FOR TRAVELLERS IN ITALY.

This Day, copiously illustrated with Coloured Plates and Woodcuts, 8vo., 21s. RICK AND MARBLE ARCHITECTURE IN ITALY. IN THE MIDDLE AGES: NOTES of a TOUR. By GEORGE EDMUND STREET, F. S. A., Architect.

JOHN MURRAY, Albemarle Street.

Second Edition, with large map, price 5s., cloth boards.

PRIZE ESSAY ON PORTU

By JOSEPH JAMES FORKESTER, of Oporto, F.R.G.S. of London, Paris, Berlin, &c., Author of "Original Surveys of the Port Wine Districts" of the "River Douro from the Ocean to the Spanish Frontier;" and of the "Geology of the Bed and Banks of the Douro;" also of a project for the improvement of the navigation of that river, and of various other works on Portugal.

JOHN WEALE, 59. High Holborn.

WESTMINSTER HOSPITAL,

Broad Sanctuary, opposite Westminster Abbey. The Westminster Hospital was instituted in the year 1719, and was the first of the kind in the United Kingdom established and supported by Voluntary Contributions. The principle of admission is based chiefly on the urgency and nature of the symptoms of the patient, and during the past year 1,123 accidents and urgent cases have been received as in-patients without letters of recommendation, while 14,381 out-patients have obtained medical or surgical assistance with no other claim than their sufferings. Patients are constantly received from distant districts; admission is also freely given to Foreigners who are ill and in distress; and relief is often afforded to patients who are sent as urgent cases by the clergy of all denominations. The number of patients admitted in 1854 was, in-patients 1,754, out-patients 19,545 total 21,299. The demands on the Hospital are annually increasing, while the income from all sources has seriously declined. Thus in 1854,

£ d. 8. 4667 2 10 6112 19

- 1445 16 4

These increasing demands on the Hospital may, to a certain extent, be explained by the increase of population. Three wards, affording accommodation for 42 patients, are still unfurnished and unoccupied; and to open these wards, and thus render the Hospital as efficient as originally designed, would require an increased income of 1500l. a year, besides the cost of fitting up the wards for the reception of the patients. Efforts are being made to increase the Hospital accommodation of the metropolis, but the duty is more imperative to make the accommodation already existing available. No new establishment is required, no additional officers, no increased buildings, but only means to receive and support in a long-tried establishment an increased number of the poor and destitute.

During the recent epidemic 170 cases of Asiatic cholera were admitted, and 104 of the number were restored to health and their families. 3496 cases of choleraic diarrhoea were also received, and, through prompt attention, the further progress of disease was prevented. The Committee earnestly APPEAL to the benevolent for AID, and trust that the extent and value of the medical and surgical relief afforded to the poor from all parts may cause assistance to be given to the funds of this, the oldest metropolitan Hospital supported by voluntary contributions.

Donations and Subscriptions are thankfully received by Messrs. Hoare & Co., 37. Fleet Street; by Messrs. Bouverie & Co., 11. Haymarket; by the Joint Treasurers, the Hon. Philip P. Bouverie and Peter R. Hoare, Esq.; or by the Secretary. F. J. WILSON, Sec.

"In days like these, when so many of our new books are but old ones newly dressed up, a work of original research, and for which the materials have been accumulated by the writer with great labour and diligence, deserves especial commendation. Of such a character is the Catholic History of England; its Rulers, Clergy, and Poor, before the Reformation, as described by the Monkish Historians,' by William Bernard MacCabe ; of which the third volume, extending from the reign of Edward the Martyr to the Norman Conquest, has just been published. The volumes bear evidence in every page that they are, as the author describes them, the results of the writing and research of many hoursthe only hours for many years that I had to spare from other and harder toils.' Himself a zealous and sincere follower of the 'ancient faith,' Mr. MacCabe's views of the characters and events of which he is treating naturally assume the colouring of his own mind; many, therefore, will dissent from them. None of his readers will, however, dissent from bestowing upon his work the praise of being carefully compiled and most originally written. None will deny the charm with which Mr. MacCabe has invested his History,' by his admirable mode of making the old monkish writers tell their own story."- Notes and Queries.

