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the beginning, immersion, and emersion of several spots, and the end were observed, and the times of the phenomena respectively determined. -os Of the solar eclipse the begin. ning and end were seen, and the times noted by Dr. Cutler, and two other gentlemen, who observed in company with him.

XV. On the extraction of roots. By Benjamin West, Esq. F.A..A. The author's design in this performance we shall give in his own words. “What I chiefly aimed at was, to render the method of extracting the roots of the odd powers easier, and less burthensome to the memory; and, I think, I have not failed in my attempt. The method, followed by Ward, and others, is excellent, but is attended with too much difficulty in getting the divisors; especially for learners, who are not acquainted with the reason of the rules. That difficulty I have striven to remedy in the following work.” Dr. West here gives the investigation and exemplification of rules for extracting the third, fifth, and seventh roots ; and observes, that similar methods may be found for extracting the roots of the even powers, and that he has not met with an instance, where the approximation is not as rapid by his rules, as by those of Ward. It may be seen by looking into Ward's Algebra, in his “Young Mathematician's Guide,” that in the process of forming theorems for extracting the roots of simple or pure powers, the equation immediately preceding each theorem is of the affected quadratick kind, e representing the part of the root to be found or the unknown quantity. But instead of solving this equation in the usual manner, and

thus obtaining a rule for finding the remainder of the root, the author deduced his theorem by making the unknown quantity itself a part of the divisor. Hence arises the difficulty, which learners experience in finding the divisors in this method. The excess of this difficulty above the degree of it, which belongs to the common method of extracting the square root, Dr. West, we think, has avoided in his rules, which he obtained, as an algebraist will readily perceive, by a process differing from that of Ward in the solution of the aforesaid equations, which are treated as affected quadratick equations.

In a similar manner a general theorem for the extraction of roots may be investigated, from which these and other particular rules are easily deduced by only substituting particular for general and distinguishing quantities. But the general rule of approximation for the extraction of roots, which we prefer to any that we have seen, was discovered by Dr. Hutton, and is in his arithmetick, and in the Mathematical Text-Book, used in the University.

XVI. A new and concise method of comfuting interest at six fier cent. her annum. By Philomath.

This memoir contains two concise rules for computing the interest of any principal, expressed in pounds and parts of a pound, for any time, expressed in months and parts of a month, at the rate of 6 per centum. They are obtained by contracting the operation for finding the answer to a single example, stated in compound proportion. The conclusions however depend on general principles, and their truth is sufficiently apparent. These rules are not given as new discoveries, but probably with a view to extend the knowledge of them, and to shew their truth. And to facilitate their application tables of decimal parts of a pound and of a month, with the manner of deducing the interest at any other rate from that at 6 per cent. are annexed.

XVII. Several ways of determining what sum is to be insured on an adventure, that the whole interest may be covered. By Mercator.

Three methods are here given. The first is said to be most common. It is therefore probable, that the last is less extensively known. For we think no person, acquainted with this, would ever make use of that. To extend the knowledge of the last method, and to

show its advantage relatively to the

others by comparison we suppose to have been the object of the communication. To be continued,

ART. 4.

Joetters from Eurofle, during a tour through Switzerland and Italy, in the years 1801 and 1802, by a Mative of Pennsylvania. Philadelphia, 1805, Bartram. 2 vols, 8vo. Price $6,50.

EveRy traveller, when he breaks from the comforts of his own home, and is beginning to estrange himself from the blessings and habits of his country, creates himself, at once, a kind of hero of adventure, His fancy is chivalrous in its wanderings, and is already blazoning in the tilts and tournaments of the sublime assions of men. He rushes, with all the impetuosity of vain enterprise, into the romance of life, be

