or more misleading perversion of the 
 Critical Philosophy than ascribing to Kant the view that Space 
 and Time are in any meaning of the terms ' forms of thought.
 
 Kanfs Doctrine of Space and Time. 139 
 
 One of his chief grounds of complaint against Leibnitz is, that 
 the latter ' intellectualised these forms of the sensibility ' 
 (Meiklejohn's translation of the 'Critick,' p. 198): and lest the 
 import of this assertion should be mistaken, he explicitly tells 
 us that ' Space and Time are not merely forms of sensuous 
 intuition, but intuitions themselves ' (Meiklejohn's trans., p. 98) : 
 that is, sensuous intuitions, as he has been just before asserting 
 that all human intuitions must be. It is precisely on this dis- 
 tinction of pure sensibility and pure thought that Kant founds 
 the possibility of Mathematics a science which could never be 
 derived from a mere analysis of the concepts employed, but only 
 from the construction of them in intuition. He ridicules, for 
 example, the idea of attempting to deduce the proposition, ' Two 
 right lines cannot enclose a space,' from the mere concepts or 
 notions of a straight line and the number two. ' All your en- 
 deavours,' says he, ' are in vain, and you find yourself compelled 
 to have recourse to intuition, as in fact Geometry always does.' 
 (Meiklejohn, p. 39 : see also his long contrast of Mathematical 
 and dogmatical methods in the beginning of the ' Methodology.') 
 And not only is Kant's Mathematical theory founded on this 
 distinction, but his Physical theory also, since it is only by 
 means of pure intuition that he connects pure thought with 
 sensations (see the ' Schematism,' and still more the ' General 
 Remark on the System of Principles,' Meiklejohn, pp. 174-7) ; 
 and when he fails to make out this connection he regards the 
 Ideas of Pure Reason as possessed of no objective validity 
 (Transcendental Dialectic). In the first edition of the ' Critick' 
 he went still further, and in his remarks on the Second Para- 
 logism of Rational Psychology he speaks of ' that something 
 which lies at the basis of external phenomena, which so affects 
 our sense as to give it the representations of space, matter, form, 
 &c.' And while he abbreviated his discussion in the second 
 edition, he tells us in his preface that he found nothing to alter 
 in the views put forward in the previous one. 
 
 I might quote whole pages of the ' Critick ' in proof of these 
 views, but I ought rather to apologise for writing so much after 
 the letters which you have already published. I believe the 
 i2
 
 140 Appendix. 
 
 mistakes as to Kant's doctrine of Space and Time, his refutation 
 of Idealism, and his discussion of the Antinomies of the Pure 
 Reason, are almost without a parallel in the History of Phi- 
 losophy. W. H. STANLEY MONCK. 
 , Trinity College, Jan. 22. 
 
 In answer to my invitation, Mr. Lewes now ' freely admits 
 that Kant nowhere speaks of Space and Time as " Forms of 
 Thought," ' but still contends that ' Kant would not have dis- 
 claimed such language, as misrepresenting his meaning.' As 
 well might he argue that although Euclid never uses the word 
 epipedon (our English word plane or plain), to signify a curved 
 surface (eiriQdveta), he would not have remonstrated against the 
 use of the term cylindrical epipedon or conical epipedon, to denote 
 the surface of a cylinder or cone, in a professed exposition or 
 criticism of his Elements of Geometry, because in common life 
 we speak of rough or undulating plains, or because a plane 
 admits of being bent into the shape of a cylindrical or conical 
 surface. I think the ladies who are getting up their Planes and 
 Solids at St. George's Hall would be of a different opinion from 
 Mr. Lewes in this matter, and with good reason on their side. 
 
 Mr. Lewes, reiterating a statement contained in his previous 
 letter, goes out of his way to affirm that he ' uniformly speaks 
 of Space and Time as forms of Intuition in his pages of exposi- 
 tion ' of Kant's doctrine in his ' History of Philosophy.' Were 
 the fact so, it would not in any material degree excuse the 
 inaccuracy of subsequently styling them ' Forms of Thought ; ' 
 and, moreover, the real point at issue is not Mr. Lewes's general 
 accuracy or inaccuracy, but whether a mode of speech which he, 
 along with others, employs, is right in itself and ought to be 
 persisted in. 
 
 However, as Mr. Lewes has thought fit to put in a sort of 
 plea in mitigation of former wrong-doing, I have taken the 
 trouble of looking through his exposition and criticism of Kant 
 in his History (ed. 1867) and in no single instance have I come 
 upon the phrase forms of intuition applied to Space and Time,
 
 Kant's Doctrine of Space and Time. 141 
 
 either in the one or the other ; although he states he has uniformly 
 spoken of them as such in the former. I have marked the word 
 intuitions as occurring once, and/orww of sensibility several times, 
 but forms of intuition never. IS form of sensibility is as good to 
 use as form of intuition, form of understanding ought to be as good 
 as form of thought; but Mr. Lewes owns that the former is 
 indefensible, whilst he avers that the latter is correct. If Mr. 
 Lewes has ever called Space and Time forms of intuition in the 
 History, it will be easy for him to set me right by quoting the 
 passage where the phrase occurs, although that circumstance 
 would not in any degree better his own position, and still less 
 excuse the assertion of his uniform use of the term. 
 