"Mr.MacCabe's mode of composition is as novel as his plan. Sacrificing ordinary literary pride, he makes the old Monkish writers compose the narrative-his ingenuity being displayed in the skill with which the passages, translated directly from the original, with all their natural vigour of language, are connected, so as to produce an appearance of oneness of design and continuity. He then fuses into one whole centuries of observation and narrative, and in fact revives those dead monks and scribes till they write his book. The plan is not only new, but it was necessary, as the reader will find if he compare the garbled and inaccurate version given by Hume and some other writers, with the original statements of the same events incorporated in these pages. He will also be better able to understand, when this universality of authorities is explained, why this book should be called a Catholic History.' The work is of great literary value." -Times.

"It treats the Anglo-Saxon period under a phase quite different from that in which it is viewed by Lingard in his Anglo-Saxon Antiquities. Lingard describes the doctrine and doctrinal practice of the age; the Catholic History tells the story of its inner life. Each, therefore, may be regarded as the complement of the other. Both are indispensable to every English historical collection." - Dublin Review.

T. C. NEWBY, Publisher, 30. Welbeck Street, Cavendish Square.

Now ready, Fifth Edition, price ls. cloth. (Postage Free.)

A WORD THE

or Hints on the Current Improprieties of Expression in Writing and Speaking. By PARRY GWYNNE.

"All who wish to mind their p's and q's, should consult this little volume."- Gentleman's Magazine.

GRANT & GRIFFITH, Corner of St. Paul's Churchyard.

Just published, with 4 Illustrations, price 1s. 6d.

PARARS. ALFRED GATTY, Author of

ARABLES from NATURE.

"The Fairy Godmothers."

"Pretty little tales with allegorical truths of infinite value, and the work is nicely illustrated."- English Journal of Education. London: BELL & DALDY, 186. Fleet Street.

THE

TORIES. Twelve Cantos, in Terza Rima. By RUTHER.

"This is a scholarly little book, sweet as a meadow at hay-time, and full of summer influences. We confess this little volume excites our curiosity; and as to the writer, the skill with which the metre is carried through, the almost immaculate correctness of the rhymes, and the equality of strength which pervades the whole, would indicate a poet of some standing, although the style resembles none that we remember. Really, an imitation of some of Crabbe's works becomes in his hands a poem as dainty and fanciful as the garden scenes of Queen Fiametta in the Decamerone.' -Athenæum.

ONG

12mo. cloth, price 4s. 6d.

N THE STUDY OF LANGUAGE: An Exposition of Tooke's Diversions of Purley. By CHARLES RICHARDSON, LL. D., Author of "A New Dictionary of the English Language."

"The judicious endeavour of a veteran philologist to extend the philosophical study of language by popularising Horne Tooke's Diversions of Purley.' Dr. Richardson has done good service to the study of language in this very judicious and compact recast, for the book is much more than an abridgment."-Spectator.

London: BELL & DALDY, 186. Fleet Street.

FOR

Page

- 117 118

Belgian Sports and Pastimes, by Henry Daveney

118

Thomas Tusser's Will, by G. Blencowe 119
Military Bands in the last Century, by
G. Blencowe
Monumental Brasses, by W. R. Crabbe

MINOR NOTES:-Reference - Summer
Climate of the Crimea - Simon Wad-
loe Astounding Geographical Facts
-Historical Parallels-Shakspeare
and his Descendants (?)-"Win of
ape

121

121

122

123

- 124

NOTICE, to which we beg the particular attention of our Subscribers. "NOTES AND QUERIES" has been registered for the transmission of its stamped copies through the Post-Office beyond the limits of the United Kingdom. Subscribers are reminded, that the stamp must be exposed, and the special postage (where required) must be prepaid. The special postage varies in amount: the rate may be ascertained at any post-office. The period during which stamped copies can circulate freely through the Post is extended from seven to fifteen days after date. Unstamped copies of NOTES AND QUERIES will pass at any time through the Post-Office to all places within the United Kingdom (including the London district), with a penny postage stamp affixed.

