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ART. XVII. A Compendious Law Dictionary, containing both an Explanation of the Tams and the Law itself. By THOMAS POTTS, Gent. 12mo. pp. 620.

THE author's view in this work was to produce, in a small compass, a work which would not only be useful to professors of the legal science, but to mercantile men in general, by affording a ready explanation of the terms of law, and at the same stating in a very general way some of the leading points of law relative to each particular head respectively. Greater attention has been bestowed on those parts of the work which

relate to bankruptcy, insurance, and other branches of commercial law, it having been particularly the wish of the author to adapt the performance to the use of merchants. The whole is compressed into one octavo volume, containing above 600 pages of close print. The work appears to us to merit praise, but its accuracy can only be judged of by a frequent and habitual use of it.

ART. XVIII. The Law of Copyright; being a Compendium of Acts of Parliament and adjudged Cases, relative to Authors, Publishers, Printers, Artists, Musical Composers, Print-Sellers, &c. By JOSHUA MONTEFIORE. 8vo. pp. 59. THIS small volume containing only 59 octavo pages, treats of the law relative to the rights of literary men and artists in the productions of their genius. The work commences with abstracts of the acts of parliament, as they respectively relate to authors, artists, printers, and publishers generally, and afterwards gives the judicial decisions under the several heads of distributive arrangement, to which they respectively belong. The law of copyright is not confined merely

to what is called literary property, in the common and more confined sense of the term, but extends equally to paintings, engravings, busts, models, maps, prints, musical compositions, and other similar productions. This little treatise is more fitted for those who are particularly interested in the rights and privileges of literary productions, than for the profes sional lawyer, but even to the latter it is not without its use.

ART. XIX. The Trial of John Peltier, Esq. for a Libel against Napoleon Buonaparté, 21st February, 1803, taken in Short-Hand by Mr. ADAMS; and the Defence revised by

Mr. MACKINTOSH. 8vo.

NO trial has for many years so much attracted the public attention as that of Peltier, for libelling the First Consul of France. It was well known that the prosecution had been commenced at the instigation of the French government, and the stupendous events which had led the way to the publication complained of, and the elevation of the real plaintiff, gave to the expected eloquence of Mr. Mackintosh an interest almost beyond precedent.

The public was not disappointed; rarely has there been exhibited such powers of oratory, never was there a higher instance of the purity of law. Every auditor retired with emotions of delight from the eloquence of Mr. Mackintosh, only to be exceeded by those of his exultation and confidence, that he lived under a government, where equal justice was dealt to all, regardless of the condition of the persons, careful only of the right.

As a law publication, however, this work cannot with propriety occupy much space in our Review. The question of law was clear and unquestionable: the counsel for the defendant did

not doubt it, but endeavoured to shew that the writings complained of were general satire, and history, natural to persons situated like the defendant to compose, and not overstrained in the facts. Such a gloss could not succeed with a British jury, though supported by (in the words of the attorney general and the chief justice) almost unparalleled eloquence. In the excellent summing up of Lord Ellenborough, he stated the general sentiment of English lawyers," That a publication defaming the persons and characters of magistrates and others in high and eminent situations of power and dignity in other countries, and expressed in such terms and in such a manner as to interrupt the amity and friendship between the two countries, is a libel."

The principal part of the book is upon subjects purely political, and connected with the person and character of Bonaparte; and which, for the most part, in different shapes, have often before been published. Mr. Peltier closes the trial with a second defence of himself in an address to the public upon the peculiar hardships of his situation.

ART. XX. Select Criminal Trials at Justice Hall, in the Old Bailey; with the Opinion of the Twelve Judges on several interesting Points occurring in the Course of them, and Reserved for their Decision. Vol. I. pp. 560.

THE object proposed by the editor of this work is to combine amusement with useful information. The trials are, we think, well selected, and include such as have excited most public attention, as those of Hackman, Dr. Dodd, Barrington, &c. Short accounts are also frequently added of the general deportment and behaviour of the persons during their trials, and after their conviction. The editor promises another vo

lume in case the present should meet with a favourable reception; which we think it merits, as the accounts given are pretty full, and we believe faithful. Facts, such as are here presented to the mind, afford ample matter for reflection, and the mode in which hitherto works of this nature have been executed, makes it desirable that the present should be continued.

ANN. REV. VOL. II.

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CHAPTER XX.

MATHEMATICS AND NATURAL PHILOSOPHY.