 If Mr. Lewes cannot quote correctly from his own writings, 
 it will surprise nobody that he misquotes the language of an 
 opponent. He repeats, ' Intuition without thought is mere 
 sensuous impression,' and adds, ' Mr. Sylvester demurs to this.' 
 My words are (Nature, Jan. 13, 1870): 'To such a misuse 
 of the word energy it would be little to the point to urge that 
 force without energy is mere potential tendency. It is just as little 
 to the point in the matter at issue for Mr. Lewes to inform the 
 readers of Nature that intuition without thought is mere 
 sensuous impression.' So that, according to Mr. Lewes, to sa 
 . that a proposition is little to the point is demurring to its truth. 
 
 I should not hesitate to say if some amiable youth wished to 
 entertain his partner in a quadrille with agreeable conversation, 
 that it would be little to the point, according to the German pro- 
 verb, to regale her with such information as how 
 
 4 Long are the days of summer-tide, 
 And tall the towers of Strasburg's fane,' 
 
 but should be surprised to have it imputed to me on that 
 account that I demurred to the proposition of the length of 
 the days in summer, or the height of Strasburg's towers. 
 
 In another passage, Mr. Lewes gives me credit for ' saying 
 correctly that Intuition and Thought are not convertible terms' 
 a platitude I never dreamed of giving utterance to ; but that I 
 am ' incorrect in assuming that they differ as potential and
 
 142 Appendix. 
 
 actual ' words which, or the like of which, in any sort or sense, 
 never flowed from my pen. Surely this is not fair controversy, to 
 misquote the words and allegations of an opponent. It seems to 
 me too much like fighting with poisoned weapons. I decline to 
 continue the contest on such terms ; and, passing over Mr. Lewes's 
 very odd statement about species and genus with reference to 
 Intuition and Thought, shall conclude with expressing my surprise 
 at his and Mr. G-. C. Eobertson's confident assumption that Kant 
 uses in the title of his book pure reason in a far wider sense than 
 in the body of his work, simply because to arrive at the Pure 
 Reason he has to go through the Critick of the Sensibility and of 
 the Understanding. If in ahistory of the Eeign of Queen Victoria 
 the author should find it expedient to go back to the times of 
 the Norman and Saxon conquests, would it be right to infer 
 therefrom that he used in his title-page the name Victoria in a 
 generalised sense, to include not only her most Gracious Majesty, 
 but also the Tanner's daughter and Princess Eowena? 
 
 Perhaps by this time many of the Naturalistic readers of the 
 journal who regard the human intelligence as forming no part of 
 the scheme of Nature, wish Space at the bottom of the sea ; but the 
 more the subject is canvassed, and the greater the number of Eng- 
 lish authorities brought forward to back up Mr. Lewes in wresting 
 the words of Kant from their proper scientific signification, the 
 higher meed of praise seems to me to accrue to Dr. Ingleby for 
 stemming the tide of depravation, and banishing, as I feel con- 
 fident this discussion will have the effect of doing, from the 
 realm of English would-be philosophy, such a loose and incau- 
 tious way of talking as that of giving to Space and Time the 
 designation which the Master has appropriated to the categories 
 of his system, and to them alone. J. J. SYLVESTER. 
 
 P.S. I should be doing injustice to the very sincere senti- 
 ments of respect I entertain for Mr. Lewes's varied and brilliant 
 attainments (which constitute him a kind of link between the 
 material and spiritual sides of Nature), and of gratitude for the 
 pleasure the perusal of his ' History of Philosophy ' has afforded 
 me, were I to part company with him without disclaiming all 
 acrimony of feeling, if perchance any too strident tones should
 
 Kanfs Doctrine of Space and Time. 143 
 
 have seemed to mingle with my enforced reply. In naming him 
 in the original offending footnote (the fountain of these tears), 
 my purpose was simply to emphasise the necessity of protesting 
 against what seemed to me an unsound form of words, apropos 
 of Kant, which went on receiving countenance from such and 
 so eminent writers as himself and the others named; and I 
 should be false to my own instincts did I not at heart admire 
 the courageous spirit with which, almost unaided and alone (like 
 a good, I meant to say valiant knight of old), he has done his best to 
 defend his position and maintain his ground against all oppugners. 
 
