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does the fluxion; and there remains the very same re u't athat above stated.
But our author proceeds to the general case, in which the rod is heavy, and the wall cxerts friction. Representing the weight of the rod by m tives its length, and the friction by » times the pressure, f being that pressure, and the other quantities being exprefled as above, and p being the weight attached to the end of the rod, we obtain the following general equation for all the calis of the problem: a b (P + Ima) 2-3
P + in 20+ 2
+ na a' b2
P + 1.1
P to 1112 In this equation, m or n, separately or together, may vanith ; that is, the weight of the rod, or the friction, may one or both be supposed nothing. When m=e, and n = o alío, we get the equation formerly deduced. When m = 0, or the rod has no' weight, but the friction continues, we have a fingular paradox; P vanishes entirely from the equation, and leaves a solution quite definite, but altogether independent of the pressure exerted on the rod. If n vanishes (or the fri&tion ceases) while the rod con
P + ma *3 b*
P-+112 weight) vanishes, m vanishes also ; 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 exists at all or not. This problem is therefore completely solved, and solved much more easily and generally by ordinary rules, than by the principle of minima or maxima of forces; and Euler would evidently have seen the relations of the question in a more clear and extensive manner, had he not fettered himself by the theory which he was labouring to support.
We shall conclude with noticing a consequence deducible from the curvelinear or local construation of this problem. By an obvious process we obtain an equation between y and known quantities of this form (y being a side of the right-angled triangle, whose hypothenuse is x above investigated).
Job + (34' -- b) 2* + 3 * + 6 = 0, put 3ah=P, and go = 2, and a' = 9, the equation becomes Z + P7 +39 7 + q = 0; a very general cubic cquation. Now, the relations between , and a and b may easily be found by the solutions of Euler's problem above given; for these reduce this question to the cxtraction of a cube root. Therefore, the cubic equation now
deduced may always be resolved by that fimple process; or, in other words, we have a general method of folving any entire equation whose 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 Music: A Poem, in Six Cantos.
By William Hayley Esq. Chichester. 1804. FORTUNE has her favourites in the republic of letters as well
as in the aristocracy of wealth. Desert is sometimes left, we are afraid, to pine in obscurity, while mediocrity is occasionally promoted to a share of public notice and indulgence which appears surprising, when its claims come to be fairly investigated. To the latter class, we conceive the author of the poem before us to belong. His indefatigable industry during a long life, his character as a polite scholar, and his intimacy with men of the first literary eminence, are circumstances quite independent of the diviner inspiration of genius; but, in Mr Hayley's case, they have so well supplied the deficiency, that his name carries to the general ear a sort of classical sound. The charm diffolves, however, upon a near examination, and leaves us to discover, in all the productions of his muse, a decided and invincible mediocrity. There is scarcely any passage, in all his metrical compositions, which may not be reduced, by a few flight transpositions, to sober sensible prose, without one distinguishable fragment of the scattered poet. Even in his earlier works, when the vigour of his fancy was unimpaired, there is a continual tameness of conception, and monotony of versification, that thew he was not born for the higher flights of poetry.
In one point of view, indeed, we think our author greatly superior to many who excel him in poetical talents; and that is, as the annotator of his own works. The copious notes subjoined to his didactic poems are quite of a different character from the filly farrago which so often disgraces the volumes of our modern poets. They display a liberal and cultivated mind, and contain a most amusing fund of literary information, gleaned from an extenlive and well-directed course 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 shed a reflected lustre on what shone 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 verse for agreeable prose. For these reasons,
we were sorry to see the present poem come naked into the world, and regretted that the dignity of its epic nature should have been thought to preclude the assistance of that body-guard which had so well protected the feebleness 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 single sprig to the scanty wreath that already encircles the poet's brow.
The preface informs us, that it was the purpose of the author not to display all the various efficacy of music, but to commemorate one very striking example of its moral influence.' This declaration, and indeed the very title of the poem, prepared us to expect, that however diverGfied it might be by episodes, the efficacy of music should be the connecting principle throughout, and direct the winding up of the story. The example he alludes to, which he met with in the memoirs of some Italian musician, is nothing more than the circumstance of two hired assassins being turned from their purpose, by overhearing the music of their intended vidim and his mistress. But we shall give it in the words of the author, as a fair specimen of the îtyle 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 story: He is speaking of Lucilio and Venusia, the hero and heroine.
