This "gobemouche" was in its turn unhesitatingly accepted and devoured by our "instructors in the history of early printing and engraving," and afterwards retailed by them in turns for our improvement with a confidence which would have been charming had it any foundation whatever in fact. It is, however, now to be devoutly hoped that, inasmuch as we entirely owe to the light of St. Christopher's torch the discovery of the Venetian record, and its promotion from well-deserved neglect to a short-lived importance as an "his torical prize," so, from the moment that torch is extinguished, the boasted acquisition of 1441? will deservedly share the same fate, and thenceforth resume its former insignificance. It is undeniable, however, that on the faith of these two dates alone the majority of the systems" I have mentioned were attempted to be founded, and a superstructure erected thereon by the aid of such far-fetched absurdities as the fourteenth century town registers of "Augsburg," "Nuremberg," "Ulm," and "Nordlingen," supported by those phantom Formschneiders of unknown works, to whom credulity has given an ephemeral existence between 1398 and 1440. All this being advanced, let it be noted, solely upon the unsupported and more than suspicious statement of "C. G. Von Mürr," the greatest "literary charlatan" of his day; who, among the many notable things for which he was remarkable, obtained an European reputation by his wonderful "coffee trick"-which, for barefaced impudence, was never exceeded by the best performances of the "Wizard of the North," or any other of the "great conjurors" of our own day. 66 And yet this is the kind of evidence-this the species of genuine authority-which all writers on early engraving" have since been content not only to unhesitatingly accept as fact, but to frequently repeat and vouch for: backing it up, in the course of their works, with all the weight of their personal reputation; without one among them having ventured to give the public an assurance that he had satisfied himself, by personal inquiry and inspection, as to the truth of Von Murr's representations, or that they were in any degree worthy of reliance. The statements of that personage appearing to me to be inconsistent with common sense, I disbelieved, and subsequently, for sound reasons, altogether rejected them; and am amused, as well as surprised, that our guides to the "history of early engraving," both in England and abroad, have been so long and so completely deceived by him; and that they, nevertheless, indulge in the notion that to their dicta alone must we look, as the only pure source of information on the subject they have taken under their protection! Emboldened, however, by the statements of period probably anterior to the invention of book printing "a great many woodcuts of devotional subjects, of a by Gütenburg,' had been discovered in Germany," &c. Each and every of these allegations I now denounce as absolute fable; and I unhesitatingly challenge all writers upon the "history of early engraving and printing" to prove the affirmative of any or either of their before-mentioned declarations. Nay further, I state, without fear of well-founded contradiction, that the value of the date of the "St. Christopher" as a guide having now been destroyed, both art and literature absolutely remain without one tittle of fact, worthy the name of evidence, which can by any human possibility enable them to prove the barest exist1440"; or to identify a single individual with the ence of engraving on wood in Europe prior to exercise of that "trade," until they reach the name of "Michael Wohlgemuth" (1434-1519), to whom Albrecht Dürer was, on St Andrew's Day, 1486, duly apprenticed as a Formschneider. I here for the present leave the subject, to which I shall again have occasion to expressly refer in the course of my remarks upon "Early Printing, and the Block Books." HENRY F. HOLT. 6, King's Road, Clapham Park, Sept. 25, 1868. THE EARL OF OSSORY AND THE HON. CAPEL MOORE. I lately came into possession of a good many letters addressed to the Hon. Capel Moore (who, I see, was the son of Lord Drogheda, and married to Lady Mary Paulet). A few are from Charles Echlin (who was he?), and others, but the great majority are from the Earl of Ossory. They bear dates between 1730 and 1741, and are principally taken up with the gossip of the day; though there are several references to Swift, with whom Lord Ossory seems to have been on intimate terms. I transcribe one which (if never before published) will perhaps be interesting. I presume the Lord S- -h was Lord Scarborough: "DR. CAPY, "Caledon, Feby 20, 1739-40. "I had satt down to answer your first Letter just when I received your Second, not more than half an hour agoe. I write to Ld T. by this post, tho' the life that noble Lord leads is so different from my Ways of passing my time, that we have of late had little or no correspondence together. His LP loves the town, I love the country. His LP loves D-n, I hate it. His LP loves bad Wine, bad Women, and bad companions. I abhor them all. Let us but agree in our Freindship