 J. J. S. 
 
 I AM quite willing to leave the readers of Nature and the 
 Btudents of Kant to decide on the propriety, in English philoso- 
 phical discourse, of calling Space and Time ' forms of Thought,' 
 the more so as Sir W. Hamilton a great stickler for philosophic 
 precision uses the term in that sense and would have been sur- 
 prised to hear that he had misrepresented Kant in so doing. 
 My opponents persist in limiting the term Thought to the re- 
 stricted meaning given to it in Kant's terminology, which, in 
 English, is restricting it to Conception or Judgment : on this 
 ground they might deny that Imagination or Recollection could 
 be properly spoken of as Thought. Throughout I have accepted 
 Thought as equivalent to mental activity in general and the 
 1 forms of Thought ' as the conditions of such activity. The 
 ' forms of Thought ' are the forms which the thinking principle 
 (Kant's pure Reason) brings with it, antecedent to all experience. 
 The thinking principle acts through three distinct faculties : 
 Sensibility (Intuition), Understanding (Conception), and Reason 
 (Ratiocination) : to suppose Thought absent from Intuition, 
 is to reduce Intuition to mere sensuous impression. Therefore, 
 whatever is a form of Intuition must be a form of Thought. 
 
 The following passage from Mr. Mahaffy's valuable transla- 
 tion of Kuno Fischer's work on Kant, may here be useful : 
 ' Sensibility and understanding are cognitive faculties differing 
 not in degree but in kind, and form the two original faculties of
 
 144 Appendix. 
 
 the humaninind' The general problem of a Critick of 
 
 the Eeason ' is subdivided into two particular objects, as human 
 Reason is into two particular faculties of knowledge. The first 
 object is the investigation of the sensibility ; the second, that of 
 the understanding. The first question is, How is rational 
 knowledge possible through sensibility ? The second question, 
 How is the same knowledge possible through the understanding ? ' 
 (PP- 4, 5.) 
 
 Those "who maintain that it is improper to speak of Space and 
 Time as forms of Thought, must either maintain that Kant held 
 Sensibility not to be a faculty of the Mind (thinking principle) ; 
 or that the term Thought is not, in English discourse, a correct 
 expression for the activity of the thinking principle. I believe 
 that the student will agree with me in saying that, although 
 Kant restricted the term Thought to what we call Conception or 
 Judgment, he understood by the activity of the mental faculties 
 (Pure Eeason) what we understand by Thought. 
 
 It is not, however, to continue this discussion that I again 
 trespass on your space ; but to reply to the personal part of Mr. 
 Sylvester's letter. He charges me with misquoting myself and 
 with misquoting him. I said that, in my exposition, Space and 
 Time were uniformly spoken of as forms of Intuition and I say 
 so still. Mr. Sylvester has taken the trouble of reading that 
 exposition without taking the trouble of understanding it ; he 
 declares that he ' has marked the word intuition as occurring 
 once and forms of sensibility several times ; but forms of in- 
 tuition never.' His carefulness may be estimated by the fact 
 that the word intuition occurs four times on the two pages : his 
 comprehension by the fact that it is perfectly indifferent whether 
 Sensibility or Intuition be the term employed, since sensibility 
 is the faculty and Intuition the action of that faculty. Mr. 
 Sylvester, not understanding this, says, 'If form of sensibility is 
 as good to use as form of intuition, form of understanding ought 
 to be as good as form of thought ; but Mr. Lewes owns that 
 the former is indefensible, whilst he avers that the latter is 
 correct.' Considering that this passage occurs in a letter which 
 charges me with unfair misquotation, it is curious. So far from
 
 Kanfs Doctrine of Space and Time. 145 
 
 owning that the former is ' indefensible,' it is what I declare to 
 be true; and, with regard to the latter, though I do think a 
 form of Understanding is a form of Thought, my statement was 
 altogether away from it, namely, that Space and Time as forms 
 of Sensibility, would be incorrectly spoken of as forms of the 
 Understanding. 
 
 "With regard to the alleged misquotation of his own words, 
 which he characterises as unfair and as 'too much like 
 fighting with poisoned weapons,' it was a charge which both 
 astonished and pained me. There are few things for which I 
 have a bitterer contempt than taking such unfair advantages of 
 an adversary. I beg to apologise to Professor Sylvester for any 
 misrepresentation which, unintentionally, I may have been 
 guilty of. But, in accepting his denial of the construction I 
 placed upon his langutfge, I must still say that, after re-reading 
 his letter I am at a loss to see what other construction it admits 
 of, that has any bearing on the dispute, and that he has not ex- 
 pressed his meaning with sufficient clearness. Intuition and 
 Thought are there compared with Force and Energy as terms 
 ' not convertible ' ; Force is detached from Energy as potential 
 from actual, and Intuition without Thought is made to hold an 
 analogous position. Here is the passage; let the reader 
 judge : 
 
 ' Can Mr. Lewes point to any passage in Kant where Space 
 and Time are designated forms of thought ? I shall indeed be 
 surprised if he can do so as much surprised as if Mr. Todhunter 
 or Mr. Eouth in their Mechanical Treatises were to treat energy 
 and force as convertible terms. To such a misuse of the word 
 energy it would be little to the point to urge that force without 
 energy is a mere potential tendency. It is just as little to the 
 point, in the matter at issue, for Mr. Lewes to inform the readers 
 of Nature that intuition without thought is mere sensuous 
 impression' 
 
 Is it to use ' poisoned weapons ' to interpret this as assuming 
 that Intuition and Thought differ as potential and actual ? I repeat 
 that, since Mr. Sylvester disclaims the interpretation, my only 
 course is to apologise for it ; but, after his own misinterpretations
 
 146 Appendix. 
 
 of me, he will not, I hope, persist in attributing mine to a desire 
 to take an unfair advantage. If I make no reply to the other 
 points raised in the various letters it is in order not to prolong 
 the discussion. 
 