ATURDAY REVIEW of POLITICS, LITERATURE, SCIENCE, and ART.

This Publication will consist exclusively of original matter, or of news embodied in original comments; and it will thus be distinguished from all existing periodicals in several important respects. It will differ from the weekly newspapers in the exclusion of merely borrowed news, and from the purely literary journals in the admission of political discussion. It is intended that it shall address itself to the principal topics in the Political, Social, and Literary World, which will be impartially handled by competent writers, with that liberality and independence which educated and reflecting minds demand from those who assume to guide and represent public opinion.

The publication of the SATURDAY REVIEW is entrusted to MESSRS. JOHN W. PARKER & SON, West Strand, to whom all communications may be addressed.

Price Fourpence. Stamped Edition, 5d.

Just published, New and Cheaper Edition, price 1s.; or by Post for 13 stamps.

HE SCIENCE OF LIFE; or, THE

How to Live and What to Live for; with ample Rules for Diet, Regimen, and SelfManagement; together with instructions for securing health, longevity, and that sterling happiness only attainable through the judicious observance of a well-regulated course of life. By A PHYSICIAN.

London: PIPER, BROTHERS & CO., 23. Paternoster Row; HANNAY, 63. Oxford Street; MANN, 39. Cornhill; and all Booksellers.

Second Edition, with large map, price 5s., cloth boards.

PRIZE ESSAY ON PORTU

By JOSEPH JAMES FORKESTER, of Oporto, F.R.G.S. of London, Paris, Berlin, &c., Author of "Original Surveys of the Port Wine Districts;" of the "River Douro from the Ocean to the Spanish Frontier;" and of the "Geology of the Bed and Banks of the Douro;" also of a project for the improvement of the navigation of that river, and of various other works on Portugal. JOHN WEALE, 59. High Holborn.

It is proposed to complete the above Series in from Eight to Ten Parts, each Part containing Five or Six Photographs, in a neat cover, and accompanied by a sheet of descriptive Letterpress. Each Part will be complete in itself, and contain one or more of the Abbeys or Priories according to the extent or importance of the Ruins; at the same time the Series will form a complete whole. The Photographs are from negatives on glass, which gives a greater sharpness and clearness of outline than paper, and they will be found, on inspection, equal to anything of the kind offered to the public.

PART I., price 12s. 6d., contains Six Photographs of Fountains Abbey, viz.:

THE CLOISTERS: THE REFECTORY; THE CHOIR; BRIDGE OVER THE SKELL; GENERAL VIEW-SOUTHEAST; GENERAL VIEW-SOUTHWEST.

PART II., price 10s. 6d., containing Five Photographs of RIEVAULX ABBEY and KIRKHAM PRIORY; and

PART III., price 10s. 6d., containing Five Photographs of KIRKSTALL ABBEY, are nearly ready.

N.B.- The Photographs will be forwarded Free by Post to all parts of the United Kingdom All Communications addressed to WILLIAM PUMPHREY, Osbaldwick, near York, will meet with prompt attention.

LONDON, SATURDAY, AUGUST 18, 1855.

Notes.

ARITHMETICAL NOTES, NO. III.