for you, and I'l yeild him superiour to me in every other taste in the World. "If your Son is in the Way of Preferment and out of the Way of Temptation, His present situation may one day be of advantage. At least it is all the comfort your hopefull circumstances will allow of. Let me hear from time to time when and where he goes. It is odd to send you news from hence; but I beleive the account I can give you of La Sh's death may be more full than any you have heard within the close limits of your confinement. His LP was going to be married to a Widowa Dutchess and a Grand-Daughter of Sarah Princess of Mindleheim, even to her Grace of Manchester. To this Lady, in the soft hours of betraying love, the ill-fated Earl told an Arcanum Jovis only known to his Maj-y, Sr R. W., and himself. The Lady, in the abhorrence of secrecy too natural to her sex, communicated the trust to her Granny, the Granny to P-y (?), and P―y to all the town. Upon this Sr R. W. complained to the King that no man could serve him whilst the secrets of his Closett [sic in original] were known and divulged. The Dutchess purged herself by oaths to the E., and the E. to the King. But having dined alone on the day he shott himself merely by chance, and want of finding some Freinds unengaged, he visited his mistress in the afternoon, and found by her discourse that she had divulg'd the mighty Resolutions of his Master, and given up his own honour, His Character, and his Fidelity into the hands of Queen Sarah, who lives as usual in open war against the State. When He had drawn from her the confession, his LP retir'd to his own House, and there in his Parlour shot himself in at the mouth with a small Pocket Pistoll lightly charged with Powder that the Report might not be heard, or the wound easily discovered; and He calculated the matter so justly that it answered his purpose, and left the Ball lodg'd in his brain. This last caution must have been to prevent the Verdict of Lunacy, which, however, was brought in by the C. Inquest upon a view of the Body. Of the present E. and his Countess I know no more than what the Newspapers inform us. The enclosed letter, for which I thank you, judges right of that Skeleton Master James, who seems to be one of the Sons of Fortune loaded with riches, and still empty enough to hold more. "At Caledon we live free from all cares, all uneasinesses, and all Dependance. What we have is our own, and a Letter now and then from a Freind makes some amends for the distance of our separation. We are all alone, and have been so ever since we came hither in September. For my own part I never was so happy in my Life. My Days are Days of Joy and Chearfulness, and the Pleasures of my Nights will I hope appear in due time; so you must excuse my Lady from writing to you yet awhile. She is most faithfully yours, Lady Mary's and Miss Moore's; so are all here, especially your cousin Brogh. "0." T. G. MATHEMATICAL BIBLIOGRAPHY.* By way of supplement or correction to former papers, I would say 1°. My reference to the margin of p. 262. of Barocius's Proclus (2nd S. ix. 340. col. 1, line 5) arose probably from a slip of the pen or a misprint. I had already (1st S. x. 48) given what seems to be the true reference (see 2nd S. ix. 449). 2o. I think that a mention of Eudemus occurs at p. 276 of vol. i. of Montucla (line 1.) and of Geminus at p. 11 of Dechales; and that it is supposed that Proclus was born A.D. 410 and Eutocius A.D. 550. 3o. Mr. POTTS (Eucl. p. vii) says that none of the writings of Theophrastus or Eudemus have been preserved (compare 2nd S. viii. 465); and that Geminus (see Eucl. p. xiii) is reported to have been the author of a work entitled 'Enarrationes Geometricæ which is not known to be extant. 4°. As to Sir Dudley Diggs [Digges?] see 2nd S. x. 218. 5°. Lagrange (Equations, 3rd ed. p. 123) cites Newton's Méthode des Fluxions (as to which see 2nd S. x. 233.) and also a "Méthode des suites infinies" of Newton (Equations, 3rd ed. p. 31). Perhaps in either case a reference to one and the same work is intended. 6°. From memorandums made some time ago and now before me I infer that at 2nd S. xii. 164. col. 2. I ought to have said that the "upright" of Ganesa corresponds (not with the "upright" but) with the "base" of Taylor; that the ibid" at 2nd S. xii. 517. col. 2. line 3 from the bottom should be replaced by a reference to Colebrooke, Alg. p. xlv and perhaps to As. Res. xii. 222.; that at line 15 of the following page and column the reference should be (not to p. xxvii but) to p. xxvi; that as to the information furnished by the astronomers of Ujjayani to Hunter I might also have referred to Colebrooke, Alg, p. vi; and that after mentioning Krishna Í might have said that Viswanatha was the author of astrological commentaries (ibid. p. xxvii). These last two supplementary remarks have reference to 2nd S. xii. 518. 7°. The ratio 7:22 gives (not 3.1422 as stated at 3rd S. i. 167 and 168. but) 3.142. As to some rather remarkable properties of numbers see the Mechanics' Magazine xlvi. 512 (where a property of the decimal expression for is treated of) and xlvii. 63. 