cause every thing is new, strange, and confused. All his former anxieties, duties, and habits he leaves at the sill of his own door, and, as he departs from it into distance, he amuses the weariness of his many footsteps with the new motion of physical change, and enlivens the solitude of his mind with the strange operations of moral alteration. That our author is eminently of this character and spirit, we shall have occasion to show hereafter. The book is two stout volumes, anonymous in the title page ; but we find that vanity gets the better of the author's prudence, and he grows so charmed with himself, that he cannot help hinting to the eager world, in the second volume, who he is. It is dedicated to a Mr. Hamilton, “ of the woodlands,” partly on account of his “ liberal application to horticulture.” No book was ever less wanted,than the Pennsylvanian's, and none ever deserved type and paper less. But hear his reason for publishing; “he is the first American,who ever wrote his travels.” His columbianisms are sufficient credentials to prove to us whence he came, and whither he is going. “Debemur nos nostraque morti.” We will now perform a little of our itinerant duty with our literary traveller. We should not be able to follow him in very close succession, however, if the path had not been so well trodden before him, for his own track is so faint, that we are half the time out of sight of our guide. The Pennsylvanian begins now to show himself the hero we described. He drives off full tilt along the gay “ Boulevards de Paris,” and in his erratick ardour he declares to us, that “he happily missed running over any body in the Rue St. Dennis, or on the Pont neuf ;” and he rattles the reader to Basil, though distant from Paris some hundred miles, in the hurry of one short letter. From Basil he proceeds to Zurich, and from Zurich to Berne. Though Berne is the capital of all the Swiss cantons, and has so much to interest the traveller, our author has not said a word on the peculiar neatness and style of this city, nor even informed us, whether the French, or German language is spoken here. He says nothing of the cathedral, which is the most imposing and solemn Gothick pile in Europe; nor of the western part of the city, which hangs so strangely so many hundred feet over the rushing torrent of the Aar. The following paragraph contains every word, our

author says of Berne. “The next

morning we rose with the lark, before the easy cits had left their beds, breakfasted on the banks of the Aar on a loaf of bread and bottle of wine, and brandishing our oaken staffs went on again with fresh spirits for Thun.” We next find our guide at Altorf, the capital of the canton of Uri, situated nearly on the Lake of the four cantons. The next objects of grandeur in Swisserland, to the Alps, surround this lake. Mr. S. has passed it, and passed it without observation. Its borders are the extent of the sublimest scenery. The imaginations is here under a new and strange operation of nature. It sometimes rises to sublimity on the wild surfaces of its eternal mountains, whose frozen summits stand steadfastly in the heavens, and glitter with a faint and distant light, which has yet to reach our sight; and it sometimes sinks to the profoundest horrour, in the deep and dark vallies, which stretch

beneath. It was in these solemn and silent recesses of nature, that the Swiss heroes held their secret revolutionary meetings for the freedom of their country. It was along these cliffs and glens, that the wild Tell leapt after the thin and fleeting form of liberty. The reader is now carried through the picturesque valley of Schoellenen, without knowing it ; and he is transported over the stupendous mountain of St. Gothard by the most turgid swell of conceited description. Those, who have not experienced the hardships and terrours of the Alpine regions, will know nothing of them in the heroicks of the Pennsylvanian, though he may feel them in the lines of Pope.

At first the towering Alps we try, Mount o'er the rocks, and seem to tread the sky, Th’ eternal snows appear already past, And the first clouds and mountains seem the last; But these attained, we tremble to survey The growing labours of the length'ned way; Th’ increasing prospect tires our lab'ring eyes, Hills pecp o'ci hills, and Alps on Alps arise.

We now leave these sublime altitudes, where we have overlooked the world, and descend from that cold elevation, where we forcibly felt our proximity to the other planets, to the smooth surface of the lake Maggiore, and the still plains of Lombardy, “ diis patriis Italoque calo.”

The writer's first letter on Italy (Let. 6) begins with the different modes ef travelling in that country, by voiture, (better known there by the name of vetturino) brocache, and post. He does not approve of travelling by post, which is indeed the only mode, by which a gentleman can travel with any convenience or advantage in this country, on account of “being obliged to travel with a lacquey,” or in other words, with a courier avant. This, however, is not the case; for, if travellers do not speak Italian, they can generally make themselves current, in any part of Italy, with a very moderate share of the French language.

We have now to pass through the old states of Milan, Lodi, Parma,Modena, and Bologna, then united under the futile title of the CisalpineRepublick,and since denominated the kingdom of Italy. But of the Tolitical changes and oppressions of these dukedoms he says nothing, and the reader is not even informed, that, by the articles signed by Melas after the victory of Marengo, Buonaparte was admitted to Milan with triumphal entry, and placed over the whole of subjugated Lombardy (excepting the Venetian state) from the Alps to the Appenines, and from the Adriatick to the Mediterranean.