I find among my books the fourth edition of Van Etten's Récréations (Vol. xi., pp. 459. 504. 516.), Paris, 1627, 8vo. Ät this rate the work started with yearly editions, so that it is odd that the edition of 1660 (Vol. xi., p. 459.) should only be called the fifth. By an old note I find that Brunet also attributes the authorship to Leurichon (Vol. xi., p. 516.). It appears that Henrion, said to have been the first French translator of Euclid, very soon took up these Récréations. This fourth edition is marked D. H. P. E. M., meaning Denis Henrion, Professeur ès Mathématiques, or Philosophe et Mathématicien. The earlier editions seem to contain some foolish things which do not appear in the English translations, and were probably struck out of later editions. For example, what would happen if the stars should fall? You will tell us, says the author, that we should catch plenty of larks, and the ancient Gauls used to say that this was the only thing of which they stood in awe. But if very great heat, or other adverse influence, should not interfere, a mathematician might venture to say that since the stars and the earth are round, a star would touch the earth only in a point, and then those who were not near that point would be in no danger, &c.

I had intended in the next number of these Notes, to give some little account of the work which really suggested these Récréations, a work of some importance in the history of mathematics. Claude Gaspar Bachet de Meziriac, the author (died 1638), an account of whom is given in the supplement to Moréri, and in Bayle, published several literary works, and two of a mathematical character. His edition of Diophantus, Paris, 1621, folio (Gr. Lat.), is the first print of the Greek text, and is beautifully printed, but loaded with those unfortunate contractions which in printing are no contractions at all. Bachet had accordingly been a reader of the manuscripts of Diophantus; and there is one account, if not more, of some of the manuscripts containing commentator's allusions to the Indian algebra, though it must also be said that these manuscripts have not since been found. I mention this because we shall presently see that Bachet produced and printed one of the most remarkable points of the Indian algebra, get it how he might.

The other work is the Problêmes plaisans et délectables qui se font par les nombres. This work was first published in 1612, when the author, according to the usual accounts, was only twenty years old. The same accounts state that he joined the Jesuits, intending to become a member of

their order, at twenty years old. Bayle, however, gives authority for his being the son of a first marriage, the second marriage being made in. 1586; and this is no doubt a more correct statement. The first edition of this work is not the remarkable one; there is a copy in the British Museum and both editions are rare.

The second edition (Lyons, 1624, 8vo.) has additions by the author. One of them is the remarkable piece of Indian algebra of which I have spoken. Algebraists call it the solution of indeterminate equations of the first degree. It is a method of answering such questions as the following: - In how many ways can a thousand pounds be paid in five-shilling pieces and sevenshilling pieces? How may all the ways be de- : tected by which one man may pay another thirteen shillings when the first has nothing but five-shilling pieces, and the second nothing but seven-shilling pieces? The mode in which Bachet proceeds is that which the Hindus call the Kuttaka, or pulverizer, and which the European algebraists now, connect with continued fractions. Hence this: work is, for Europe at least, an incunabulum of the theory of numbers. Whether Bachet was an original inventor cannot be directly ascertained. His title-page tells us that the work is partly derived and partly original. His method was announced, though not fully given, in the first edition, so that he possessed it before 1612. It is his only claim to great power of original discovery. The case then stands thus: A method is known in India, where it is at least as old as the Christian æra. In the sixteenth century Bombelli, whose sufficiency as evidence is well known, found in the Vatican library a manuscript of a certain Diophantus, with which he and another were so struck that they actually translated five books, intending to publish the whole. In [the notes to] this manuscript he and his comrade found frequent citations from Hindu writers, by which they learnt that algebra was in India before it was in Arabia. But this manuscript has never been found, though, on the other hand, the Vatican library contains a great deal which we do not know to have been closely examined. Add to this that of all the Hindu algebra, the method in question is the part which a commentator on Diophantus would have cited if he had known it. On the other hand, it would be very strange (though by no means without parallel) that Bombelli should have omitted to bring away and publish so remarkable a thing, if he had ever seen it. In the next century Bachet, who had resided at Rome, with the intention of editing Diophantus, which intention he fulfilled, and who was acquainted with the assertion of Bombelli, published this Indian method in a work which, according to himself, is partly derived from other writers; and did nothing else of the same note. This is the case as it now stands; possibly farther

research may settle the question whether or not the results of Indian algebra were in Europe in the sixteenth century.