8°. With respect to Garga and Parasara (2nd S. xii. 517.) if the views of the writer in No 2076 of the Athenæum (Aug. 10, '67, p. 168) be adopted the reputation that Garga was a priest of Krishnah (see Diary for 1862, 3, 4; and supra 2nd S. xii. 517.) must be regarded as an unfounded rumour. 9o. I am indebted to Miss Elizabeth Good for obtaining for me through Mr. Fennell from Mr. G. Weigle information of which I have already (2nd S. ii. 444.) availed myself. Some years ago Professor DE MORGAN showed me a number, which even then was not, so far • Continued from 3rd S. xi. 515. as I can remember, a recent one, of a little work called, I think, the Christian Missionary and wherein was contained a paper on Indian astronomy or science of which to the best of my recollection, Archdeacon PRATT is the author. The paper is a short one and I was desirous (if so permitted) of having it reprinted in "N. and Q." But I left England without having accomplished that object. The number in question had only been lent to Prof. DE MORGAN, so that I had but a cursory glance at it, and could not succeed in obtaining another copy, though I believe I tried so to do for the purpose of the reprinting. The Indian astronomical records, though not to be summarily thrown aside, should of course be subjected to proper scrutiny, and due allowance should be made for the inaccuracy of observers, the defects of their instruments and any uncertainty that there may be as to the position of the Indian asterisms or of the points or lines to which measurements are to be referred. Thus we know that Brahmegupta was wrong (I think to the extent of about half a degree of latitude) in the position which he assigned to his residence or native city. But perhaps it does not thence follow that we are to suppose that all earlier observations are necessarily affected with an error of like magnitude. There is reason to think that Indian science had culminated before the time of Brahmegupta and it is not easy to conceive how Aryabhatta could have estimated so correctly (see 3rd S. i. 168) the dimensions of the earth unless he had access to tolerably accurate observations. The conclusions of Davis as to the date of the Vedas have been confirmed not only by my own calculations but also by the inferences (ibid. 167) of Professor MAX MÜLLER which are based upon totally different grounds. More than seven years ago (during 1861) in a letter dated Nov. 30 and wherein he acknowledged a separate copy of my paper on Indian Chronology in the Diary for 1862 Prof. MAX MÜLLER kindly furnished me with important information. After a tribute to Colebrooke he observes "... A good deal has been done since his [Colebrooke's] time and I doubt whether he would still maintain the antiquity of the Jyotisha. That Compendium belongs to a period of Sanskrit literature later than the 3rd century B.C. The Surya Siddha'nta has been published complete with English translation and diagrams; and I have just received the last Essay of Biot's on the subject of the Nakshatras which he still maintains to be of Chinese origin. You find his articles in the Journal des Savants 1861; and 1860, p. 785. He had treated the same theory some ten years ago in the same Journal..." I am not aware whether Prof. MAX MULLER has since discussed the question of the Nakshatras but it must not be inferred from the above extract that he assigns to them a Chinese origin. Archdeacon PRATT has (Phil. Mag. S. iv. vol. 23, "An Appendix to the larger edition of Euclid's Elements of Geometry; containing additional Notes on the Elements, a short Tract on Transversals, and Hints for the solution of the problems, &c. By," &c. pp. 95. Quarto. Cambridge, eighteen-sixty two. TODHUNTER, I. "The Elements of Euclid for the use of Schools and Colleges; comprising the first six books and portions of the eleventh and twelfth books; with notes and an Appendix. By I. Todhunter." pp. xvi + 384. Duodecimo. London, eighteen-sixty four. POTTS, Robert. "The School Edition. Euclid's Elements of Geometry, The first six books and the portions of the eleventh and twelfth books read at Cambridge, .....; a series of questions on each book; and a selection. papers; with hints &c. By, &c. Corrected and Improved." pp. viii+410. Duodecimo. London, Eighteen-forty one. DAVIES, Thomas Stephens. Com "A Course of Mathematics. In two volumes. posed for the use of the Royal Military Academy. By Charles Hutton . . . Continued and amended by Olinthus Gregory..... Vol. I. Twelfth Edition, with considerable alterations and additions, by Thomas Stephens vi+536 pages. Davies..." Octavo. On the history of arithmetic reference is made (at p. 6) to Leslie, to Peacock, to a paper by Humboldt read before the Royal Academy of Berlin, of which a translation is said to be printed in the Journal of the Royal Institution vol. xxix; and to a paper in the Bath and Bristol Magazine for Oct. 1833 (No. viii) by Mr. Davies. The work itself contains many historical fragments, as on rules operations and tables (pp. 8. 37. 40. 59-61. 69. 73. 203-4. 224-6. 438. 475-7.), on the theory of numbers (p. 44), on instruments* and constructions (pp. 84. 