reprobate the conduct of the more zealous advocates for the abolition of negroe slavery. We allow, indeed, that some of them have been highly intemperate and indiscreet: but we also hope and we believe that, with a very few exceptions, they were actuated by humane and benevolent motives. We think that the deplorable events, which our author has so feelingly described, and which have been indisputably produced, in St. Domingo, by the extravagant doctrines and unwise measures of those who had too inconsiderately engaged in the momentous project of emancipating the negroes of that island, ought to produce extreme caution, on a subject of such magnitude; lest humanity and benevolence, the best affections of our nature, by an intemperate and injudicious indulgence, should re-produce in other places those conflagrations, massacres, and devastations, which have either exterminated or ruined the white inhabitants of St. Domingo. To the concluding chapter, the author has subjoined a Tableau du Commerce et des Finances de la Partie Francoise de St. Domingue; together with several additional tables, notes, and illustrations; among which are comprehended a copy of the "Testament de Mort d'Ogé," and other important documents. The remarks which we have already made on this work, joined to the extracts given from it, will, as we believe, more than suffice to recommend it strongly to public attention; and will convince our readers of the great importance, as well as novelty, of the facts and opinions which it contains. We are persuaded that it will be long read with pleasure and instruction; and that it will ever be considered as an honourable proof of the vigorous and comprehensive powers of mind, and of the energetic, correct, and extensive command of language, which the author appears eminently to possess. ART. XII. Lectures on Natural and Experimental Philosophy, consi dered in its present State of Improvement: describing in a fami liar and easy Manner, the principal Phenomena of Nature; and shewing, that they all co-operate in displaying the Goodness, Wisdom, and Power of God. By George Adams, Mathematical Instrument Maker to his Majesty, and Optician to his Royal Highness the Prince of Wales. In Five Volumes. 8vo. Price Il. IOS. Boards. W WHETHER we consider the laudable design with which this comprehensive work was undertaken, or the attention and diligence which were employed in the execution of it, we are constrained to pay a tribute of respect to the deceased author. Our personal acquaintance with him enables us to bear testimony testimony to the assiduity of his research, to the variety of his knowlege, to the labour which he bestowed on this work, and, above all, to the integrity of his mind and the virtues of his character. Differing from him in many opinions, unconnected with the immediate object of this performance, and which some readers may think he has introduced into it without necessity, and without adding to its value and use, we nevertheless highly esteemed his talents and his worth; and we are happy in being able to recommend this work, the completion of which employed the latter years of his life, as a repository of observations and experiments, of which the proficient in philosophy may occasionally avail himself, and which will be instructive and amusing to those who devote any part of their time to philosophical inquiries and pursuits. If he had lived to revise this publication, and to re-consider some opinions that are advanced in it with respect even to philosophical subjects, Mr. Adams would probably have seen reason for adopting different sentiments; and he might also have contrived to condense his materials into a more narrow compass, and, by a style of writing less diffuse and declamatory, to diminish the magnitude of the work without depreciating its value. Without entering into a critical examination or minute detail of its contents, however, we shall satisfy ourselves with a general recommendation of it; and with informing our readers that the first volume comprehends 4 lectures on the Nature and Properties of Air, a 5th on Sound, 4 lectures on the Nature and Properties of Fire, and a 10th lecture on the Nature and Properties of Elastic Fluids:-that vol. II. contains 12 lectures, 2 of which are on the Nature and Properties of Water, another on the Method of reasoning in Philosophy, and 9 on various subjects that may be classed under the general title of Optics :that the IIId vol. consists of 13 lectures, the 1st on the Nature and Properties of Matter, the 2d on the Opinions of the Antients concerning Matter and Materialism, the 7 succeeding lectures on Mechanics, the 3 next on Hydrostatics and Hydraulics, and the last on Astronomy:-that vol. IV. pursues the subject of Astronomy in 9 lectures; to which are added 4 lectures on Electricity, I on Magnetism, and 2 on Meteorology;—and that the Vth vol. contains a general index, and a collection of plates *. *Our notice of the above mentioned publication has been too long protracted through mere accident; with the circumstances of which it is unnecessary to trouble our readers. ART. XIII. The Principles of Mathematics and Natural Philosophy, In Four Volumes. Printed at Cambridge. The Elements of Algebra: designed for the Use of Students in the Uni versity. Vol. I. By James Wood, B. D. Fellow of St. John's College, Cambridge. pp. 284. 8vo. 4s. Boards. Elmsley. ART. XIV. The Principles of Fluxions; designed for the Use of Students in the University. Vol. II. By the Rev. S. Vince, A.M. F.R.S. 8vo. pp. 230. 4s. Boards. Elmsley. T 'HE University of Cambridge has been long distinguished by the patronage and encouragement which it has afforded to the study of Mathematics and Philosophy; and a work, therefore, which comprizes the substance of the lectures on those subjects that are usually read in this University, cannot fail of engaging attention. A compendious and correct system of this kind, adapted to the use both of teachers and learners, has been much wanted; and we have often had occasion to express our surprise that persons of competent abilities, who are employed in this department of education, and who must have provided themselves with a course of lectures for their own use, have not extended the benefit to others, with whom they have had no immediate connection. Works of this kind, we are well apprized, are not likely to be profitable in a pecuniary view to those who undertake them; and perhaps, all circumstances considered, they may not expect to derive a great accession of reputation from their labours. They must pursue a beaten track. They must be contented to avail themselves of what others have written on