This work of Bachet is the one which must have suggested the Récréations of Leurichon or Van Etten, and was itself probably suggested by the sort of questions with which Diophantus is filled. Both the French treatises are divided into questions of a numerical character, and others. Of some of these others I shall speak in a future communication. The numerical questions are mostly methods of finding a number thought of; and some are of the simplest character. In one of those of Van Etten, the person who thinks of the number is told to add and subtract any number he pleases, to add the results together, and to give the sum to the conjurer, who thereupon detects the number thought of. Such a puzzle, gravely printed by a learned Jesuit, is an excuse for the schoolboys who used to be much mystified by the following: The conjurer said, think of a number, double it, add twenty, halve the result, take away the number you first thought of—and then he astonished his auditor by adding, And there remains ten. A. DE MORGAN.

66 THE MENAGIANA."

The anecdote of Pontanus and Scriverius (ante, p. 7.) is in The Menagiana, 3rd edit., vol. i. p. 16. Whether a transfer like this is authorised by the laws of "N. & Q.," let the Editor decide. I may, however, be allowed to say, in defence of N. L. T., that other writers have borrowed from The Menagiana without acknowledgment, and among

them Jonathan Swift.

Those pleasant verses, which exhibit papersparing Pope and the deaf Dean in company without conversation, end thus :

"Of Sherlock thus, for preaching fam'd,
The sexton reason'd well,
And justly half the merit claim'd,
Because he rang the bell."

Is not this like Swift? But still more like
Menage.

"Un prédicateur avoit fait un excellent sermon, et quelques-uns de ses auditeurs ne pouvoient se lasser d'en admirer la beauté, tant du côté des pensées que de l'expression. Après s'être épuisez à le louer, le bedeau, qui les écoutoit, leur dit: Messieurs, c'est moi qui l'ai sonné.". Menagiana, ii. 65.

Swift bears the character of being one of our most original authors. Even Dr. Johnson, who, Boswell says, "seemed to have an unaccountable prejudice against Swift," allows him this merit. In his Life of the Dean, after quoting the opinion of a former editor, that Swift had never been known to take a single thought from any writer, ancient or modern, he says:

66

This is not literally true; but perhaps no writer can

Perhaps a short attempt to sketch the domestic sports and pastimes of the people of Belgium may not prove unacceptable to your readers. Those I have selected are, I am aware, trivial; but the sports of the Carnival, but too often tinctured with viciousness and vice, are of course well known to all, and varied to the whims and caprices of fertile inventions.

"St. Nicholas," Dec. 6. The children place empty baskets or basins in various parts of the mammas, who are expected to deposit therein a house, particularly in the bedrooms of papas and variety of sweetmeats, delicacies, or fruits; dependants and servants participate in the sport, ceptacle. This is followed by an excess of merriand no habitable apartment is left without a rement as the various utensils are produced with the welcome freight, and the remainder of the day is devoted to alloting and consuming the treasure found.

"St. Martin," November 11. This day is devoted by little urchins assembling in groups, blacking each others' faces, and tieing many coloured papers and ribbons about their persons; one of the gang, the hero of the fun, is very generally borne upon a rickety stool. In this manner they go from house to house, begging the very humble gratuity of a few apples, a donation very often made in kind, but more generally in cents or centimes.

"Half Vasten," March 26. The fun of this day very much resembles the scenes of St. Nicholas, but the ever-varying depository is placed upon the mantelpiece, wherein the donations are expected to be of the same description, but the fun and frolic is confined to the family.

"Onnoozele Kinderen," Innocents' Day, December 28. This is a day of positive misrule. Masters and mistresses are alike subjected to the dominion of the prevailing influence. The whereabouts of every schoolmaster and governess is keenly watched by the self-emancipated pupils