EDUCATION. ART. 13.-ΛΟΥΚΙΑΝΟΥ ΣΑΜΟΣ ΑΤΕΩΣ ΑΝΑΛΕΚΤΑ. Selections from Lucian, with a Latin translation and English notes; to which are subjoined, a Mythological Index, and a Lexicon adapted to the work. Compiled for the use of Schools. By JOHN WALKER, formerly Fellow of Dublin College. Glasgow, printed for the Editor. London, Law and Whittaker. 1816. pp. 357. THIS edition from Lucian, is by a gentlemen who was formerly fellow of Dublin College, familiarly called " The Silent Sister," with reference to our English Universities, and to the rare occasions on which her inmates assist the public with the learning they have acquired within her walls. The purity and simplicity of the style of Lucian, as well as the cheerful humour he displays, occasioned his reception as one of the earliest Greek authors to whom the juvenile student is introduced, and the errors in the collection by Mr. Murphy being numerous, from the deficiency of the editor in learning and taste: the present work, as a substitute, will be the more acceptable to the youth of Ireland. If we have any objection, it is neither to the original, or to the translation in the body of the work, but to the smallness of the type, both of the lexicon, and the alphabetical catalogue of words superadded to it. Indeed, for the last, we see no necessity at all, it appearing to us to contribute to the enlargement of the volume without any substantial utility. It is a novelty to this sort of publication without any sufficient motive. MATHEMATICS. ART. 14. An Introduction to the Method of Increments, expressed by a new form of Notation; shewing more intimately its relation to the Fluxional Analysis. By PETER NICHOLSON, Private Teacher of the Mathematics. London, Davis and Dickson, 8vo. pp. 130, 1817. To o prevent the misunderstanding of works of this kind in different languages, it may be convenient to observe, that foreigners usually define the method of fluxions, the arithmetic or analysis of infinitely, or rather indefinitely small variable quantities: or the method of finding an infinite simal, or infinitely small quantity, which being taken an infinite number of times, becomes equal to a given quantity. Sir I. Newton altered the nomenclature, calling these infinitely small quantities moments, considering them as the momentary increments, or decrements, of variable quantities, as of a line generated by the flux of a point, or of a surface, by the flux of a line. Hence the variable quantities are called fluent, and the method of finding either the fluxion or the fluent, the method of fluxions. In the present work, the problem (page 52) for finding the integrals of the successive powers of a variable quantity, with those A B C and D (at the conclusion) are probably new: also the method of notation, (page 55) which will be found to be perfectly indicative of the operation, either of taking the increment or integral, and it may be employed likewise in shortening many algebraical expressions. The author gives the following explanation: "Since the time I first made the discovery of the transformation of products, in any form of progression, to those of any other form of progressional products, as dependent on the doctrine of combinations, I have made considerable research both into English and Foreign works, but have not met with any principles deduced from that kind of analysis which will effect the same purpose.so generally and with so little trouble, and which, when reduced to practice, are entirely independent of their original investigation. Though tables for reducing powers into arithmetical progressions which consist of succeeding values have been given by Stirling in his Differential Method, yet the process by which he constructs these tables is derived from principles altogether different from mine, which result entirely from the doctrine of combinations. "Much has been said on the combinatorial analysis, particularly by Hindenburg, a German mathematician; but, I do not find in his work any rules which will admit of the same application, "I have not only applied the combinatorial analysis to the reduc tion of powers into progressions, and the reciprocals of powers into progressional reciprocals, and also reversed these problems, but have introduced it in the most complex cases of multiplication and division of algebra, independent of the analytical investigation from which it is derived." (p. iv.-v.) The author recommends, that those who wish to prosecute the interpolation and summation of series, as congenial with the method here pointed out, may consult the differential method of Stirling, translated by Halliday, (1749,) and the method of Increments by Emerson, (1763,) the perusal of which works will amply repay the reader for his time and trouble by a greater variety of problems than are to be found in this introduction. NOVELS. ART. 15.-The Cavern of Roseville, or, the Two Sisters, a Tale. Translated from the French of Madame HERBSTER. BY ALEXANDER JAMIESON. London. Law and Whittaker, 12mo. 1817. pp. 174. THIS tale is confined to the illustration of two leading objects: the one is, to teach young people that the path of life is often difficult to be traversed, and, that at every step they may meet with impediments which would disappoint the fond hopes they have entertained; the second is, that the Supreme Being never abandons those who put their trust in Him, and that whatever mortifications they may receive. from vain expectation, they may always indulge hope in God, who, if he afflict them for a season, will ultimately reward their obedience and fidelity. The author has endeavoured, but not with perfect success, to represent every thing in its simple and natural state, as in childhood, and she has rather painted sentiments than passions, because she wrote for that period of life when the descriptions of the latter would, in her opinion, produce too much influence on the former. This story does not deserve further notice. POETRY. ART. 16.