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a digression concerning hair-breadth escapes, and (however oddly it may feem to be introduced) a sketch of the antient history of Ireland; in which the Author hath shewn either a great deal of reading, or a great deal of invention, or both together : but, to return to his journey.

After paffing and re-passing fuch horrible heights, and dismal descents, as were enough to have frighted not only Mr.' Buncle, but Mr. Belzebub himfelf, out of his wits, he arrives at a pretty hermitage, in an open plain, like a ring, and go{ing up to it, found the skeleton of a man. He lay on a

couch, in an inward room, without any covering, and the « bones were as clean and white, as if they had come from

the surgeon's hands. The pismires, to be sure, had eaten off the desh, Who the man was, a paper lying on the table, in a strong box, informed me. It was called the case of

John Orton. A copy of this paper follows; and it contains the history of the life of said Orton: who, according to this his own account, had been a most profligate, abandoned fel. low: but being converted by a sort of miracle, had retired to this out-of-the-way place, to spend the rest of his days in solitary penitence, and to add one wonder to the list of the many Itrange ones which Mr. Buncle was to meet with among the hills of Stanmore.

Our Author was so affected with this adventure, that he began to entertain thoughts of ending his days also in this folitary place. Accordingly, having, fans ceremonie, taken poffeffion of all the goods and chattels of the late Mr. Orton, of which an exact inventory is given, he falls to planning his scheme of life, and a most romantic and pretty one it is: but for the particulars, we refer to his book. One thing, how. : ever, muft not be paffed over, as it cannot fail to make the Reader smile. Mr. Buncle, it seems, thought it incumbent upon him (being fo well paid for it, by making himself heir to the deceased) to bestow a decent interment on the bones of Mr. Orton ;-all but the fkull: " which,' says he, • I kept, 6 and still keep, on my table, for a memento mori; and that I « may never forget the good lesson which the Percipient, who ! once resided in it, had given. It is often the subject of my ( meditation. When I am alone of an evening, in my closet, 4 which is often my case, I have the skull of John Orton be& fore me, and as I smoke a philosophic pipe, with my eyes 6 fastened on it, I learn more from the folemm object, than I

could from the moft philosophical and laboured speculations. What a wild and hot head once: how cold and still now; poor skull, I say, and what was the end of all thy daring

fro

frolics and gambols--thy licentiousness and impiety ?--A fe

vere and bitter repentance. In piety and goodness, John Or«ton found at last that happiness the world could not give « him. There is no real felicity for man, but in reforming < all his errors and vices, and entering upon a strict and con« ftant course of virtue. This only makes life comfortable;

renders death serene and peaceful; and secures eternal joy 6 and blessedness hereafter. Such are the lessons I extract from 6. the full of John Orton.'

: For the manner of our Author's quitting Orton's hermitage; his meeting with a wonderful cave; his falling in with a lo ciety of philofophers, in the wilds of Stanmore; his curious microscopical observations; his account of several uncommon books; his ascent through the inside of a mountain, from the bottom to the top; his arrival and extraordinary entertainment at Mr. Harcourt's; his working the Athanafians, in a flaming discourse concerning religion, delivered to Miss Harcourt; his fine account of that extraordinary young lady; his return to the philofophical society, by 'a strange and dangerous way; the odd manner of his stumbling upon the dwelling of his friend Mr. Turner; with an hundred other notable adventures, till his accidental meeting again with Miss Melmoth, and marriage with that peerless beauty ;--for all these we refer to the book: of which, however, we must not take leave, without giving one other short extract from it. We have, in our accounts of this volume, and of the Memoirs of several Ladies, presented our Readers with a sketch of this Author's character and performances, as a Divine, Philofopher, Poet, and Knight-errant; but we have not yet brought them acquainted with his capacity as a Mathematician. For fpecimen, however, of his talent in this branch of learning, we fhall add the following new method of drawing tangents to curves, as it is much more concise than the common way.

• Suppofe BD E the curve, BC the abcissa = x, CD the ordinate =), A B the fubtangent line t, and the nature of the curve be such, that the greatest power of y ordinate be on

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one side of the equation; then y} =-*3-**+*y, a 3 ta ay saa x ta xx

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but if the greatest power of y be wanting, the terms must be put = 0.

• Then make a fraction and numerator ; the numerator, by taking all the terms, wherein the known quantity is, with all their signs; and if the known quantity be of one dimension, to prefix unity, and of two, 2, if of three, 3, and you will have 3a3+ 2.a ay -2 aa x taxx- - ay ý :

• The fraction, by affuming the terms wherein the abscissa x occurs, and retaining the signs, and if the quantity * be of one dimension, to prefix unity, as above, etc, etc; and then it will

3* - 2 xxy + xyy- a a x + 2 a xx: then diminith each of these by x, and the denominator will be - 3*.*

2 x y tyy aa + 2 6.%. • This fraction is equal to A B, and therefore + is — 323 + 2 aayı 2 aastax*—ayy

3** - 2xy + ymaat 2 a x. • In this easy way may the tangents of all geometrical curves be exhibited ; and I add, by the same method, if you are skilful, may the tangents of infinite mechanical curves be determined.