 GEORGE HKNEY LEWES. 
 
 I DO not know whether Mr. Sylvester and Dr. Ingleby will 
 be satisfied with Mr. Lewes' letter in yours of the 27th. I am 
 not, and I think, in defending his former mistake, Mr. Lewes has 
 fallen into additional errors. 
 
 It is undoubtedly fair to translate an author into your own 
 language before criticising him, provided you found no criticism 
 on the language that you have put into his mouth. But this I 
 think Mr. Lewes has done. He accuses Kant of inconsistency 
 in speaking of pure a priori cognitions, when, on his own system, 
 pure thought only supplies one element to these cognitions, the 
 other being derived from sense or intuition. Now (not to insist 
 here that Kant constantly uses the term cognition in a wider 
 sense than that which Mr. Lewes insists on fastening upon him), 
 this criticism is evidently invalidated by the simple remark that 
 Kant admits pure intuitions as well as pure concepts, and ex- 
 plains the nature of mathematics, as a system of a priori cogni- 
 tions, by the fact that its object-matter consists of nothing but 
 pure intuitions. 
 
 Mr. Lewes now informs us that Kant's Intuition and Thought 
 ' differ as species and genus.' According to Kant they differ in 
 kind ; and Leibnitz was as wrong in making sensibility a species 
 of thought as Locke was in making Thought a species of sen- 
 sibility. Space and Time, Mr. Lewes adds, are forms of 
 ' mental activity ' and, therefore, are properly termed ' forms 
 of Thought,' in the meaning of the latter term which is usually 
 current in this country. If they were forms of mental activity 
 they would be forms of Thought, according to Kant, likewise ; 
 for the criterion by which Kant distinguishes between Intuition 
 and Thought (under which term he includes both the under- 
 standing proper and the reason proper) is that, in the former, the
 
 Kant's Doctrine of Space and Time. 147 
 
 mind is passive (receptive) while, in the latter, it is spontaneously 
 active ; and it is precisely on this ground the passive reception 
 of them by the mind that he refers Space and Time to Sensi- 
 bility rather than Thought. This is repeatedly brought out in 
 the Transcendental Deduction of the Categories. See in parti- 
 cular Sections 11 (Meiklejohn, p. 80) and 18 (Meiklejohn, p. 90). 
 
 I think if Mr. Lewes will turn to the preface to the first edi- 
 tion of the ' Critick,' he will see that the transcendental logic 
 only (and perhaps I might limit it to the transcendental dialectic) 
 grapples directly with the problem indicated by the title of the 
 book. The Aesthetic is a preliminary inquiry, which proves after- 
 wards of great use ; but is not to be considered as a Critick of 
 Pure Reason in this particular department. His using the term 
 ' concept ' of space, is certainly confusing ; but its explanation, 
 I think, is to be found in a passage in the ' Transcendental 
 Exposition ' of this ' concept ' (Meiklejohn, p. 25), where he 
 says, ' It must be originally intuition, for from a mere conception 
 no propositions can be deducted which go out beyond the con- 
 ception, and this happens in geometry.' In the preceding page 
 he similarly qualifies his statement that Space is an intuition. 
 ' No conception as such,' he says, ' can be so conceived as if it 
 contained, within itself, an infinite multitude of representations.' 
 We may now have a concept as well as an intuition of Space and 
 Time ; but the intuition was the original form of the idea, and it 
 is to the intuition that we must always have recourse in mathe- 
 matics when we wish to discover a new truth. 
 
 I think, if Mr. Lewes will again read over the Transcendental 
 Aesthetic and the parts of the Transcendental Analytic which are 
 closely related to it, he will see that Kant never designates the 
 original representations of space and time ' concepts,' or refers 
 their origin to ' pure reason.' W. H. STANLEY MONCK. 
 
 Trinity College, Dublin. Jan. 29. 
 
 [This correspondence must now cease. ED.]
 
 148 Appendix. 
 
 IN order that the reader may judge of the correctness of 
 the assertions made by Mr. Lewes in his concluding 
 letter, and his general fairness in controversy, I request 
 attention to the annexed catena of passages drawn from 
 the above correspondence.* 
 
 No. 1. The AUTHOR. 
 
 ' It is very common not to say universal with English -writers 
 even such authorised ' (I meant to say authoritative) ' ones as 
 Whewell, Lewes or Herbert Spencer to refer to Kant's doctrine as 
 affirming space to be "a form of thought," or " of the under- 
 standing." This is putting into Kant's mouth words which he 
 would have been the first to disclaim.' 
 
