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Many philosophers, struck with the order which reigns in Na ture, and with the fecundity of her means in the production of phanomena, have imagined that she always arrives at its end by the most simple ways. In extending these views to mechanics, they have inquired what was the economy which Nature proposed to herself, in the employment of forces. After many fruitless trials, they haye at length ascertained that, among all the curves which can be described by a body moving from one point to another, that is always selected to be described, in which the integral of the product of the mass of the body, by its velocity and the element of the curve, is a minimum; so that, the velocity of a body moving in a curve surface, and unsolicited by any force, being constant, it proceeds from one point to another by the shortest line. The preceding integral has been called the action of a body; and the reunion of like integrals relative to each body of a system has been named the action of a system. The economy of Nature consists, then, according to these philosophers, in sparing this action, so that it may be the least possible; it is this which constitutes the principle of the least action.
This principle, examined thoroughly, is only a curious result of the primordial laws of motion; laws which, as it has appeared, are the most simple and natural that can be imagined; and which, on that account, seem to flow from the very essence of matter:-but, as all the laws which are mathematically possible offer analagous results, it ought not to be elevated to the dignity of a final cause; and, far from having given birth to the laws of motion, it has not been even accessory to their discovery; without which it would be still a subject of dispute, what was to be understood by the least action of Nature.'
In Vol. II. Chap. III. the author explains the perturbations of the elliptical motion of the planets. In Chap. IV. on the perturbations of the elliptical motions of comets, he thus di gresses into an account of the effects which probably would be produced by the shock of a comet :
To the terrors inspired by the appearance of comets, has succeeded the apprehension that, out of the vast number of those which traverse in every direction the planetary system, some one should overthrow the earth :-but they pass so rapidly by us, that the effects of their attraction are not to be dreaded. It is only by striking against the earth, that they can here produce disastrous ravages: but this shock, although possible, is probable in a very slight degree during the course of a century. That two bodies, so small when compared with the immensity of space in which they move, should im. pinge against each other, requires a concurrence of circumstances so extraordinary, that we are not warranted in entertaining on this head any reasonable fear. Nevertheless, the small probability of such a shock, by accumulating during a long series of ages, may become considerable, It is easy to represent the effects of this shock on the earth. The axis and the motion of rotation changed; the seas aban doning their antient beds, in order to precipitate themselves towards the new equator; great numbers of men and animals, overwhelmed in
this universal deluge, or destroyed by the violent concussion of the earth; entire spaces annihilated; all the monuments of human industry overthrown; such are the disasters which the shock of a comet would produce.'
Chap. V. treats on the perturbations of the Moon's motion. Chap. X. On the tides: the matter of this chapter was contained in the author's memoir on this subject, in the volume of the Academy of Sciences for 1790, and of which memoir we gave a considerable account in our last Appendix.
Chap. XI. treats on the stability of the equilibrium of the scas; and the XVth contains reflections on the law of universal gravitation.
The last part of this volume is occupied by a short history of Astronomy.
In the present article, we have not attempted to exhibit, in an abbreviated manner, the matter and order of M. LA PLACE'S reasoning; because the book itself, in many of its parts, gives little more than an outline of operations which are prolix in their detail; or a summary of observations and processes which, if expanded, would astonish by their extent and intricacy. We have judged it proper to give the titles of most of the chapters, as certain marks and signals of the route pursued by the author; with occasional extracts, as specimens of his clear, acute, and forcible reasoning. This treatise on astronomy, considering its object and extent, unites (in a much higher degree than any other work, on the same subject, that we ever saw,) clearness, order, and accuracy. It is familiar without being vague; it is precise, but not abstruse; its matter seems drawn from a vast stock deposited in the mind of the author; and this matter is impregnated with the true spirit of philosophy. Other treatises of the same kind have been patched up, in the expectation of small gain or smaller fame, by men who were not extensive in their knowlege, enlarged in their views, nor curious in their discernment; who read purposely to write; and who, when writing, exhausted themselves to the minutest particle of what they had acquired. Yet, one evil seems to attend the circumstances of men high in talents descending to write treatises like the present; we mean that, the most abstruse parts being familiar to their minds, they are apt to expatiate on them, as much as on parts more known, and more within the compass of the understandings of the generality of readers; and to think that an outline of a chain of reasoning, which exists in their minds connected and complete, may convey an idea of it: when, to any thing like a distinct conception and adequate comprehension of it, the intermediate processes are necessary. Several parts of M. LA PLACE'S
second volume are open to this remark: what he says concerning the secular inequalities, &c. will only be understood by those who have bestowed a considerable degree of attention on this subject.—The world must look forwards with impatience to the appearance of the work which the author has promised on physical astronomy; and in which, what now seems to be obscure will be made evident by mathematical demonstration, and what is concise and summary will obtain its just developement.
ART. VI. Les Caracteres de Théophraste; &c. i. e. The Characters of Theophrastus, from a Manuscript in the Vatican, containing Additions which never appeared in France; a new Translation, with the Greek Text; Critical Notes; and a preliminary Discourse on the Life and Writings of Theophrastus. By CORAY, M. D. of the Faculty of Montpelier. 8vo. pp. 410. Paris, 1799. London, imported by De Boffe. Price gs. sewed.
