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escape now, when to all my other faults are added, so many outrages in Geography ? With wbat triumph of critical sagacity will they say, (after the necessary ftri&tures on the story, thoughts, and verses) “ If our Author was determined to send her Pegasus into Spain, in queft of adventures, the ought to have consulted Salmon about the licuation of its provinces. She would there have found that Arragon is fifty miles from the sea; and that the Moors could not poflibly have debarked on its confines, unters, 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 Castile to Saragoffa in about thirty hours—another miracle; which was doubtless accomplished by the interposition of a friendly necromancer, who furnished the army with wings, in exchange for some chaste damsel, or beautiful princess. Had this Lady-Writer's reading extended to a translation of the Iliad, she would have found no examples of such liberties there. Homer gives an exact map of the countries he carries as through; and from Ithaca to Troy not a village or river is misplaced."

• 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 succesion of ages, had been subject to the ravages of Africa; and that during this period, sovereigns had been robbed of their crowns, and been obliged to resign their sceptres to their swarthy conquerors, The relation of the particular events of these remote times, the Hiftoric Mufe has generally left to her creative Sifter, who never fails io profit by their obscurity, in relating them to the world in her own manner; the geography of the heart, and the history of the passions, are the only realities to which the attends. If, in describing these, I Diall be found deviating from the laws of Truth and Nature, I shall have failed in my intention ; but I protett, if the cacoëthes fcribendi Mould continue on me, or if I should ever wander again into the regions of Romance, I Thall treat oceans and provinces with as little ceremony as rivulets and meadows: I will avail myself of the established privileges, and raise mountains, sea's, or kingdoms, in any part of the babitable globe that hits my fancy; or, if it strikes me, brild a temple to Duiness-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 stage, and to the Writer-“ Nothing to console 'me, alas !--but the approbation of the Public."

But the approbation of the Public ?-Kind Public! Cruel Reviewers ! But after all, why, Madam, sin against geogra. phy? and where is the imagination discovered in the trespais ?

The madmari, ard 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 same thing. The fine phrenzy” of the poet is,

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or ought to be, in some measure regulated, and not like the fancy of the lunatic, entirely disordered.

One fees more devils ihan vaft hell can hold,

The madman But the imagination of the poet, or as the Greek term fignifes Creator, TOINTn5, bodies forth forms, and afsigns to airy nothing probable habitation and name. The idea of Shakespeare callies exactly with the precept of Horace,

Fita 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 passions are best delic neated by adhering to the real map of the world, and not de. parting too wantonly from authenticated facts. If the fair Writer supposed the wreck of a vefsel on the coast of Bohemia, an inland country, to be one of the brightest pallages in the Winter's Tale of Shakespeare, why does the, with more conformity to geographical truth, make the croops from Leon enter at the Weftern gate of Arragon?

In from the Wiffern gare, like bees retorning
From their diurnal circuit, ruth'd amain
Ten thousand sons of war.

P. 12. Shameful accuracy! Scandalous breach of the poetical privilege 6 to raise mountains, seas, or kingdoms, in any part of the habitable globe that hits. my fancy!' And how fatally has our Poetess been blinded by her relentment, when the winds up this fentence, and concludes her Deprecation by adding -- Or, if it Atrikes me, build a temple to Dullness in the chamber of a Reviewer.' This circumstance being enumerated as the boldest of fictions, and the climax of all improbability, is the highest compliment that has ever yet been paid us.

We shall endeavour, however, mortal men as we are, not to fuffer our impartiality to be warped or biafled by menace or fattery. The Tale before us, as far as we can judge from this first part of it, is wild and romantic, here and there affecting in iis circumitarces, and delivered with much freedom, sometimes perhaps tediousness, of narration. The blank verse is, in general, eaiy and flowing; but the measure is often unneceslanily, as well as inharmoniously, deficient or redundant, and the Atyle abounds with inaccuracies of exprellion. Rhyme, perhaps, on this occafion, would have been more agreeable to the generality of readers than blank verse; at least the admirers of Dryden's Fubles will not be among the blindeft idolaters of Mrs. Cowiev.

To the Tale of the Maid of Arragon are subjoined some lines in imitation of our Poetess's great namesake of illuftrious memory: The lines are pretty enough, but not fo much crouded with

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thought and metaphysics, as the verses of the original Cowley, The following passage has little or no resemblance to him ;

When in a penfive mood I fit,
And Melancholy takes her tit,
Mild, tender, fost thou halt appear,

Like the first bloßoms of the year :
But when in brikker tides my spirits run,

L Ailgro thail the pencil ake,

Describe rhy look, thy step, thy make,
And thew thee lively as bright Mala's sou.