THE present year does not afford us a great number of works in the mathematical department, but it is distinguished by the names of men of great celebrity in science, and of one who is generally known by his fortunes in the political world. Carnot, the ex-director of France, was known as a mathematician, by his smail work on Fluxions; his reputation will be increased by his Geometry of Position, in which he has laboured with great assiduity to reconcile together algebra and geometry, and correcting some erroneous opinions which had been long maintained by very eminent mathematicians. This may be considered as the most important publication that we have to announce. The reputation of Baron Maseres, not only as an author, but as a patron of science, is firmly established, and whilst he is con tinuing with such ardour and industry his great work on Logarithms, he can find time for tracts, in which the very important question of the generation of equations is discussed with great precision, and the question is placed on its true footing. The Baron is one of the few persons who has studied Vieta with attention, and is qualified to appreciate justly the merits of the founder, we might say, of true alge. bra. Dr. Small, of Edinburgh, in a work or no great bulk, has displayed indefatigable industry. Such calculations could not have been examined without equal talents and labour. We have introduced Montucla into this volume, because from accident he could not appear in the last. His history forms an important æra in mathematical science, but it contains much too great a variety of topics, and its general merits were previously too well established for us to enter into a minute detail of every particular. The author, however, could not be passed over without some account of a life occupied in science, but which, from the melancholy events of the late years, was too much embarrassed in matters foreign from study, to per mit him to give his work that perfection at which he aimed. Lalande, in succeed ing to him, performed the office of friendship, but was evidently overwhelmed by his many numerous engagements. The French are at present attached more to these studies than the English: in the midst of their preparations for war they seem to be duly sensible of their merits; and from their numbers we may expect either many new discoveries, or great improvements, in the mode of communicating in

struction.

ART. 1. Histoire des Mathematiques. History of Mathematics; in which are described their Origin and Progress to the present Day; the principal Discoveries made in every Part of the Mathematics; the Disputes that have been raised among Mathematicians; and the principal Actions of those who have been most famous. Second Edition. By J. F. MONTUCLA, of the National Institution of France. 3 vols. 4to.

THE former work of this celebrated world, and every one must regret that writer is well known in the mathematical he did not live to finish this work, and

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that his studies should have been interrupted by the horrors of the French revolution. Montucla was born at Lyons the fifth of September 1725. His father was a merchant, who gave him an excellent education, and after studying at the Jesuits college in his native town, and pursuing the law at Thoulouse, he came to Paris and formed a connection with the most celebrated mathematicians of his times. The "Recreations of Ozanam" seem to have been the first work that he gave to the press; but he kept his secret so well, that it was sent to him as the reviewer of mathematical publications. About this time he was employed in the Gazette de France, and in 1756 he translated from the English every thing relative to inoculation for the small-pox, which was then introduced into France under the auspices of the court. The "History of the Mathematics" appeared first in 1758, in two volumes quarto, and was received with the approbation which such an effort at such a time deserved. He had announced his intentions of giving a third volume to the public; but the immediate execution of his plan was frustrated by an appointment as secretary to the administration at Grenoble, to which place he retired in 1761, and there, in 1763, formed a matrimonial connection. In 1764 he was removed from this place to Cayenne, where he acted as first secretary in the formation of the colony, and was also honoured with the title of king's astronomer. On his return to Grenoble, after an absence of fifteen months, he soon gained another appointment, and became first clerk in the office of Public Buildings, or, as we may term it, the Board of Works, in which office he continued twenty-five years, employing his leisure hours in his favourite pursuits. In this time the only work published by him was a translation of "Carver's Travels," which he produced in 1783; when he was urged by Lalande to give a new edition of his History of the Mathematics, with the assurance of indemnification from loss by the bookseller.

A long time elapsed before this edition appeared, and the eventful years of the revolution account easily for the delay; but at last, on the seventh of August 1799, the two first volumes were published. The printing of the third volume was begun; but death interrupted its progress at the 336th page of the third volume, on the 19th of December 1779.

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From this place Lalande undertook the completion of the work, in which it will not be difficult to discover what proceed'ed from his own pen, and what from the original author.

The revolution naturally produced a change in the circumstances of Montucla; but the new government was not totally insensible to his merits. He was a mem ber of the national institution at its origin; in 1794 he was placed on the list of pensions; and in 1795 was employed in the analysis of foreign treaties. The state of his health did not permit him to accept the place of professor in the central schools; but the department fixed him in the central jury of instruction. For two years the subsistence of himself and family was derived from a lotteryoffice, and for four months only he enjoyed the benefits of a pension of about a hundred and twenty pounds a-year, granted to him on the death of Saussure. But, if in this respect he shared the usual fortune of men of his talents, the sight of those who acquired property without efforts did not create envy; and his modesty and generosity in such moderate circumstances rendered him a truly admirable character. His first introducer to the office at Grenoble was M. Baudouin de Guemadouc, who was overwhelmed in the calamities of the revolution, and banished; but Montucla did not forget his benefactor in distress, and displayed that courage in his defence and support which entitled him to universal praise.

