does the fluxion; and there remains the very fame re u't as that above stated. But our author proceeds to the general cafe, in which the rod is heavy, and the wall exerts friction. Reprefenting the weight of the rod by m times its length, and the friction by n times the preffure, f being that preffure, and the other quantities being expreffed as above, and p being the weight attached to the end of the rod, we obtain the following general equation for all the cafes of the problem: x642 ab2 (P+ma) x3 P+ma + (n2 + 1 ) a2 b2 + n2 a2 b3 In this equation, m or n, feparately or together, may vanish; that is, the weight of the rod, or the friction, may one or both be fuppofed nothing. When me, and no alfo, we get the equation formerly deduced. When mo, or the rod has no weight, but the friction continues, we have a fingular paradox; P vanishes entirely from the equation, and leaves a folution quite definite, but altogether independent of the preffure exerted on the rod. If vanithes (or the friction ceafes) while the rod continues heavy, we get x3 = a b (+), in which, if P (or the P+ma weight) vanishes, m vanishes alfo; whence another paradox, that if there is no friction, and no weight attached to the extremity of the rod, the equilibrium is not at all affected by its own weight, but is the fame, whatever that may be, or whether it exifts at all or not. This problem is therefore completely folved, and folved much more eafily and generally by ordinary rules, than by the principle of minima or maxima of forces; and Euler would evidently have feen the relations of the queftion in a more clear and extenfive manner, had he not fettered himfelf by the theory which he was labouring to support. We shall conclude with noticing a confequence deducible from the curvelinear or local conftruction of this problem. By an obvious procefs we obtain an equation between y and known quantities of this form (y being a fide of the right-angled triangle, whofe hypothenufe is x above inveftigated). No + (3 a2 — b) ja + 3 aa y2 + ao = 0, put 3 a2 —— b — P, and y=Z, and a'q, the equation becomes Z+PZ' + 39' Z +q3=0; a very general cubic equation. Now, the relations between y and a and b may eafily be found by the folutions of Euler's problem above given; for thefe reduce this question to the extraction of a cube roct. Therefore, the cubic equation now deduced may always be refolved by that fimple process; or, in other words, we have a general method of folving any entire equation whofe fourth term bears to the coefficient of its third term, the relation of the cube to three times the square of the fame quantity. ART. V. The Triumph of Mufic: A Poem, in Six Cantos. By William Hayley Efq. Chichefter. 1804. FORTUNE has her favourites in the republic of letters as well as in the aristocracy of wealth. Defert is fometimes left, we are afraid, to pine in obfcurity, while mediocrity is occafionally promoted to a fhare of public notice and indulgence which appears furprising, when its claims come to be fairly inveftigated. To the latter clafs, we conceive the author of the poem before us to belong. His indefatigable industry during a long life, his character as a polite fcholar, and his intimacy with men of the first literary eminence, are circumftances quite independent of the diviner infpiration of genius; but, in Mr Hayley's cafe, they have fo well fupplied the deficiency, that his name carries to the general ear a fort of claffical found. The charm diffolves, however, upon a near examination, and leaves us to discover, in all the productions of his mufe, a decided and invincible mediocrity. There is fcarcely any paffage, in all his metrical compofitions, which may not be reduced, by a few flight tranfpofitions, to fober fenfible profe, without one diftinguishable fragment of the fcattered poet. Even in his earlier works, when the vigour of his fancy was unimpaired, there is a continual tamenefs of conception, and monotony of verfification, that fhew he was not born for the higher flights of poetry. In one point of view, indeed, we think our author greatly fuperior to many who excel him in poetical talents; and that is, as the annotator of his own works. The copious notes fubjoined to his didactic poems are quite of a different character from the filly farrago which fo often difgraces the volumes of our modern poets. They difplay a liberal and cultivated mind, and contain a most amufing fund of literary information, gleaned from an extenfive and well-directed courfe of reading. To them he is indebted for the best part of his fame: they prop the weakness of the poetry that produced them, and fhed a reflected luftre on what fhone but feebly by its own light. When Mr Hayley refers us to a note, it is not an interruption, but a relief; and we gladly quit languid verfe for agreeable profe. For these reasons, we we were forry to fee the prefent poem come naked into the world, and regretted that the dignity of its epic nature should have been thought to preclude the affiftance of that body-guard which had fo well protected the feeblenefs of former productions. As it is, it must stand or fall by its poetical merit alone; and we fear it is not likely to add a fingle fprig to the fcanty wreath that already encircles the poet's brow. The preface informs us, that it was the purpose of the author not to difplay all the various efficacy of mufic, but to commemorate one very ftriking example of its moral influence. ' This declaration, and indeed the very title of the poem, prepared us to expect, that however diverfified it might be by episodes, the efficacy of mufic fhould be the connecting principle throughout, and direct the winding up of the ftory. The example he alludes to, which he met with in the memoirs of fome Italian musician, is nothing more than the circumstance of two hired affaffins being turned from their