*

These lines are succeeded by a Monologue to the memory of Chatterton, deploring his fate, and celebrating his genius. Why this Níonclogue, or the lines in imitation of Cowley, thould be annexed to the Maid of Arragon, we cannot discover. Uncommon excellence is not their recommendation,

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ART. XII. Conclufion of our Account of the PhiloSOPHICAL TRANS.

ACTIONS 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 Institute of Bononia, Lucasian Professor of Mathematics in the University of Cambridge.

HE method of interpolating, now so well known and so

often practised by aftronomers, was first invented by our countryman Mr. Briggs, Savilian Professor of Geometry in the University of Oxford, and put in practice by him in the calcuJarion 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 solution of the problem for drawing a curve line through the extremities of any number of given ordinates; and in the subsequent propofition applied the solution of this problem to that of finding, from certain observed places of a comet, the place of it at any given intermediate time. Dr. Waring says, perhaps a ftill more elegant solution of the problem, in some accounts, has since been given by Messrs. Nichole and Stirling : and he adde, the same problem is resolved, and rendered somewhat more general in the paper before us, without having recourse to finding the succeffive differences.

The paper consists of two theorems and a problem. In the theorems, the Professor demonstrates 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 same thing. In the problem, he thews how, from these properties, to find certain corrections, which being applied to a series of numbers, found from certain affumed ones, according to any given law, the sums or differences may be equal to the results deduced from certain other numbers according to the fame law: and he adds, that from these theorems, several others of a similar nature may be easily demonstrated. Art. IX. On the general Resolution of Algebraical Equations. By

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the same. In this Article Dr. Waring informs us, that in 1757 be sent some papers to the Royal Society, which were printed in 1759, and copies of them given to several persons 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 Miscellanea Analytica ; and reprinted, with additions and emendations, in the years 1767, 1768, and 1769, and published in 1770 under the title of Meditationes Algebraicæ. 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 resolution of every algebraical equation of which the general resolution had then been given; namely, the resolution of quadratic, cubic, and also of M. De Moiure's and M. Hudde's equations ; likewise of the equation of which Mr. Berout has fince published the resolution. It moreover discovers the resolution of an equation of any given number (n) of dimensions, the same number (n) of its roots being also given; and also deduces innumerable equations of any given number (n) of dimenfions, which contain n-1 independent coefficients. From which the Doctor infers, that it is probable this new method of his contains the most general resolution of algebraical equations that ever has, or perhaps ever will be invented.

Having thus given us the history of his publications on this head, he proceeds to lay down the general formula for the resoJution of equations, and then illustrates it by examples in the sesolution of equations of particular dimensions.

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 resolving algebraical equations ; which, as we gather from the paper before us, and what he has said in the preface to his Medit. Analyt. for we have not seen the work which he refers to, has been since published by some foreign mathematicians of the first rank *, without such acknowledgment, as the Doctor seems to think was necessary, of his being the first discoverer of them. If this be not the case,

# M. M. Euler and Le Grange.

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we must own that we cannot account for his giving us, so often, a chronological history of the times when the books ia which they are contained were written and published ; namely, twice in the paper before us, and once in the Preface to his Meditationes Analyticæ. If it be really the case, 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 Efsay containing the Theory of the Machine for driving Piles. By Thomas Bugge, Astronomer Royal, and Professor of Astronomy and Mathematics in the Academy of Copen. hagen, and Member of the Societies of Sciences at Copenhagen and Drontheim. Communicated by Sir John Pringle, Bart.

Our Author sets out with observing, that among the nu. merous advantages which civil society 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 passages in Vitruvius : for although this celebrated author does not describe the machine by which they did it, yet their knowledge, in this respect, is placed beyond all doubt, seeing that without it, it would have been impoffible for them to have built bridges, moles, dams, bulwarks, pyramids, columns, and other edifices, the size, majesty, firmness and durability of which we admire, but can scarcely imitate; and all these things require the most firm and solid foundations. If the foundation of a building is to be laid in a marshy 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 stones, gravel, fand, and mortar, before the foundation of that building can be laid,

The exact form of the machine by which the ancients drove these piles is not now sufficiently known. Several forts have been described by Leopold, Defaguliers, and Belidor. But amongst all those, that which was invented by Vauloüe, described by Dejaguliers, and brought into use while the foundation of Westminsterbridge was laying, has greatly the pre-eminence over all others. Its peculiar advantages are, that the weight, usually called the Ram, may be raised with the least force ;-that when it is raised to a proper height, it readily disengages 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 fewest lar bourers, I

Mr.

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