escape now, when to all my other faults are added, so many outrages in Geography? With what triumph of critical fagacity will they fay, (after the neceffary ftrictures on the ftory, thoughts, and verfes)" If our Author was determined to fend her Pegafus into Spain, in queft of adventures, the ought to have confulted Salmon about the fituation of its provinces. She would there have found that Arragon is fifty miles from the fea; and that the Moors could not poffibly have debarked on its confines, unless, like fith to the London markets, their fleet had arrived by land-carriage. With equal facility, the troops of the King of Leon are brought across Old Caftile to Saragoffa in about thirty hours-another miracle; which was doubtlefs accomplished by the interpofition of a friendly necromancer, who furnished the army with wings, in exchange for fome chafte damfel, or beautiful princefs. Had this Lady-Writer's reading extended to a tranflation of the Iliad, fhe would have found no examples of fuch liberties there. Homer gives an exact map of the countries he carries us through; and from Ithaca to Troy not a village or river is mifplaced.' True: but Homer (I name him as a modern painter mentions a Corregio, and a Raphael) Homer united the Historian with the PoetI deal entirely in fiction. It was enough for me, that Spain, through a fucceffion of ages, had been fubject to the ravages of Africa; and that during this period, fovereigns had been robbed of their crowns, and been obliged to refign their fceptres to their fwarthy conquerors, The relation of the particular events of these remote times, the Hiftoric Mufe has generally left to her creative Sifter, who never fails to profit by their obfcurity, in relating them to the world in her own manner; the geography of the heart, and the hiftory of the paffions, are the only realities to which the attends. If, in defcribing these, I fhall be found deviating from the laws of Truth and Nature, I shall have failed in my intention; but I protett, if the cacoëthes fcribendi fhould continue on me, or if I should ever wander again into the regions of Romance, I fhall treat oceans and provinces with as little ceremony as rivulets and meadows: I will avail myself of the eftablished privileges, and raife mountains, feas, or kingdoms, in any part of the habitable globe that hits my fancy; or, if it ftrikes me, brild a temple to Duinefs-in the chamber of a Reviewer.' This Deprecation was evidently written in the hour of infolence and vanity-probably juft after the treasurer of the theatre had humbly offered the balance of three benefit-nights of The Belles Stratagem, a new comedy, which has, we hear, been attended with great profit to the ftage, and to the Writer-" Nothing to confole me, alas !-but the approbation of the Public." -But the approbation of the Public?-Kind Public! Cruel Reviewers! But after all, why, Madam, fin against geogra phy and where is the imagination discovered in the trefpals? The madman, and the lover, and the poet, Are of imagination all compact. True! and yet the madman, or mad woman, and the poet, are not quite the fame thing. The "fine phrenzy" of the poet is, er or ought to be, in fome meafure regulated, and not like the fancy of the lunatic, entirely difordered. One fees more devils ihan vaft hell can hold, The madman But the imagination of the poet, or as the Greek term fignifies Creator, months, bodies forth forms, and affigns to airy nothing probable habitation and name. The idea of Shakespeare tallies exactly with the precept of Horace, Fica voluptatis caufâ fint PROXIMA VERIS. Good poets, with a kind of holy witchery, "lie like truth." The geography of the heart, and history of the paffions are beft delineated by adhering to the real map of the world, and not departing too wantonly from authenticated facts. If the fair Wri ter fuppofed the wreck of a veffel on the coast of Bohemia, an inland country, to be one of the brighteft paffages in the Winter's Tale of Shakespeare, why does fhe, with more conformity to geographical truth, make the troops from Leon enter at the Western gate of Arragon? In from the Western gate, like bees returning Shameful accuracy! Scandalous breach of the poetical privilege to raise mountains, feas, or kingdoms, in any part of the habitable globe that hits my fancy! And how fatally has our Poetefs been blinded by her refentment, when the winds up this fentence, and concludes her Deprecation by adding- Or, if it ftrikes me, build a temple to Dullnets-in the chamber of a Reviewer.' This circumftance being enumerated as the boldeft of fitions, and the climax of all improbability, is the highest compliment that has ever yet been paid us. tery. We fhall endeavour, however, mortal men as we are, not to fuffer our impartiality to be warped or biaffed by menace or flatThe Tale before us, as far as we can judge from this first part of it, is wild and romantic, here and there affecting in its circumitances, and delivered with much freedom, fometimes perhaps tedioufnefs, of narration. The blank verfe is, in general, easy and flowing; but the measure is often unneceffa rily, as well as inharmoniously, deficient or redundant, and the ftyle abounds with inaccuracies of expreflion. Rhyme, perhaps, on this occafion, would have been more agreeable to the generality of readers than blank verfe; at least the admirers of Dryden's Fables will not be among the blindeft idolaters of Mrs. Cowley. To the Tale of the Maid of Arragon are fubjoined fome lines in imitation of our Poetefs's great namefake of illuftrious memory. The lines are pretty enough, but not fo much crouded with thought thought and metaphyfics, as the verfes of the original Cowley, The following paffage has little or no refemblance to him: When in a penfive mood I fit, Defcribe thy look, thy ftep, thy make, Thefe lines are fucceeded by a Monologue to the memory of Chatterton, deploring his fate, and celebrating his genius. Why this Monologue, or the lines in imitation of Cowley, thould be annexed to the Maid of Arragon, we cannot discover. Uncommon excellence is not their recommendation. ART. XII. Conclufion of our Account of the PHILOSOPHICAL TRANSACTIONS of the ROYAL SOCIETY, Vol. LXIX. Part 1. for the Year 1779. See Rev. for March. MATHEMATICS. Problems concerning Interpolations. By Edward Waring, M. D. F. R. S. and of the Inftitute of Bononia, Lucafian Profeffor of Mathematics in the Univerfity of Cambridge. HE method of interpolating, now fo well known and fo Te often practifed by aftronomers, was