 No. 2. Mr. G. H. LEWES. 
 (a) ' Kant assuredly did teach as Professor Sylvester says, and 
 
 as I HAVE REPEATEDLY STATED, THAT SPACE IS A FOEM OF INTUI- 
 TION.' 
 
 () ' Every student of Kant knows that intuition without 
 thought is mere sensuous impression.' 
 
 (7) ' While therefore anyone who spoke of space as " A FORM 
 
 OF THE UNDERSTANDING " WOULD CERTAINLY USE LANGUAGE WHICH 
 
 KANT WOULD HAVE DISCLAIMED, Kant himself would have been 
 surprised to hear that space was not held by him as a form of 
 thought.' 
 
 [ (a) In no one single instance in his fifty pages of exposition 
 and criticism has Mr. Lewes ever once stated that Space is a 
 Form of Intuition.] 
 
 No. 3. The AUTHOR. 
 
 ' Can Mr. Lewes point to any passage in Kant where Space 
 and Time are designated forms of thought. I shall indeed be 
 
 * The words in SMALL CAPITALS are in ordinary print in the original
 
 Kanfs Doctrine of Space and Time. 149 
 
 much surprised if he can do so as much surprised as if Mr. 
 Todhuuter or Mr. Eouth in their mechanical treatises were to 
 treat energy and force as convertible terms. To such a misuse 
 of the word energy it would be as little to the point to urge that 
 force without energy is mere potential tendency. It is just AS 
 LITTLE TO THE POINT in the matter at issue for Mr. Lewes to 
 inform the readers of Nature that intuition without thought is 
 mere potential tendency.' 
 
 No. 4. Mr. G. H. LEWES. 
 
 ' In the pages of exposition I uniformly speak of Space and 
 Time as forms of intuition ; no language can be plainer.' [In no 
 one single instance does Mr. Lewes so speak of Space or Time.] 
 
 (a) ' Mr. Sylvester correctly says that intuition and thought 
 are not convertible terms. (/3) But he is incorrect in affirming 
 that they differ as potential and actual.' 
 
 [These are words put into my mouth by Mr. Lewes, which I 
 disclaim as Kant would have disclaimed the words put into his. 
 I nowhere have stated the truism (a). I nowhere have affirmed 
 the absurdity (0).] 
 
 No. 5. Mr. G. CBOOM KOBEBTSON. 
 
 ' If indeed any of them ever speaks of space as a " form of the 
 understanding," which was part of the original charge, the case 
 is very different, Kant being so careful with his Verstand. But 
 Mr. Lewes at least would never be caught speaking thus.' 
 
 No. 6. The ATJTHOE. 
 
 ' (o) If form of sensibility is as good to use as form of intuition, 
 form of understanding ought to be as good to use as form of 
 thought (0), but Mr. Lewes owns that the former is indefensible 
 whilst he avers that the latter is correct.' 
 
 [In proof of (/3) above see (7) of No. 2. (a) above evidently 
 implies the proportion : 
 
 sensibility : intuition : : understanding : thought. 
 The first and third terms representing faculties, the second 
 and fourth the actions of those faculties respectively.]
 
 150 Appendix. 
 
 No. 7. Mr. G. H. LEWES. 
 
 ' His [the author's] carefulness may be estimated by the (a) fact 
 that the word intuition occurs four times on THE TWO PAGES ; his 
 comprehension by the fact that it is perfectly indifferent whether 
 Sensibility or Intuition be the term employed, since Sensibility 
 is the faculty and Intuition the action of that faculty. (j3) Mr. 
 Sylvester not understanding this, says, " if form of sensibility is 
 as good to use as form of intuition, form of understanding ought 
 to be as good as form of thought ; but Mr. Lewes owns that the 
 former is indefensible whilst he avers that the latter is correct." 
 (7) So far from averring that the former (form of under- 
 standing) is " indefensible," it is what I declare to be true.' 
 
 (8) ' I said that in my exposition Space and Time were uni- 
 formly spoken of as forms of intuition, and I say so still.' 
 
 As regards (a) what does Mr. Lewes mean by the use of tha 
 definite article THE ? The whole question was about the use of the 
 phrase forms of intuition ; it was a mere work of surplusage in 
 me to count the number of times that the word intuition unsup- 
 ported occurs ; but I did wade through the whole of the criticism 
 and exposition, covering between them 50 pages, viz. 35 of expo- 
 sition (439-474), 15 of criticism (474-489). I can only account 
 for my inadvertence in this quite immaterial point by supposing 
 that a clerical or typographical error (no one who knows my 
 handwriting would wonder at this) has crept in, and that I pro- 
 bably meant to say, as I ought to have said, not ' once ' but 
 ' more than once' or 'often.' 
 
 (i8) How, in the face of the proportion so plainly indicated in 
 No. 6, Mr. Lewes could have the hardihood to make such an 
 assertion is to me incomprehensible. 
 
