n + &c. and thus to reduce it to the form x + a=0 by this means he obtained the refolution of a cubic equation, and Lagrange has fince obtained that of a biquadratic. n-2 n-3 "Waring alfo affuming x Ay + By + &c. has given the refolution of a biquadratic, by deftroying the fecond and fourth terms. "In these the principle is indeed fimple, but the application exceedingly tedious, from the length of the calculations it obliges us to perform." Waring, Euler, and Bezant afterwards reverfed the prin ciple, and thereby greatly abbreviated the operations. Lagrange and Laplace have given a moft beautiful theory, by affuming certain functions of the roots of the propofed equa tion, deduced from an attentive confideration of their values by which the dimenfions and often the form may be determined, but no important refolution has been obtained from it. In this treatife the principle of folution confifts merely in comparing different refolutions of general problems of general quadratic, cubic, and biquadratic, from which comparison it appears that the firft equation affumed in each is of n n-1 N2 n-3 - 0, the general nature +py +9 try += 0; the fecond in each is of the form y-P which laft only involving the fingle power of y may be made much more general by introducing the higher powers. Af fuming then the form of the fecond equation to be y m-1 m-2 1-3 m +Py +Qy +Ry. + U = o, P, Q, &c. being any functions of x whatever; from thefe equations the author proceeds to fhow, that it is eafy to deduce the different methods of refolution which have at different times been propofed, by which Cardan, or rather Tartalea, refolved a cubic, and Ferrari Defcartes and Bezant a biquadratic; Demoivre, a reciprocal equation, and the general theories propofed by Tfchirhaus, Waring, Euler, &c. As thefe propofed theories are in themselves fimple and incomplex, and the application to the more abftrufe queftions eafy and regular, and the procefs of investigation that which we have confidered of the moft univerfal utility, we think in proportion as every thing which tends to introduce arrange. ment, abbreviation, and perfpicuity into fo hitherto complicated a fcience, worthy the attention and gratitude of every student in this branch of philofophy. BRITISH BRITISH CATALOGUE. POETRY. ART. 12. The River Wye, and other Poems. 8vo. Sherwood 1812. The author of theft poems is a very fpirited and elegant, though perhaps, youthful bard. He defcribes the River Wye, and its beautiful variety of fcenery, with an animated pencil, and a juft difcrimination of its claims to admiration. He shows himself alfo familiarly acquainted with the hiftorical incidents, which have taken place in its vicinity. We are glad to fubjoin a fpecimen of this little volume, being fully perfuaded, that this author will probably write more, and certainly write better, as he feems to want no more than the ordinary requifites of experience and study. 44 TO THE RIVER CHERWELL; IN ANSWER TO WARTON'S POEM, ENTITLED THE COMPLAINT OF CHERWELL." "Sweet Cherwell, from thy crystal tide What note of forrow meets my ear, While nature laughs in fummer's pride, And flings her choiceft treasures here! "Though neighbouring Ifis proudly swell "Thy groves and milder fhades beneath, "And here as oft the star of eve, "Then Cherwell flow in native pride, Her flow'ry banks, her Naiad throng. Of Fancy's dreams would take his fill, Mm 4 We We could not help finiling at the inconfiftency of the vignette at the conclufion of the fonnet, and a very elegant fonnet too, in honour of the harp of Spenfer, which reprefents an English heavy Dragoon in the coftume of thefe days with a Kevenhuller hat, and the huge trappings of the present time. ART. 13. The Rofary, or Beads of Love, with the Poem of Sula; in Three Cantos. 8vo. 10s, 6d. Murray. 