firft invented by our countryman Mr. Briggs, Savilian Profeffor of Geometry in the Univerfity of Oxford, and put in practice by him in the calculation of logarithms. The principles on which he proceeded were afterwards explained by Reginald and Mouton in France. Sir Isaac Newton, in Lemma v. book iii. p. 486, Phil. Nat. Princip. Mathemat. edit. 1726, gave a most elegant folution of the problem for drawing a curve line through the extremities of any number of given ordinates; and in the fubfequent propofition applied the folution of this problem to that of finding, from certain obferved places of a comet, the place of it at any given intermediate time. Dr. Waring fays, perhaps a ftill more elegant folution of the problem, in fome accounts, has fince been given by Meffrs. Nichole and Stirling: and he adds, the fame problem is refolved, and rendered fomewhat more general in the paper before us, without having recourfe to finding the fucceffive differences. The paper confifts of two theorems and a problem. In the theorems, the Profeffor demonftrates certain properties which belong to a series of the differences of numbers, or to a series of numbers which have given differences; for both amount to the fame fame thing. In the problem, he fhews how, from these properties, to find certain corrections, which being applied to a feries of numbers, found from certain affumed ones, according to any given law, the fums or differences may be equal to the refults deduced from certain other numbers according to the fame law and he adds, that from these theorems, feveral others of a fimilar nature may be easily demonftrated. Art. IX. On the general Refolution of Algebraical Equations. By the fame. In this Article Dr. Waring informs us, that in 1757 he fent fome papers to the Royal Society, which were printed in 1759, and copies of them given to several perfons at that time: that these papers, somewhat corrected, with the addition of certain properties of curve lines, were published in 1762, with the title of Mifcellanea Analytica; and reprinted, with additions and emendations, in the years 1767, 1768, and 1769, and published in 1770 under the title of Meditationes Algebraica. He farther informs us, that these papers contained, among many other inventions, the most general resolution of algebraical equations yet known; as it contains the refolution of every algebraical equation of which the general refolution had then been given; namely, the refolution of quadratic, cubic, and also of M. De Moivre's and M. Hudde's equations; likewife of the equation of which Mr. Berout has fince published the refolution. It moreover difcovers the refolution of an equation of any given number (n) of dimenfions, the fame number (n) of its roots being alfo given; and alfo deduces innumerable equations of any given number (n) of dimenfions, which contain - independent coefficients. From which the Doctor infers, that it is probable this new method of his contains the most general refolution of algebraical equations that ever has, or perhaps ever will be invented. 2 Having thus given us the history of his publications on this head, he proceeds to lay down the general formula for the refoJution of equations, and then illuftrates it by examples in the refolution of equations of particular dimenfions. Dr. Waring's principal motive, in the publication of this paper, appears to be, the vindication of his claim to the invention of this general mode of refolving algebraical equations; which, as we gather from the paper before us, and what he has faid in the preface to his Medit. Analyt. for we have not seen the work which he refers to, has been fince published by fome foreign mathematicians of the first rank*, without fuch acknowledgment, as the Doctor feems to think was neceffary, of his being the first discoverer of them. If this be not the cafe, M. M. Euler and Le Grange. We we must own that we cannot account for his giving us, fo often, a chronological hiftory of the times when the books in which they are contained were written and published; namely, twice in the paper before us, and once in the Preface to his Meditationes Analytica. If it be really the cafe, we think the Profeffor might have spoken more plainly without any breach of modefty or decorum. MECHANICAL. Art. XII. Tentamen continens Theoriam Machine fublicarum -An Effay containing the Theory of the Machine for driving Piles. By Thomas Bugge, Aftronomer Royal, and Profeffor of Aftronomy and Mathematics in the Academy of Copenhagen, and Member of the Societies of Sciences at Copenhagen and Drontheim. Communicated by Sir John Pringle, Bart. Our Author fets out with obferving, that among the numerous advantages which civil fociety have derived from the knowledge of mechanics, the art of driving piles, that is, large oblong beams, into the earth, by repeated blows, is not the leaft. This art was not unknown to the ancients, as may be proved from many paffages in Vitruvius: for although this cele brated author does not defcribe the machine by which they did it, yet their knowledge, in this refpect, is placed beyond all doubt, feeing that without it, it would have been impoffible for them to have built bridges, moles, dams, bulwarks, pyramids, columns, and other edifices, the fize, majefty, firmness and durability of which we admire, but can fcarcely imitate; and all these things require the moft firm and folid foundations. If the foundation of a building is to be laid in a marfhy place, large piles must be driven, by means of engines of this kind, to great depths, and the spaces between them filled up with great ftones, gravel, fand, and mortar, before the foundation of that building can be laid. The exact form of the machine by which the ancients drove thefe piles is not now fufficiently known. Several forts have been defcribed by Leopold, Defaguliers, and Belidor. But amongst all those, that which was invented by Vauloüe, defcribed by Defaguliers, and brought into ufe while the foundation of Weftminfterbridge was laying, has greatly the pre-eminence over all others. Its peculiar advantages are, that the weight, ufually called the Ram, may be raised with the leaft force ;-that when it is raifed to a proper height, it readily difengages itself and falls with the utmost freedom;-that the forceps are lowered down speedily, and inftantly, of themselves, again lay hold of the Ram, and lift it up on which account this machine will drive the greatest number of piles, in the least time, and with the feweft la bourers. I Mr. |