379. 382-4. 388. 401-2. 509.), fractions (pp. 145-7) and numerous references to on other matters (pp. 195. 200. 526), on continued * On the derivation of the word Theodolite see Phil. Mag. S. 3. vol. xxviii. p. 287; vol. xxxvi. p. 292. and Mech. Mag. vol. xlv. p. 159. books (pp. 25. 53. 168-9. 171. 264. 274. 388. 394. 396. 430. 442. 511. 519. 525. 528). There are brief notes on ratio (p. 323) and on infinitesimals (p. 364). As to porisms (a subject to which Davies had paid great attention) see pp. 290 and 371. From a footnote at p. 210 we learn that Davies once had an intention of publishing Mr. Horner's works on Equations. At p. 220, footnote, speaking of the rule which in the text he calls the "rule of Harriot" Davies says "By the foreign writers this rule is always attributed to Descartes, and most English writers follow their example. There is, however, undeniable evidence that the rule was obtained indirectly by Descartes from Harriot; and it may be mentioned in support of this view, that Harriot gives a reason for the rule, while Descartes gives none." "On the other hand, it has been alleged that the failure of its generality in consequence of the existence of imaginary roots was not perceived by Harriot, and that there is no evidence that he was even acquainted with the existence of imaginary roots. It must however be replied that the Ars praxis Analytica was a posthumous work, edited by Warner, who does not appear to have fully understood Harriot's views, and who, therefore, thought he exercised a sound and kind discretion towards his friend in suppressing certain parts of the work; a suppression which we know did take place. We cannot, therefore, say more as to the views which Harriot entertained on this subject, till some of his papers, still in existence, are more completely examined than they have been. With respect, however, to his knowledge of imaginary roots we have sufficient proof that he understood their forms and their meaning too. In the Supplement to the works of Bradley, published by my estimable friend, the late Professor Rigaud, plate 5, will be seen a solution of the equation 1-aa=-2a+34, and the solutions are separately put down; viz. a=1+ √ −32 and a=1-√-32. Even this, were this all, would remove the imputation of his ignorance of the existence of imaginary roots." At p. 226 appears Budan's Criterion as arranged by Horner, and in a footnote it is observed As to Budan's Criterion, which seems to be a valuable practical rule, see further Lagrange, Eq., 3me ed., p. 165; Ladies' Diary for 1839, p. 71; Davies, Hutton, vol. i. p. 235 and Mech. Mag. vol. xlviii. p. 604. To the literature of Porisms Mr. T. T. WILKINSON has recently (Manchester Proceedings, vii. 68) made a contribution. In connection with the footnote at pp. 250-1 of Davies's Hutton (vol. i) I would refer to Garnier's Analyse, Chap. XVIII (2me ed. p. 365). Of Davies there are imperfect sketches in the Mech. Mag. (see vols. liv. p. 33 and Iv. p. 432) and in the Expositor. A description more in detail of his Speaking of the question of finding the root common to two equations M. SERRET says (p. 57) — "C'est précisément la question qu' Abel a résolue dans un Mémoire publié dans les Annales de Mathématiques de Gergonne, tome XVII, et qui ne fait pas partie du Recueil de ses œuvres complètes." Then follows a summary of Abel's analysis. Similar omissions may occur in the most valuable repertories, though it may be my own deficiency of memory or observation which leaves me under an impression that in Ellis's Report on Elliptic Functions no mention is made of Galois and that in Professor Smith's Report on Numbers (of which however I have not seen the latest part) no mention is made of Ivory in connection with the subject of primitive roots. At pp. 254-5 of vol. xlix of the Mech. Mag. there is a short paper of Boole on logic which is not I think included in the list that follows Mr. TоDHUNTER'S Preface to the Supplementary Volume of Boole's Differential Equations. I was about to add that Peacock does not mention Sturm, but Sturm's theorem I think was not published until 1835 (?) and after the Report was printed or prepared. A remark of Prof. DE MORGAN at the end of a set of papers in vol. i. of the Quarterly Journal (see pp. 1. 80. and 232.) induces me here to give a reference to Chap. XVII (p. 339) of Garnier's Analyse (2me ed.) where the process of Newton's parallelogram is given. The process has since been given by Mr. TODHUNTER (see p. 193 of his 'Equations'). I notice that at pp. 4. 165. 166. of M. SERRET'S Cours the name of Galois is spelt "Gallois" while at pp. vi. 349. 357. 366. 371. 560. 565. 569. 