 (7) This statement is in direct contradiction to what Mr. 
 Lewes has stated in his first letter see No. 2 (7). 
 
 (8) This assertion is simply untrue. Mr. Lewes has in no one 
 single instance in his exposition, or his criticism, 3rd edition, 
 1867, spoken of ' Space and Time as forms of Intuition.' As Mr. 
 Lewes and myself are here at direct variance on a matter of fact, 
 I undertake to pay 50 to anyone who will discover a single 
 instance where the phrase ' form of Intuition ' occurs in Mr.
 
 Kant's Doctrine of Space and Time. 151 
 
 Lewes' article on Kant, chaps, i., ii., iii., p. 436-489, 3rd edi- 
 tion, 1867. 
 
 So much, and more than I could have wished, in the 
 way of settling the personal issue raised by Mr. Lewes. 
 The original and only worthy part of the controversy is 
 one of much greater consequence than the proof or dis- 
 proof of Mr. Lewes' trustworthiness and self-consistency. 
 
 The question to be decided was whether a form of 
 language conveying a completely erroneous view of the 
 fundamental principles of Kant's philosophy was to be 
 adhered to by English writers on the ground of pre- 
 scription and authority. I think that that question, 
 thanks to Dr. Ingleby's intrepidity and Mr. Lewes' 
 persistency, has now been settled for once and for ever. 
 
 In looking over Mr. Lewes's article on Kant for the 
 third or fourth time, to satisfy myself (in the face of 
 his positive and reiterated asseverations to the contrary) 
 that he had not in any one single instance used the 
 phrase ' form of intuition,' I came upon the following 
 passage in a footnote : 
 
 ' Mr. Spencer seems to me less happy in his objection 
 that " if space and time are forms of thought, they can 
 never be thought of; since it is impossible for anything 
 to be at once the form of thought and the matter of 
 thought." ' First Principles, p. 49. 
 
 Such an observation proceeding from so able a writer 
 as Mr. Herbert Spencer, is a very instructive instance 
 of the serious practical mischief arising from the habit 
 (so obstinately defended by Mr. Lewes) of ascribing to
 
 152 Appendix. 
 
 Kant the statement of Space and Time being forms of 
 Thought. It is clear that if Mr. Spencer had been 
 made aware of the broad line of demarcation in Kant's 
 system between Intuition, the action or product of 
 Sensibility, and Thought the action or product of the 
 Understanding (the two belonging, according to Kant, 
 to entirely different provinces of the mind), he would 
 have seen that his supposed refutation proceeded on a 
 mere misapprehension of Kant's actual utterance and 
 doctrine on the subject. If Mr. Spencer will restore 
 to Kant the words really used by him, the sentence 
 will run thus : ' if space and time are forms of intuition, 
 they can never be thought of; since it is impossible for 
 anything to be at once the form of thought and the 
 matter of thought ; ' and his epigram (for Mr. Spencer 
 must have meant it rather as an epigram than as a serious 
 argument) loses all its point. Was it likely a priori 
 that Kant (the Kant) should have laid himself open to 
 such a scholars-mate at the very outset of his system ? 
 
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 INDEX. 
 
 ACTON'S Modern Cookery 
 
 ALCOCK'S Residence in Japan 
 
 ALLIES on Formation of Christendom .... 
 
 Alpine Guide (The) 
 
 ALTHAUS on Medical Electricity 
 
 ANDREWS'* Life of Oliver Cromwell 
 
 ARNOLD'S Manual of English Literature .. 
 
 AttNOTT's Elements of Physics 
 
 Arun dines Cami ... 
 
 Autumn Holidays of a Country Parson .... 
 AY RE'S Treasury of Bible Knowledge 
 
 BACON'S Essays, by WHATELY 
 
 Life and Letters, by SPEDDINQ .. 
 
 Works, edited by SPF.DDING 
 
 BAIX'S Louie, Deductive and Inductive .... 
 
 Mental and Moral Science 
 
 on the Emotions and Will 
 
 on the Senses and Intellect 
 
 on the Study of Character 
 
 BALL'S Alpine Guide 
 
 BARNARD'S Drawing from Nature 
 
 BATLDON'S Rents and Tillages 
 
 Beaten Tracks 
 
 BECKER'S Charicles and Gullus 
 
 BENFEY'S Sanskrit Dictionary 
 
 BERNARD on British Neutrality 
 
 BLACK'S Treatise on Brewing 
 
 BLACKLEY'S Word-Gossip 
 
 German-English Dictionary .. 
 
 BLAINK'S Rural Sports 
 
 Veterinary Art 
 
 BOURNE on Screw Propeller 
 
 BOURNE'S Catechism of the Steam Engine . 
 
 Handbook of Steam Engine 
 
 Improvements in the Steam 
 
 Engine 
 
 -Treatise on the Steam Engine .. 
 
