the beginning, immersion, and emersion of several spots, and the end were observed, and the times of the phenomena respectively determined. Of the solar eclipse the beginning and end were seen, and the times noted by Dr. Cutler, and two other gentlemen, who observe ed 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 at tended 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 inves tigation 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 ap, proximation 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 a voided in his rules, which he ob tained, 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 distin gulshing quantities. But the gen eral 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 Math emutical Text-Book, used in the University. XVI. A new and concise method of computing interest at six per cent. per annum. By Philomath. This memoir contains two con、 cise 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 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 dis tance, 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 au thor 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 that he cannot help hinting to the grows so charmed with himself, 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,wl.o 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 litera ry 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 de◄ scribed. 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 beneath. It was in these solemn The reader is now carried through the picturesque valley of Schellenen, without knowing it; and he is transported over the stu pendous 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. 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 At first the towering Alps we try, And the first clouds and mountains seem the last We now leave these sublime altitudes, where we have over looked the world, and descend from that cold elevation, where we forcibly felt our proximity to the other planets, to the smooth sur face of the lake Maggiore, and the still plains of Lombardy, "diis patriis Italoque cælo." The writer's first letter on Italy (Let. 6) begins with the different modes of travelling in that coun try, 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, 88 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 mod erate 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 Cisalpine Republick,and since denominated the kingdom of Italy. But of the political changes and oppressions of these dukedoms he says nothing, and the reader is not even in formed, that, by the articles sign ed by Melas after the victory of Marengo, Buonaparte was admitted to Milan with triumphal entry, and placed over the whole of subjugated Lombardy (except ing the Venetian state) from the Alps to the Appenines, and from the Adriatick to the Mediterranean. and so dark, as that of Michael Angelo! In his letter on Florence, our au thor has said little of this intellec tual prodigy; little of the bright Machiavelli; & nothing of the dark Gallileo; nothing of the intricate spirit of Dante, who declares to us, he will often make holy visitations on the still banks of the Arno. American, (and," for that reason," We think also, as our author is an troubles his countrymen with his travels) he might have done more, than merely to mention the name of Americus Vespucius, and tho' with the history of his enterprises, no sarcophagus, proudly fretted contains his bones, still he ought to have entered the church of Santombstone, is this incription : ta Bourgona, where, on a rough S. Amerigo Vespucio suisque amicis, XXXIII. Mr. S. here speaks of that to have descended from the ancient strange order of men, who seem Troubadours, and who call themselves Improvisatori, and quotes Dr. Moore upon them; but as neither the Doctor, nor himself, has given a specimen of their pow Di Bartolo, e di Baldo, illustre figlio, We now meet our guide at Florence, and our curiosity is highly excited to have all the interesting objects of "Firenze la bella," 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 "Dayers of impromptu, we will subjoin and Night," and of " Morning and the following courteous address. Evening 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 behold. ing the splendour of Day breaking from a body of marble, or without feeling his whole soul overshadowed with the thick and impenetrable darkness of Night; 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, instituted by Cosmo, finished by Of the Florentine Gallery, tho❜ ceeding families of the Medici, our Lorenzo, and protected by the sucauthor 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, who is still listening. Among the 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 Cathedral has a linsey-woolsey appearance." 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. * Si te grata quies, et primam somnus in horam, Delectat, si te pulvis, strepitusque rotarum, Si lædit caupona, Ferentinum ire jubebo." Horat. We are now in the ancient сарital of the world, and seem forever to have lost our guide among ruined temples and falling monu ments. 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 This was an ancient town, situated between Montefioscone and Viterbo. Vol. III. No. 2. M again is the same fulsome inflation of the writer's style; and because his subject is more sublime, he thinks he must become more tur gid. 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 an cient 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 for its dome. But the lines of Bramante, bea ing reduced by the succeeding ar tichects of St. Peter's, the dome feet in diameter, and in 1588 Do was consequently reduced a few menico Fontana hung this bright hemisphere over that world of ar chitectural beauties. The colon nade, 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 |