• It chanced one morn, a morn of awful note!
To facred music they their souls devote.
The hymn that spoke his confidence in God.
But mark! how Heaven defeats the sul tlelt p'an,
By the blest talent of this godlike man !
Conversion in our souls surpassing thought,' &c. P. 40.
Music having so soon achieved its grand conquest, is obliged to content itself, during the remainder of the poem, with the inglorious task 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 most enchantingly) to words of their own composition. Here is no triumph of music, except over the ennni of idleness; and, to have made even that victory in any degree probable, the charms of the music, we conceive, must have far exceeded those of the poetry. If any of our readers be curious to know the 1 real story of this metrical narrative, he will probably be satisfied with the outline that follows:
Venulia, the heroine, is brought up by Donado, an old Ve. netian nobleman, as his own, but is in fact the daughter of Manfredi, who, having been the unfortunate cause of the death of an only son, had resolved to seclude himself from the world, and devote his life to atone for his involuntary crime. In prosecution of this plan, he sends his infant daughter to a distant nurse, who happened at the same time to have under her care an only daughter of Donado. The latter dying, Donado, whose enjoyment of a large fortune depended on his having a child, bribes the nurse to pretend it was Manfredi's daughter that had died, and adopts the neglected infant. These facts are unfolded in the course of the story: for the poem, in the true epic style, in medias res rapit, and opens at that eventful period when, as the author expresses it,
• To woman's height the young Venusia greit,
(A form more lovely nature never knew :)' p. 2. Donado destines her to be the bride of a rich gouty old lord; but she is rescued from this fate by Lucilio, the hero of the poem, a man far above her own age, and who had already lost a wife and a daughter. He was first introduced to Venusia as her music-master; but they soon became enamoured of each other; a circumstance that was hastened' by Donado's obstinate perseverance in the match he had proposed. After a faint struggle with filial duty (for there is not as yet the least suspicion againit Donado's paternity), Venusia consents to make her lover happy; and the marriage ceremony being privately performed, they repair to Milan, where they
• With delight, Hide their endearments from the public fight.' p. 36. Donado's rage upon the occasion is stern and inflexible; not a momentary gust of passion, but a fixed determinat on to fucrisice Lucilio to a revenge which absorbs every other principle of action. This is now the leading intereit of the poem. We hear alternately of the fanguinary projects of the old villain; the various retreats in which the lovers eluded his rengeance, and the occupations and amusements with which they filled up the years of their concealment. Their last place of thelter is the retreat of Manfredi; and Donado, having traced them thither, determines to execute his vengeance in perfon, and, disguising himself like a Turk, enters à fhrine devoted by Lucilio to morning prayer. As the poem is now drawing to a clot, the reader perceives the necessity of fome revolution in Donado's character, and is prepared to find music once more triumphant. It would not have been easy indeed to make it probable, that a soul so hardened in guilt, which througlout the poem had never betrayed one symptom of goodness, thould be softencd and subdued by the magic of sweet sound; but the principle which does operate so sudden a change is still more unaccountable, He had suppored Manfredi confined by fickness; but he is mistaken; Manfredi appears before him; and the fight of this man, instead of exasperating his rage, which was the more natural effect, extinguithes all delire of revenge, and unexpectedly awakens in his mind a moral sensibility of a very amiable description. This transförination le is the various parties through the usual forms of explanation, confession, and reconciliation,
After this account of the plot, and specimen of the verGfication, we believe moit of our readers will agree with us in thiuking, that the author would have saved himself a good deal of unnecefTary trouble, had he given us the story in the common form of a novel. At present, it is nothing but a novel in rhyine : for we cannot call that poetry, where the glimmerings of fancy or poetical fire are so 'few and far between.' Nothing, indeed, but an ill directed ambiiion could have induced him to put on those fetters, which he carries so ungracefully, that they are for ever clanking in our ears. The humbler plan we suggest would also 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 considers it as an essential improvement, to diver. fify a long heroic poem with smaller pieces of various measure ; and he presents the Triumph of Music as a grand experiment on