 Cabinet Lawyer 18 
 
 CALVERT'S Wife's Manual *1 
 
 CATES'S Biographical Dictionary S 
 
 CATS' and FARLIE'S Moral Emblems It 
 
 Changed Aspects of Unchanged Truths .... * 
 
 CHESNEY'B Euphrates Expedition 22 
 
 Indian Polity 3 
 
 Waterloo Campaign 3 
 
 CHILD'S Physiological Essays 1ft 
 
 ChoraleBook for England 16 
 
 CLOUOH'S Lives from Plutarch * 
 
 COBBE'S Norman Kings of J nglaud 2 
 
 COUOreO (Bishop) on Pentateuch and Book 
 
 of Joshua M 
 
 Commonplace Philosopher in Town and 
 
 Country - ft 
 
 CONINGTON'S Chemical Analysi 
 
 of VIRGIL'S 
 
 Examples of Modern Engines .. 18 
 
 BOWDLER'S Family SHAKSPEARK 
 BRAHDE'S Dictionary of Science, Litera- 
 ture, and Art 
 
 BRAY'S (C.) Education of the Feelings 
 
 Philosophy of Necessity .... 
 
 on Force 
 
 BROWNE'S Exoosit ; on of the 39 Articles 
 
 BUCKLE'S History of Civilization 
 
 BULL'S Hints to Mothers 
 
 Maternal Management of Children 
 
 BUNSEN'S (Baron) Ancient Egypt 
 
 God in History 
 
 Memoirs 
 
 BUNSEN (E. DE) on Apocrypha 
 
 's Keys of St. Peter 
 
 Bt-iiKK's Vici.vitiidi.-* of Families. 
 
 I'.) 
 
 CONTANSEAU'sFrench-English Dictionaries S 
 CONYBEARE and HOWSON'S Work on St. 
 
 Paul It 
 
 COOK on the Acts 19 
 
 COOK'S Voyages 5 
 
 COOPER'S Surgical Dictionary 14 
 
 COPLAND'S Dictionary of Practical Medicine 15 
 
 COTTON'S Introduction to Confirmation.... 19 
 
 COULTHART'S Decimal Interest Tables 28 
 
 Counsel and Comfort from a City Pulpit 9 
 
 Cox's Aryan Mythology 4 
 
 Manual of Mythology 5 
 
 Tale of the Great Persian War 2 
 
 Tales of Ancient Greece 15 
 
 CRESY'S Encyclopaedia of Civil Engineering 18 
 
 Critical Essays of a Country Parson 9 
 
 CROWE'S History of France 2 
 
 CULLEY'S Handbook of Telegraphy 17 
 
 CUSACK'S History of Ireland I 
 
 I D'AUBIONE'S History of the Reformation 
 
 I in the time of CALVIN t 
 
 ' DAVIDSON'S Introduction to NewTestament S 
 
 Dead Shot! The), by MARKSMAN 26 
 
 DE LA RIVE'S Treatise on Electricity 12 
 
 DKNISON'S Vice-Regal Life 1 
 
 DE TOCQUEVILLE'S Democracy in America 2 
 DISRAELI'S Lothair 
 
 28 DonKLL's Reports on the Progress of Medi- 
 
 BURTOS'S ("ii'istian Church 
 
 Vikram ami the Vumj.ire 
 
 cine . 
 
 DonsON on the Ox 27 
 
 DOVE on Storms 11 
 
 DOYLE'S Fairyland 16 
 
 DYER'S City of Rome S 
 
 EASTLAKE'S Life of Gibson 16 
 
 Hints on Household Taste.... 17 
 
 History of Oil Painting U
 
 30 
 
 NEW WORKS PUBLISHED BY LONGMANS AND CO. 
 
 EDMTWDS'S Names of Places .............. 9 
 
 EDWARDS'S Shipmaster's Guide ............ 27 
 
 Elements of Botany ........................ 13 
 
 ELLICOTT on the Revision of the English 
 
 NewTestament ................ 19 
 
 _____ 's Commentary on Ephesiaus .... 19 
 
 __ Commentary on Galatians ---- 19 
 
 _ . - . -- Pastoral Epist. 19 
 
 _____ Philippians,&c. 19 
 
 ____ Thessalonians 19 
 
 Lectures on the Life of Christ. . 19 
 
 __ 
 
 Essays and Contributions of A. K. H. B ..... 
 
 EWALD'S History of Israel .................. 
 