A work that is swelled out from two to four volumes large quarto, must contain much new, and probably great improvement in the old matter. This will be evident to any one who compares together the two works; yet we may say that the field is still open to future exertions, and the present work may be considered as a good guide to, rather than the completion of history. We do not speak this in disparagement of the author, who is entitled to great praise; but the very circumstance of its being completed by another person naturally renders the whole less perfect than it might otherwise have been. Throughout the work a spirit of nationality prevails; but if a jealousy of our nation is predominant, the more honourable are the testimonies which the author is compelled to render to some of our writers. Much may also be pardoned to him who dared, in bad times, to apologize for the unfortunate; and his indignation at the injustice done

to the monks, and proofs of the obligations we are under to the religious orders, ought not to be passed over in silence.

led their disciples into inextricable laby. rinths. We are willing therefore to allow to Vieta much more than his countryman has done, for science is of no country; "I wish not," he says, "to shock the pre- and of all men in the world scientific men sent manner of thinking on this subject, nor have little reason to boast of country, as to undertake the defence of monkery. There their history is a proof of the little value were, it must be allowed, abuses in the set their labours when living, whatmonasteries; but what human institution, upon even those of philosophical or literary socie- ever boasts they may afford to those who ties, is always freed from them? Abuses are scarcely will or can read their works like the ivy, which will at last cover old build- when dead; and we allow also to Vieta ings, or diseases which destroy the human the praise of leading the way by his py body. I allow it to be right and necessary to ramidal numbers to the famous binoreduce these institutions extremely, and to al- mial theorem, generally though improlow in them only an easy and honourable sub-perly, and even by Montucla ascribed to sistence, and by public authority the chains of the unhappy victims of ignorance, of youth, of family ambition, might have been broken. But was it necessary to drive back into the world, with a pitiful pension, cut to pieces a thousand ways, and oftentimes refused, a crowd of old men who, on entering into the world, must be a prey to misery or death? A few years would have put an end to their convents, and the reservation of twenty or thirty houses, as asylums for them, in such an immense territory, could not have been an object for envy or finance in a great and powerful nation, priding itself on generosity and humanity."

The history of algebra is extremely well given, and due respect is paid to the memory of Vieta; yet with all the wish to detract from the merits of Harriot, and to shew the errors in the account given by Wallis, the author does not seem to have been conscious himself of all the worth of his countryman. Victa discovered the fundamental property of equations, or the nature of the co-efficients: he did not carry it to the whole extent of the proposition; but, on the other hand, he did not divert into any error. The property discovered by Viesa, and demonstrated by him in the case of certain equations, was said to be made general by Harriot; but in this generalization a strict regard was not paid to truth, nor to the rigour of mathematical demonstration. Vieta could not have made the discovery of Harriot, because he could not have allowed of the expression of negative, or false, or impossible roots; nor could he possibly have seen or allowed that such a root could enter into an equation. Where an equation really does admit of more roots than one, he shews the order of the co-efficients as far as he has considered the equations; and if his successors had followed him in the same track, they would, like him, have delivered only truth, and not have

Sir Isaac Newton.

We may observe that in the history of algebra, as well as every part of the work, this edition is much improved by the increased number of writers quoted on every subject, and we might add, that this is a very considerable part of the merit of the work; and we should have been under greater obligations to the index he had rendered the access to every successor of Montucla, if by a copious fact, discovery, and writer easier than it is at present. The book will be possessed by every mathematician of eminence, and must be considered by him chiefly as a book of reference; every thing therefore should have been calculated to increase the utility of the publication.

The interesting history of fluxions, from their disputed origin to the great improvements made in that part of science, is detailed with great accuracy and perspicuity; butwe regretted that theworks of La Grange, La Croix, and Arbogaste, could not have been sufficiently examined by this industrious writer. The present is an interesting period for the doctrine of fluxions: the French writers are taking bold steps; but, in general, in adopting new methods, and aiming at generalising their ideas, they run into a degree of obscurity which is not easily penetrated by those who are fond of the ancient mathematical precision. The important question on assurances, in which so much has been done in this country, is not noticed with the attention it merits. The works of Price, and Morgan, and Maseres, are indeed mentioned, but the extent of their discoveries is not properly laid before the reader.

In optics the former work is much improved; but it is evident that the com pletion of this part lay with the editor of the two last volumes. Newton and Herschel here meet with deserved praise;

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