-The Shades of Waterloo! a Vision, in verse. By M. YOUNG, London; printed for the Author, and sold by Simpkin and Marshall, 8vo. 1817, pp. 144. SOME readers may be of opinion, that this poem presents itself to them at too distant a period after the event; the author himself allows, that he follows" where Scott, where Campbell, and where Byron led;" in as much, however, as the battle of Waterloo, as a military atchievement, can never but be present to the recollections of all Englishmen, so poems upon such a theme can seldom be unwelcome in their subject, or tedious in their execution, especially when as much spirit is displayed in them as in the small work before us. It is, undoubtedly, not regular in its construction, or equal in its execution; but it is unfair to try an author by rules which he did not profess to obey, and the writer before us admits that it is of "unfashioned form" and of "digressive length;" he meant it to be the former, and the latter is the almost necessary consequence of it: yet his digressions seldom deserve the epithet of dull, which he in diffidence applies to them. He seems a deadly foe to critics; we apprehend, from the nature of this production, that his enmity does not arise from previous suffering; and, at least, he cannot charge us with meriting it from unnecessary cruelty: poets of established reputation ought to have their errors pointed out, since their faults are always more epidemical than their beauties; but young writers not only require, but deserve encouragement. One object Mr. Young has in view, is stated in the following lines, "How blest that Bard whose Harmony can soothe Prefatory Dedication, p. vi. We do not exactly understand, in what way the author applies the title of "The Shades of Waterloo," or why he terms it "A Vision:" the dead and the living who fought on that day, are equally the subjects of his enthusiastic admiration, and he dwells on all the circumstances of the conflict with as much detail and accuracy, as if he had really been upon the field. In this department of our Review, wę cannot, of course, enter at length into the poem; and we lament on With laurels trembling where his talents guide. Where brave MACKENZIE conquer'd but with life? Nor all his glories match this field of flame! What pity if so fair a Name Should ever grace the Rolls of Shame.” SURGERY. ART. 17.-Memoir on the Cutting Gorget of Hawkins, (containing an Account of an Improvement on that Instrument, and Remarks on the lateral Operation for the Stone.) By ANTONIO SCARPA, Member of the National Institute of Italy, and Professor of Anatomy and Clinical Surgery in the University of Pavia, &c. &c. &c. Translated from the Italian by JAMES BRIGGS, Surgeon to the Public Dispensary. 8vo. pp. 29. London. Cadell and Davies, and Callow, 1816. Ir is probable that most surgeons interested in the subject of this memoir, have already made themselves acquainted with the remarks of a writer so justly celebrated as Scarpa. If there be any who have not yet done so, they may be assured of finding the enquiry conducted with critical discernment, and all that minuteness and preci"CRIT. REV. VOL. V. Jan. 1817. Q sion which might be expected from the Professor. The alterations · which he has made in the gorget, and the directions given for its use, are clearly founded on a nice study of the anatomy of the parts concerned in lithotomy, and, we think, demand the consideration of operating surgeons. Another translation of the memoir has been published by Mr. Wishart, well known as the translator of some of the more voluminous works of the same author. THEOLOGY. ART. 18.-The Golden Key, proving an Internal Spiritual Sense to the Holy Word, and containing a variety of interesting and entertaining Subjects, introduced as Dreams of Translations into Para dise. London. Simpkin and Marshall. royal 8vo. pp. 416. 1817. THIS Golden Key is to unlock a very valuable treasure, if, as is stated in the advertisement, it will confirm the Christian, allure and persuade the sensual and worldly-minded, confute the atheist, remove the objections of the deist and sceptic, and banish the narrowness of sectarism. The means to derive the benefit of this treasure are described in a way that may lead us to doubt of its acquisition, as they are not by substantial instruction to correct and inform the mind, but by various dreams of translations into Paradise, said to be 66 opened by the Golden Key, which unlocks a cabinet of curious truths." The author, not perfectly satisfied with human expedients, introduces angels as supernatural agents to assist him in his purpose. His intentions are good, but we very much doubt their fulfilment in the method he contemplates. ART. 19.-Sermons on the Epistles and Gospels for the Sundays throughout the Year (including Christmas-day and Good-Friday), for the use of Families and Country Congregations, and chiefly adapted to the Conditions of the lower Classes of Society, with a prefatory Discourse. By the Rev. R. WARREN. In two volumes. pp. 367-400. Bath, Črutwell; London, Longman & Co. 1816. THE prefatory discourse to these Sermons is very short, containing only general observations on religious instruction, and on the charges against the clergy of the established church, for attaching too much importance to what is called human learning. Of the Sermons, it is said that they are offered to the public, not as models of composition, but as a humble attempt to illustrate, by example the way in which instruction to the common people ought to be conducted. They are plain and concise, and the texts are taken from the epistles or gospel of the day, that they may be the more appropriate to each Sunday. The author has considered Bishop Wilson as one of the most perfect gospel preachers, and has endeavoured to adopt his style, but with what success we must leave to our readers to determine by the inspection of the work. The first volume is embellished by a portrait, which has so much more of the courtly and military, than of the sedate and priestly in |