purpose, by overhearing the mufic of their intended victim and his miftrefs. But we fhall give it in the words of the author, as a fair fpecimen of the tyle and execution of the poem; for it is natural he should put forth all his powers on that which he regards as the most important part of the ftory: He is fpeaking of Lucilio and Venufia, the hero and heroine. It chanced one morn, a morn of awful note! The hymn that spoke his confidence in God. Shaking with ftrong compunction, not with dread, But But mark! how Heaven defeats the ful tleft p'an, His harmony, infpired by angels, wrought Converfion in our fouls furpaffing thought,' &c. p. 40. But this, fo far from being the hinging point of the ftory, is narrated as a little fubordinate incident in the fecond canto, and tends in no refpect to advance the plot. Mufic having fo foon achieved its grand conqueft, is 'obliged to content itself, during the remainder of the poem, with the inglorious talk of filling up a vacant hour. Whenever the lover and his lady have nothing better to do, they fit down to the organ or piano-forte, and fing and play (Mr Hayley affures us moft enchantingly) to words of their own compofition. Here is no triumph of mufic, except over the ennni of idleness; and, to have made even that victory in any degree probable, the charms of the mufic, we conceive, must have far exceeded thofe of the poetry. If any of our readers be curious to know the real ftory of this metrical narrative, he will probably be fatisfied with the outline that follows: Venufia, the heroine, is brought up by Donado, an old Venetian nobleman, as his own, but is in fact the daughter of Manfredi, who, having been the unfortunate caufe of the death of an only fon, had refolved to feclude himself from the world, and devote his life to atone for his involuntary crime. In profecution of this plan, he fends his infant daughter to a diftant nurfe, who happened at the fame time to have under her care an only daughter of Donado. The latter dying, Donado, whofe enjoyment of a large fortune depended on his having a child, bribes the nurfe to pretend it was Manfredi's daughter that had died, and adopts the neglected infant. Thefe facts are unfolded in the courfe of the ftory: for the poem, in the true epic style, in medias res rapit, and opens at that eventful period when, as the author expreffes it, To woman's height the young Venulia grew, (A form more lovely nature never knew :)' p. 2. Donado deftines her to be the bride of a rich gouty old lord; but he is refcued from this fate by Lucilio, the hero of the poem, a man far above her own age, and who had already loft a wife and a daughter. He was first introduced to Venufia as her mufic-mafter; but they foon became enamoured of each other; a circumstance that was haftened' by Donado's obftinate perfeverance in the match he had propofed. After a faint ftruggle with filial duty (for there is not as yet the leaft fufpicion against Donado's paternity), Venufia confents to make her lover happy; and the marriage ceremony being privately performed, they repair to Milan, where they • With • With delight, Hide their endearments from the public fight.' P. 36. Donado's rage upon the occafion is ftern and inflexible, not a momentary guft of paffion, but a fixed determinat on to fucrifice Lucilio to a revenge which abforbs every other principle of action. This is now the leading intereft of the poem. We hear alternately of the fanguinary projects of the old villain; the va rious retreats in which the lovers eluded his vengeance, and the occupations and amufements with which they filled up the years of their concealment. Their laft place of fhelter is the retreat of Manfredi, and Donado, having traced them thither, deter mines to execute his vengeance in perfon, and, difguifing himfelf like a Turk, enters a fhrine devoted by Lucilio to morning prayer. As the poem is now drawing to a clofe, the reader perceives the neceffity of fome revolution in Donado's character. and is prepared to find mufic once more triumphant. It would not have been eafy indeed to make it probable, that a foul fo hardened in guilt, which throughout the poem had never betrayed one fymptom of goodne fs, thould be foftened and fubdued by the magic of fweet found; but the principle which does operate fo fudden a change is ftill more unaccountable. He had fuppofed Manfredi confined by ficknefs; but he is mistaken; Manfredi appears before him; and the fight of this man, instead of exafperating his rage, which was the more natural effect, extinguishes all defire of revenge, and unexpectedly awakens in his mind a moral fenfibility of a very amiable defcription. This transformation leads the various parties through the ufual forms of explanation, confeffion, and reconciliation. After this account of the plot, and fpecimen of the verifica tion, we believe most of our readers will agree with us in thinking, that the author would have faved himself a good deal of unneceffary trouble, had he given us the story in the common form of a novel. At prefent, it is nothing but a novel in rhyme': for we cannot call that poetry, where the glimmerings of fancy or poetical fire are fo few and far between.' Nothing, indeed, but an ill directed ambition could have induced him to put on thofe fetters, which he carries fo ungracefully, that they are for ever clanking in our ears. The humbler plan we fuggeft would allo have afforded him a better opportunity of introducing his lyrical pieces, according to the example of many who have adopted that method of embalming their fugitive poetry. But our author, Manii carminis ales, foared higher. It appears from the preface, that he confiders it as an effential improvement, to diver fify a long heroic poem with fmaller pieces of various measure; and he prefents the Triumph of Mufic as a grand experiment on the |