N opening this volume, we were struck with the enthu siasm which dictated its dedication. It is inscribed to the free Grecians of the Ionian Sea;' whom the writer exhorts to make themselves acquainted with antient Greek, and modern French, preparatory to their emancipation from their subjection to Turkey. At present, there seems little probability that the modern Greeks will become much connected with France: but, should they ever fall under the dominion of the Great Nation *, it is to be feared that the French commissaries will find as summary a method of making themselves understood, as that which is now practised by their Turkish task-masters.
The translator professes to give a more literal version of his original than that of La Bruyere: but, on comparing them together, we have not perceived that Dr. CORAY's translation is much more faithful, and we think that it is inferior in elegance. La Bruyere has frequently given a turn to his expressions, slightly different from that of Theophrastus, where the French idiom required it: but such variations cannot be deemed inaccurate. We observe, also, that the present translation is not shorter than the former; and, as far as we can pretend to decide on French style, it does not compensate by simplicity for the happy ironical turn of La Bruyere.
The notes are copious, and contain many useful and curious observations.
* It remains to be seen whether the French will continue thus presumptuously to style themselves.
ART. VII. A View of the English Editions, Translations, and Illustrations of the Antient Greek and Latin Authors, with Remarks. By LEWIS WILLIAM BRÜGGEMANN, Chaplain in ordinary to his Prussian Majesty. 8vo. pp. 838. Stettin. 1797.
ANY of our editions of the Greek and Roman Classics will be highly esteemed as long as those works are read; and a considerable number of English translations from the Greek and Latin will be admired for their accuracy and elegance, as long as our language continues to be understood. It must, therefore, be an object of importance with the lovers of antient literature, and especially with those who habitually study some favorite author, or who wish to distinguish themselves in the same path, correctly to know whatever has been contributed by our countrymen towards the advancement of classical erudition. Several attempts to facilitate that knowlege have been made; among the rest, by the late Dr. Edward Harwood, in his View of the various Editions of the Greek and Roman Classics, a book which is deservedly esteemed. Its plan, however, is very different from that of the present publication, which treats exclusively of English editions of the classics; and shews, at one glance, how greatly multiplied have been the endeavours of British scholars in cultivating a very valuable branch of literature, from the revival of it, down to the present period. The author must have been at very considerable pains in collecting his materials, as he executed the work without any personal assitance from this country. It certainly would have received material additions, if he had enjoyed free access to our universty-libraries: but, such as it is, we must regard the execution of it as a national compliment, and we can recommend it as an useful performance, and as the most complete of its kind.
The remarks, subjoined to the titles of the various editions. enumerated, are extracted from the different literary journals which have existed in this country, and from other occasional
ART. VIII. Oeuvres Posthumes de D'Alembert, &c. i. e. The Post-
*The circumstances attending the death of this celebrated have been sufficiently related in our late Reviews.
the private life, the opinions, and the particular affections, of a philosopher so dear to science, to literature, and to friendship, will (the editor presumes) interest his surviving friends, edify even the wise, and instruct the public. The present volumes will, moreover, furnish matter of astonishment to those who are of opinion that a profound thinker and a geometrician can neither feel nor love like other men.
The eager curiosity for particulars relative to celebrated men, which is always manifested by the world, precludes the neces sity of any apology for printing them. The editor of these volumes, however, has misused that power of gratifying public curiosity which he possessed: if we grant that he has been impelled to the publication of them by the desire of enhancing the reputation of his deceased friend, we cannot suppose that he has been uninfluenced by the wish of swelling his work to its present size.
It were vain to expect that every new book should contain new truths: we must be satisfied if old truths be served up after a new fashion, with proper seasoning and garniture:-but, if editors furnish only what has been set before the world these forty years, we shall wish to see the rigor of Cardan's law enforced: "non ab edendo deterreo, modo novum aliquid inveniant,"
Of the letters contained in the first volume, some have appeared before; and the greatest part are not written by D'ALEMBERT. These letters, though replete with good sense, contain very few interesting particulars, and no documents relative to the grand conspiracy denounced by the Abbé Barruel. In the second volume, most of the synonyms are extracted from the Encyclopedie, and have appeared likewise in the Abbé Girard's treatise: the articles of literature, &c. are known to the public: but the excellence of the three dissertations on taste, by D'Alembert, Voltaire, and Montesquieu, pleads the excuse of their re-appearance. Very little of the second
volume is new.
Volume I. is introduced by a brief history of M. D'ALEMBERT, written by himself. The documents relative to this philosopher are numerous, and have produced different impressions. In matters of pure and abstract science, the evidence is irresistible, and the conviction uniform: mathematicians, therefore, are thoroughly impressed with the vastness of his genius. His accuracy and judgment on subjects of taste and literature would probably be not less decidedly acknowleged, had his attack on Erudition and the Eruditi been less forcible and impressive. His moral character, if we regard the zeal of his friendships, his scorn of wealth, and his castigations of