1812. This author has evidently a very lively fancy, and no inconfi. derable portion of poetical tafte; he is fomewhat too amorous for our graver ftyle of reading, and often deserves a flagellation from the deity whom he fo enthufiaftically venerates, for his careJeffness. Thus in the first page is a violation of grammar: "Which dreams of extacy is wont to bring." And in the third a still greater offence against accuracy; "And bade in dalliance they no longer toy." Yet it is impoffible to deny the praise of ingenuity, and we willingly fubmit a fpecimen for the reader's judgment, THE ADMONITION. "Scorn the dull cold difpaffion'd fage, Thy foul from every pleasure tear. Nature o'er fancy held the reign; Thou'ft felt or thought thou'ft felt the blifs, Imparted in a lover's kifs: Ther. nature's child, fair Thais prove, And leave philofophy for love," There There is a larger poem at the end of the volume, which is called Sula, and is a tale, of which the fcene is laid in South America; this alfo has much merit, but is characterized by the fame defect of carelessness, for we will not use a harsher appel. lation. ART. 14. Heroical Epifle from Death to Benjamin Mofely, M. D. on Vaccination; with a Poftfcript on fome collateral Subje&s. 4to. 39 PP. 2s. 6d. J. J. Stockdale. 1810. The very idea of this Epiftle is a fevere fatire. Death writes to Dr. Mofeley, to exprefs his ardent love for him, on account of his ftrenuous oppofition to Vaccination. What is ftill worfe for the delinquent, Death expreffes his love with great power of poetry, and not lefs of wit. For example: "Feel not alarm'd, my Mofeley! let no fear Love, ftrong as death, 'twas faid of old could prove; The grim monarch thus further expreffes his well-founded affection. "Dear though I own, 'midft medicine's various tribe, The irony is fo well fuftained throughout, and in fuch very good verfes, that we should have honoured the unknown author with a very favourable guefs at his name, but from fome flippant lines aimed at us in the poftfcript, which we are certain would not have been so aimed by the perfon of whom we thought. The author feems alfo, inconfiftently with that conjecture, to mean to praife the Northern Reviewers for foftering young genius, which after their fhameful attacks on Montgomery, and on a truly poetical authorefs, never ought to be faid of them. This line, however, feems to impute to them a love of poison. "Though not without a fting thefe honey bees, That That is furely, to dift Laurel-water, the most deadly of all poifons. In the poetry of Death this may indeed be appropriate praife: but if it be fo taken, what becomes of the rest of the panegyric? Putting, however, all perfonal feelings afde, the poetry is excellent. NOVELS. ART. 15. Temper, or Domeftic Scenes; a Tale, in Three Volumes. By Mrs. Opie. 12mo. 11. 19. Longman and Co. 1812. We were among the first to hail Mrs. Opie's entrance upon the literary theatre, zealously cheered her progress towards celebrity, and with the animation of a friendly partiality extolled her merits and accomplishments. Notwithstanding these testimonies of our good will, and perhaps in proportion to their warmth, earneftnefs, and fincerity; we confefs that we have been fadly difappointed. As profperity is hard to bear, fo is too much praife, and there is reafon to fear that Mrs. Opie has been fpoiled. Amid the falfe fplendour of a delufive flattery her judgement has been warped, her tafte corrupted, her imagination miled. In fhort fhe feems to have over-written herself. Thefe volumes certainly exhibit indubitable marks of mental ability, of good thinking, and of judicious obfervation, but all this is fo deformed by a tiflue of abfurdities and improbabilities, that it requires no common exertion of patience and perfeverance to linger through the whole. It is ufelefs to expatiate upon thefe, for they occur perpetually, but how could Mrs. Opie fo far lofe fight of confiftency, as to reprefent in her firft volume the mother of her heroine at one moment in the anguish of despair, and prepared for felf-destruction, and in the very next, calmly fitting down to fhow her talents in drawing flowers and sketching likemees. Two accomplishments by the way which do not often meet in the fame individual. Or how again fo extravagantly caricature the heroine herself, as to reprefent her in that foolish fituation in the poft-chaife, feeing her grandmother feafting through the window. Many fuch abfurdities occur. We nevertheless muft willingly acknowledge, that fcattered through the narrative are many falutary maxims of difcipline for the management of temper, many fenfible and judicious obfervations on the human character, and a certain knowledge of life. We always liked this lady's poetty better than her profe, and her tales better than her novels. In our opinion, the has never printed any thing in greater excellence than one of her very firft poetical productions, called the Virgin's First Love, which may be found in one of the volumes of the Gentleman's Magazine. ART |