 FAIHBAIRX on Iron Shipbuilding .......... 18 
 
 __ 'S Applications of Iron .......... 18 
 
 _ Information for Engineers .. 18 
 
 . Mills and Millwork .......... 18 
 
 FARADAY'S Life and Letters ................ 4 
 
 FARBAB'S Families of Speech .............. 9 
 
 __ Chapters on Languase .......... 7 
 
 FELKIX on Hosiery and Lace Manufactures 18 
 
 FEXXELL'S Book of the Roach .............. 26 
 
 FFOULKES'S Christendom's Divisions ...... 21 
 
 FlTZWYGRAM on Horses and Stables ...... 27 
 
 Five Years in a Protestant Sisterhood ...... 20 
 
 FORBES'S Earls of Granard ................ 5 
 
 FOWLER'S Collieries and Colliers .......... 28 
 
 FRAHCIS'S Fishing Book .................... 28 
 
 FRESHFIEI.D'S Travels in the Caucasus. ... 22 
 
 FROTJBE'S History of England .............. 1 
 
 _ Short Studies on Great Subjects 9 
 
 GAXOT'S Elementary Physics .............. 11 
 
 GILBERT'S Cadore, or Titian's Country .... 22 
 
 GILBERT and CHURCHILL'S Dolomites 23 
 
 GIRDLESTONE'S High Alps without Guides 24 
 
 GOLDSMITH'S Poems, Illustrated .......... 25 
 
 GOULD'S Silver Store ...................... 26 
 
 GRAHAM'S Book about Words .............. 7 
 
 GHAUT'S Home Politics .................... S 
 
 _ Ethics of Aristotle ................ 6 
 
 Graver Thoughts of a Country Parson ...... 9 
 
 GRAY'S Anatomy .......................... 15 
 
 GREEXHOW on Bronchitis .......... ........ 14 
 
 GROVE on Correlation of Physical Forces . . 12 
 
 GURXEY'S Chapters of French History .... 2 
 
 G WILT'S Encyclopaedia of Architecture ---- 17 
 
 HARE on Election of Representatives ...... / 
 
 HARTWIG'S Harmonies of Nature .......... !: 
 
 _ Polar World .................... 13 
 
 _ Sea and its Living Wonders .. 12 
 
 _ Tropical World ................ IS 
 
 HAUOHTOX'S Manual of Geology . ......... K 
 
 HAWKER'S Instructions to Young Sportsmen 2b 
 
 HERSCHEL'S Outlines of Astronomy ........ 11 
 
 HEWITT on Diseases of Women ............ 14 
 
 Ho DGSOX'S Theory of Practice ............ 
 
 , _ Time and Space ................ 10 
 
 HOLMES'S System of Surgery ..... ......... H 
 
 __ Surgical Diseases of Infancy .... 14 
 
 HOOKER and WALKER-ARXOTT'S British 
 
 Flora ................................ 12 
 
 HORNE's Introduction to the Scriptures.... 20 
 
 __ Compendium of ditto ............ 2C 
 
 How we Spent the Summer ................ 22 
 
 HOWARD'S Gymnastic Exercises .......... 15 
 
 Ho WITT'S Australian Discovery . . . . ....... 23 
 
 _ Northern Heights of London .... 24 
 
 _ Rural Life of England .......... 24 
 
 __ Visits to Remarkable Places. . - 24 
 HuBXER'S Memoir of Sixtus V ........... 
 
 HUGHES'S (W.) Manual of Geography 
 HUME'S Essays .......................... 
 
 _ Treatise on Human Nature 
 
 HUMPHREY'S Sentiments of Shakspeare .... 16 
 
 IHNE'S Roman History 3 
 
 IXGELOW'S Poems 25 
 
 Story of Doom 26 
 
 Mopsa 26 
 
 JAMESOX'S Saints and Martyrs 17 
 
 Legends of the Madonna 17 
 
 Monastic Orders 17 
 
 JAMESOX and EASTLAKE'S History of Our 
 
 Lord * 17 
 
 JOHXSTOX'S Geographical Dictionary 11 
 
 JUKES on Second Death 21 
 
 on Types of Genesis 21 
 
 KALISCH'S Commentary on the Bible 7 
 
 Hebrew Grammar 
 
 KEITH on Fulfilment of Prophec 
 
 ecy. 
 
 Destiny of the World '. _ 
 
 KKRL'S Metallurgy by CROOKES and 
 
 RiiHRIG 19 
 
 KESTEVEX'S Domestic Medicine 1S> 
 
 KIKBY and SPEXCE'S Entomology 13 
 
 LAXDOX's (L. E. L.) Poetical Worka 26 
 
 LATHAM'S English Dictionary 7 
 
 River Plate 11 
 
 LAWI.OR'S Pilgrimages in the Pyrenees 24 
 
 LECKY'S History of European Morals 3 
 
 Rationalism 3 
 
 Leisure Hours in Town 9 
 
 LESLIE on Land Systems 1 
 
 Lessons of Middle Age 9 
 
 LETHEBYon Food 29 
 
 LEIVKS' History of Philosophy 4 
 
 LKVHS'S Letters 5 
 
 LIDDELL and SCOTT'S Greek- English Lexi- 
 con and Abridgment a 
 
 Life of Man Symbolised 16 
 
 Life of Margaret M. Hallahan 20 
 
 LlXDLEY and MOORE'S Treasury of Botany IS 
 
 LINDSAY'S Evidence for the Papacy 20 
 
 LOXGMAX'S Edward the Third a 
 
 Lectures on the History of Eng- 
 land ft 
 
 Chess Openings . 
 
 Lord's Prayer Illustrated 16 
 
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