We have extracted the above method of our Author's, not only as a specimen of his mathematical talents, but as it may be of use to those who are not well acquainted with the doctrine of fuxions; such, however, who have made fome progress in that noble branch of science, may possibly prefer the following very concise and easy rule.

Find the Auxionary value of the abscissa from the equation expresfing the nature of the curve: multiply this Auxionary value by y the ordinates, and divide this last product by j, the Auxion of the fame ordinate. Or, which is the same thing, in the room of y, in the fluxionary value of the subtangent, substitute the fluent itself, and the result, in either case, will be the value of the fubtangent in the terms of the first given equation.

At the end of this book is an advertisement, concerning a fecond volume of Mr. Buncle's life; which we shall be glad to see, whenever the ingenious writer shall think fit to publish it; for though he may be, as himself candidly intimates, Preface, p. ix. somewhat of an odd man, he is nevertheless a respectable man. Whatever are his imperfections, his whims, and peculiarities, as an Author, this will, perhaps, be found incontestible, viz. That he is master of a vast compass of literary knowlege; that his learning is very considerable; his invention prodigious; his imagination, for the most part, grand and elevated ; his stile and spirit, free and manly; and his design, throughout his whole performance, benevolent towards men, and pious towards God. In fine, as he is truly original in all things, inimitable in fome, and despicable in none; so his very faults seem to be only the deviations of a great genius, a little warped,

Travels through Germany, Bohemia, Hungary, Switzerland,

Italy, and Lorrain, &c. By John George, Keysler, F.R.S. &c. Vol. IId. 4to. 125. Linde.

I

N our Number for May laft, we gave a view of the first

volume of this valuable work; to which we prefixed a short account of Mr. Keyfler, its learned and judicious Author :-a further mention of whom may now be added, from the English Editor's Preface to the whole.

This worthy German, we find, was born in 1689, at Thurnau, a town belonging to the Counts of Giech. His father, who was of the Count de Giech's Council, took extraordinary care of his education. His early years were not idly spent in the usual diffipations of youth; on the contrary, he was so well fixed in the principles of religion, that he never was carried away by the torrent of Libertinism, or tainted by the prevalence of custom, or fashion. His inclination for learning was visible very early, and he received his first instrưctions under the best masters that could be procured. When at the univerfity of Hall, he grew fond of the Civil Law; but was not so attached to it, as to neglect the Latin, Greek, and Hebrew Languages, History, Antiquities, and, in fine, the whole circle of the Sciences.

Mr. Keysler's abilities were soon distinguished ; and, on his leaving the university, an honourable field was opened to him, for the exercise of his talents, in quality of Preceptor to the two young Counts of Giech-Buchau; with whom, in 1713, he returned to Hall; and afterwards attended them in their travels; and nothing could have happened more agreeable to Mr. Keyller's inclination of knowing the world from his own experience.

The first place of note they visited, was Utrecht; where Mr. Keyfler contracted an intimate acquaintance with the learned Profeffor Reland; who persuaded him to put in execution à design, of which he had before entertained fome thoughts, viz, the writing an accurate History of the Antiquities of his own country.

Leaving Leaving Utrecht, Mr. Keyfler attended his young Pupils through the chief cities of Germany, France, and the Ne therlands; and, wherever he came, he failed not to gain fome literary acquisition; and he always bestowed his attention on such objects; as not only made him the wiser, but the better man. His acquaintance with books was of confiderable advantage to him, in visiting public and private libraries, and focieties of learned men. Bandolet, Montfaucon, and other celebrated persons in France, departing from their prejudices against the Germans, heartily joined in friendship with a man, of whose abilities, particularly as an Antiquarian, they had entertained the highest opinion, grounded on full experience of the excellence to which he had attained, in that branch of science.

On his return with his Pupils, so high an idea was conceived of his qualifications for such an important truft, and he was spoken of, in such honourable terms, to Baron Bernftorf, First Minister 10 his Britannic Majesty, as Elector of Brunswic-Lunenburg, that this Nobleman gladly committed to him the education of his grandson, a youth of the greatest hopes, and the happy, consequences have thewn, that no person could have been more worthy of the Baron's choice. His talent of insinuating himfelf into the affections of young persons of quality, and reftraining their natural impetuosity, and love of pleasure, by delicate remonftrances, delivered with great mildness and cordiality, appeared with the greater ad, vantage, as proceeding from a mind, actuated by virtue, and undiffembled religion, and a singular disinterestedness in the discharge of his duty. These were the laudable means by which he lo establithed himself in the favour of this noble family, that the two brothers, one of whom is Gentle man of the Bed-chamber to the King of Denmark, and the other, the present Baron Bernstorf, rewarded this worthy guide of their youth, with extraordinary liberality; the fruits of which he enjoyed to the day of his death.

In 1718, Mr. Keyfler made a voyage to England; to which, whatever other commissions he might execute, he gave

the appearance of a philosophical journey; and the same free access to learned societies, by which he had reaped fuch great advantages in France, and the Low Countries, render, ed London and Oxford highly agreeable to him. A signal proof of the esteem he acquired in England, is, that he was unanimously chosen a Member of the Royal Society; an ho. nour which he particularly owed to a learned Effay De Dea Nehalennia numine veterum Walachrorum topica : in which

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