We now meet our guide at Florence, and our curiosity is highly excited to have all the interesting objects of “Firenze labella,” pointed out to us. We regret, that the limits of a review preclude our filling up the deficiencies of our author's letter on this city. How cold and stupid must he be, who has gazed on the figures of “Day and .Wight,” and of “ Morning and Fvening Twilight;" resting on the tombs of Julio and Lorenzo of Medici, not to mention more than their mere names and place; who could view these, without beholding the splendour of Day breaking from a body of marble, or without feeling his whole soul overshadowed with the thick and impenetrable darkness of Wight : or who would not perceive his sight was dimmed, and that light was mysteriously stealing away from every surrounding object, in the effect of the figures of Twilight ! These are the powers of a genius so bright, so mysterious,

and so dark, as that of Michaef Angelo 1 In his letter on Florence, our author has said little of this intellectual prodigy ; little of the bright Gallileo ; nothing of the intricate Machiavelli; & nothing of the dark spirit of Dante, who declares to us, he will often make holy visitations on the still banks of the Arno. We think also, as our author is an American, (and, “for that reason,” troubles his countrymen with his travels) he might have done more, than merely to mention the name of Americus Vespucius, and tho’ no "sarcophagus, proudly fretted with the history of his enterprises, contains his bones, still he ought to have entered the church of Santa Bourgona, where, on a rough tombstone, is this incription : S. Amerigo Vespucio suisque amicis, XXXIII.

Mr. S. here speaks of that

strange order of men, who seem to have descended from the ancient Troubadours, and who call themselves Imsirovisatori, and quotes Dr. Moore upon them ; but as neither the l]octor, nor himself, has given a specimen of their powers of imfiromfitu, we will subjoin. the following courteous address.

Di Bartolo, e di Baldo, Illustre figlio,
Colmo di zel, di probita, di onore
Alla tua patria accresci un gran splendore.

Ampio di mente, e multo piu di core.
Non ti pone in sgomento alcun pen 'glio,
E di prospera sorte ogni favore
Recevi ognor senza in arcasi il Ciglio.

Of the Florentine Gallery, tho’ instituted by Cosmo, finished by Lorenzo, and protected by the succeeding families of the Medici, our author gives no history. Of its splendid treasures he does not think much, though still among them are the beautiful antiques of the young Apollo; the head of Alexander, sighing after other worlds to conquer; and the Roman slave,

1.ETTERs from £URoPE,

who is still listening. Among thc pictures, are the Holy Family of Corrigeo, the young St. John of Raphael, a Maddalena of Guido, and the Venus of Titian. These are mentioned by Mr. S. merely as articles in his hotch-potch catalogue. As the corridors of this gallery are replete with chronological specimens of the fine arts, and as its saloons contain still so many exquisite pieces of the classical painters, we would recommend the reader to consult “Saggio Istoria della Galleria di Firenze,” 8vo. 2 vols. and a more modern description in French, printed at Florence, 1804. •. We leave Florence for Siena, and though the country to this city is so picturesque, we hear nothing of it. At Siena, our traveller “staid, while his horses were feeding,” and makes not an observation, except this very sensible one, the athedral has a linsey-woolsey asfearance.” He now passes along the still and retired regions of Balsena and Montipascone, without a single remark, though the poet here recommended so strongly, this pleasant and sweet retreat from the cookshops, and noise, and dust of the city. * Site grata quies, et primam somnus in horam, Delectat, site pulvis, strepitusque rotarum, $i laedit caupona, Ferentinums ire jubebo.” Horat. We are now in the ancient capital of the world, and seem forever to have lost our guide among ruined temples and falling monuments. We sometimes see him leaning against a tottering column, and sometimes catch him gliding through the broken arches of huge aqueducts ; and so do we the lean and cold-blooded priest, or the fat and sweltering capuchin. Here

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again is the same fulsome inflation of the writer’s style ; and because his subject is more sublime, he thinks he must become more turgid. It will be too fatiguing to us, and too uninteresting to our readers, to trace the heavy and Gothick feet of our author through the solemn and dark ruins of imperial Rome. We will not profane its deep gloom and awful assemblage of stupendous objects, by here holding communion with him. Of St. Peter's he has said much, and much incorrectly. In his history of it, he asserts, that it was three hundred years in building ; it was but one hundred and six. Instead of its being begun in 1450, in the time of pope Nicholas fifth, it was commenced under Julio second, in 1506, by Bramante, on the spot where the first christian church was built by Constantine. Bramante, in the sublimity of his genius, so projected St. Peter's, that the most perfect of the ancient temples, the pantheon, could be sustained by this solid superstructure of christian faith. That is, that the dimensions of this cathedral should be proportionable to the dimensions of the pantheon jor its dome. But the lines of Bramante, being reduced by the succeeding artichects of St. Peter's, the dome was consequently reduced a few

feet in diameter, and in 1588 Do

menico Fontana hung this bright hemissisiere over that world of architectural beauties. The colonmade, which was afterwards added, (and which our author calls a “sweeping forest of 300 columns,”) is the splendid work of Bernini. We must now confess, that we have no sympathy in a single description of Mr. S. at Rome, and we can remain with him there no

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