570. the correct spelling Galois is employed. I understand that there is a subsequent edition, which I It is in Note VI have not seen, of the Cours. (p. 465) of the 2nd ed. that M. MINDING's method, which gave rise to Prof. DE MORGAN'S papers, is expounded. Paris, eighteen-thirteen. LAGRANGE, J. L. Principes du Calcul différentiel, dégagés de toute conThéorie des Fonctions Analytiques, Contenant Les sidération d'infiniment petits, d'évanouissans, de limites et de fluxions, et réduits à l'analyse algebrique des quantités finies. Par J. L. Lagrange. Nouvelle Edition, revue et augmentée par l'Auteur." pp. xii +383. Quarto. Regard being had to the progress of recent research art. 66 (pp. 104-109) of this work is deeply interesting. In it Lagrange differentiates a cubic, treating the absolute term as the dependent variable, the other coefficients as constant and the root as the independent variable. He thus constructs a linear differential equation of the second order whereof the coefficients are rational and entire functions of the root involving five undetermined constants, the equation, moreover, not being assumed homogeneous. He then succeeds in giving the differential equation a form such that it admits of a first integral which is not only a linear equation with separated variables but is moreover of such a form that the root can be expressed explicitly and the cubic thus solved. The taking of the root as the independent variable may possibly limit the extent of Lagrange's process as well as give it a character widely diverse from that of the recent theory of differential resolvents but I have thought it well to call attention to this (so far as I am aware) little known solution of a cubic. In more remote connection with these resolvents pp. 92-100 (more particularly pp. 97-99) of Waring's Miscellanea Analytica may be found interesting. Waring gives quadratics and cubics of which the roots are the fluxions of the roots of other quadratics or cubics wherein the root (the ordinate) is the dependent variable and the coefficients are functions of the absciss, which is treated as the independent variable. Lagrange solves a cubic by means of a linear differential equation, but I doubt whether differential equations constructed on the model of Lagrange's could in general be strictly called resolvents. Their resolution would not lead to that of the algebraical equations whence they should be derived unless its form were such that by its means the independent variable (the root) could be expressed explicitly in terms of the dependent variable (the absolute term). From a memorandum which I am unable, for the present at least, to verify it would seem that Fourier (at p. 35 and perhaps elsewhere) in his Analyse mentions or employs the "parallelogram" process of Newton or some analogous process. D'Alembert too (see Lagrange, Eq., p. 172) availed himself of the parallelogram. Chief Justice COCKLE, F.R.S. "Oakwal" near Brisbane, Queensland, Australia, June 25, 1868. The text, however, is perfectly right, and the description most accurate. We must recollect that previous to the present century poets and other writers were not at all solicitous about suitableness and so forth. They gave the manners, the scenery, and everything else such as they had known them from their early days, without considering whether they were those or not of the country in which their works were published. Thus in the Vicar of Wakefield and the Deserted Village, the scenery and manners are almost always Irish, and in like manner we have in the Seasons the manners, scenery, and agricultural operations such as Thomson had witnessed them in his early days in his native Roxburghshire. His memory, by-the-way, sometimes betrayed him: thus his description of sheep-washing in "Summer" is not by any means so accurate as that in Dyer's beautiful, but neglected, Fleece. also when he says "Before the ripen'd field the reapers stand Autumn, v. 153, So we might infer that the women also reaped in Scotland. But it could not be so if the reaping was as in Ireland; for there their only part was to bind the sheaves, and they were of course fewer in number, and apart from the reapers. I have, however, heard that there is a mode of reaping in some parts of the North of Scotland in which the men and women work together in pairs, and it may have been this that the poet had in view. To return to white. At the time when wheat and other grain used to be sown broad-cast and in ridges, the seed was, I believe, carried in a basket in England, while in Scotland and Ireland the sower had a bed-sheet, which of course was white, fastened round his neck and shoulders, and forming a sinus in front held up by his left hand, which contained the seed. He therefore stalked along the furrows, with his steps always of equal length, and it really was wonderful how evenly a good sower scattered the seed. I have witnessed it hundreds of times, and can vouch for the perfect accuracy of every word in the poet's description. By the word harsh applied to the harrow is indicated the force and roughness, as it were, with which it crushed and pulverised the clods so as to cover in the seed. In "Spring" there is a remarkable instance of the error which I pointed out in one of Collins's Odes, in what I wrote on that subject in a former volume of "N. & Q."-the division of a paragraph. From "From the moist meadow," &c. (v. 87) to "The little trooping birds," &c. (v. 136), forms in reality only a single paragraph; while in all editions that I have seen, a new paragraph com |