particular subjects; and they must condescend to what some may deem the humble office of collecting and compiling from a variety of publications, to which proficients in the sciences have long had access, and with which they are supposed to be well acquainted. The privilege of the University press, however, removes one of the objections above stated from those who, being in the situation of the authors whose works are now before us, are allowed to avail themselves of it; and it is scarcely necessary to add that a judicious compilation of comprehensive and useful treatises, on different branches of mathematical and philosophical science, will most probably increase, in a considerable degree, the reputation of those who undertake it, and eventually ensure the ap probation of the public. The general plan adopted by the authors of the two treatises now announced, which by some accidents have too long remained unnoticed, is such as may lead us to expect that the whole work will be executed with credit to themselves, and with satisfaction to competent judges. In a multifarious undertaking of this kind, kind, it is natural to imagine that some parts may be more complete and perfect than others; and a candid critic, approving the utility of the design, and apprized of the number and variety of subjects which it comprehends, will not ani. madvert with severity on trivial omissions and inaccuracies that are almost unavoidable. We are of opinion, however, after an attentive perusal of the two volumes already published, that the authors are entitled to the favour of the public in the prosecution and completion of their plan. Its extent, as well as the manner in which they' propose to conduct it, and which seems to us not only unexceptionable but peculiarly advantageous, may be known from the general advertisement prefixed to the first of these volumes: The present work is intended to comprize the substance of the lectures in Mathematics and Natural Philosophy, which are usually read in the University. The want of a system of this kind having been long complained of, Mr. Vince and the author of this first volume agreed to undertake the work jointly; the former engaging to draw up the Fluxions, Hydrostatics, and Astronomy; and the latter, the Algebra, Mechanics, and Optics. That the whole might form one system, the parts drawn up by each were submitted to the consideration of the other, and such alterations and additions made as were thought necessary by both. The whole will consist of four volumes: the first and second containing the principles of Algebra and Fluxions; and the third and fourth the elements of Mechanics, Hydrostatics, Optics, and Astronomy. These will be published in succession, and as soon as possible.' Some of our readers may possibly be surprised that, in a work professedly comprehending the principles of mathematics, &c. no notice has been taken of other parts of science, such as geometry, trigonometry, and conic sections, which belong to this class, and ought to be included in a course of mathematical lectures as well as algebra and fluxions. Should it be said that we have many excellent treatises on the subjects now mentioned, which supersede the necessity of any new publications, it may be alleged that this is the case with respect to algebra and fluxions:-but, in a complete course, such as is adapted to the use of students in an University, and such as would preclude the inconvenience of referring to other works, and at the same time afford the advantages of unity, connection, and easy citations, the sciences that are omitted have an equal claim to notice with those that have been introduced. We cannot, therefore, but consider the omission as a real defect in this work; and it was natural to expect that some reason would have been assigned for restricting the plan to the subjects which it includes, while others, not less necessary and useful, are altogether O 3 together omitted. The work is not only incomplete in itself, but it does not correspond to the general title which it bears; nor to the advertisement prefixed to it, which announces to us 'the substance of the lectures in Mathematics and Natural Philosophy, which are usually read in the University.' If this hint should be noticed, and induce the authors to enlarge their plan by the addition of a volume or two on the subjects now mentioned, as well as on some branches of Natural Philosophythat are not recited in their Advertisement, we are persuaded that their work would be more acceptable and more useful. The first volume, appropriated to Algebra, commences with an introduction, containing as much common arithmetic as relates to the management of vulgar and decimal fractions. As Mr.Wood has thought it proper to assign 22 pages to this subject, we cannot forbear to express a wish that he had extended his introduction farther, and made it comprehend, at least, the higher rules of arithmetic. This might have been done by a little management, without adding much to the bulk of the volume, and it would certainly have contributed to enhance its utility and value. As common arithmetic, however, does not seem to have been part of the plan of the projectors and com-' pilers of this work, we think that every thing really necessary on the subject of fractions, both vulgar and decimal, might have been comprised in a small compass, if it had been introduced in its connection with algebraic fractions; under which head. several of the same rules are unavoidably repeated. The treatise on Algebra is divided into four parts. The first comprehends definitions, general axioms, the common rules of addition, subtraction, multiplication, and division, the operations relating to fractions, involution and evolution, simple and quadratic equations, the doctrine of ratios, proportion, the investigation of variable quantities and their relation to each other, arithmetical and geometrical progression, permutation and combination of quantities, the binomial theorem, and surds. The second part comprises the nature of equations, their transformation, the limits of their roots, the depression and solution of them, the solution of recurring equations, Cardan's rule for the solution of a cubic equation, Des Cartes' method of resolving a biquadratic, and Dr. Waring's solution of the same, the method of divisors, the method of approximation, the reversion of series, the investigation of the sums of the powers of the roots of an equation, and the impossible roots of an equation. The third part treats of unlimited problems, continued fractions, hermonical proportion, binomial surds, logarithms, interest and annuities, the sumraation of series, |