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tained in their Memoirs' are devoted to the development of the theory of gravitation, and of these few by far the most remarkable is the production of a foreign associate. This backwardness, to say the least of it, on the part of our geometers to direct their labours to physical astronomy, is felt and regretted by the most enlightened members of the Society itself; and the Council, by proposing medals and other encouragements, have made repeated appeals to their mathematical members, who, however, have shown no haste to respond. From all this we are inevitably led to the inference, that the knowledge of the higher branches of mathematical science is not yet very generally diffused among our astronomers. Good observations are unquestionably the foundation of all astronomy, and are even indispensable to the theorist, as they afford him the only data from which his calculus can deduce any useful or interesting result. Yet it will be acknowledged that the art of observing is an art purely mechanical, and requires for its successful practice only eyes, patience and industry. It is independent of mathematical acquirements, and is, perhaps, more likely to be injured than benefited by a solicitous attention to physical causes, or the difficulties of the integral calculus. Certain it is, that some of the most eminent observers-those from whose labours practical astronomy has gained its greatest advancement-have been men who seldom troubled their heads about theory; and when the successful cultivators of the science can thus dispense with knowledge which is not to be acquired without labour and difficulty, it would be unreasonable to look for any great degree of it among amateurs. In fact, to point a telescope, or compute from a formula, is the utmost that is aimed at by the greater part of those who betake themselves to the harmless amusement of star-gazing.

We have no fear that the mathematical science of this country is in danger of retrograding, or falling into 'decay; but it is to be deplored that our public institutions provide so ill for the effectual instruction in the abstract sciences of those through whom theoretical knowledge can be turned to the greatest practical account, and rendered most productive of advantage to the country. The higher branches of the mathematics are taught nowhere excepting at Cambridge; but our engineers, civil and military, the officers of our army and navy, cannot, for obvious reasons, receive their education at Cambridge. We have no Polytechnic School, as in France, where promising talent, or early success in mathematical studies, is matured and prepared by a course of elaborate instruction for the public service. Of the great utility of such institutions, no more striking instance could be adduced than what is offered by the work which has occupied our attention in

the preceding pages. A young man belonging to a profession not peculiarly devoted to the prosecution of severe studies—a captain in the Etât-Major-disporting himself with the most recondite and difficult theories of mechanics and pure analysis-dandling as it were with the paw of the lion, subjects which have given full occupation to the minds of the greatest masters of science-is a phenomenon which must necessarily be rare anywhere, but of which we hold the occurrence, in this country, to be all but physically impossible. Supposing a young officer of our own army to be possessed of all the qualities of mind requisite for the successful imitation of so splendid an example, where is he to acquire the preliminary instruction, without which he cannot advance a step? Not assuredly at those institutions expressly destined for his education, whose humble courses, confined to the merest rudiments of geometry and algebra, and terminating at a point far short of what admits even of a single practical application beyond the measurement of heights and distances, would form but a sorry introduction to the Mécanique Céleste.' The careful instruction in the mathematical sciences of that class of individuals who are destined to fill the different departments of the public service, is of the utmost consequence not only in reference to the nature of the duties they may be called on to perform, but also to the general extension of scientific knowledge. In the church the successful aspirant to university honours soon forgets his mathematical learning, for which, indeed, he has in general very little use; but the engineer, the artillery officer, the naval commander, the surveyor, have at all times, in the very exercise of their professional duties, a certain degree of elementary science at least forced on them, and, in many situations, the strongest inducements to pursue it to a greater extent. It is therefore much to be regretted, if their course of mathematical instruction has been either too superficial to be of any practical advantage, or directed to objects which, in the present state of science, are comparatively of little importance. Such, however, there is reason to apprehend is generally the case; and it is really matter of astonishment how few of the great and obvious improvements which the elementary courses of mathematics have recently received on the continent have been adopted in this country. The geometry of planes and solids, which in the hands of our neighbours has assumed an entirely new form, remains in most of our school treatises nearly in the same state at which it had arrived in the time of the Ptolemies. Trigonometry has gained nothing from the labours of Lagrange or Legendre, or even from Euler's Arithmetic of Sines. The Conic Sections may fairly be said to have retrograded, inasmuch as Apollonius is still far superior, in every point of view, to those treatises still in com

mon use. The Descriptive Geometry, which is of the most extensive application in engineering, in fortification, and indeed in all cases where it is necessary to form an accurate conception of the forms of surfaces, or represent them on paper, has never been heard of in our public seminaries as a separate branch of instruction. This is the more extraordinary, on account that it deservedly forms a prominent part of the mathematical instruction in all the military schools on the continent, and is that application of geometry which, to practical men, is the most generally and extensively useful.

Public institutions for the education of a particular class of individuals labour under this disadvantage, that their courses must necessarily be limited to what can be accomplished by average talent and industry. But experience shows that no more hopeless labour can be undertaken, than that of attempting to convey instruction in the abstract sciences to all, indiscriminately, who may be destined by their parents to follow a particular profession. It was by acting on the knowledge of this fact that the Polytechnic School, towards the end of the last century, was enabled to give so great an impulse to the progress of scientific knowledge in France, the effects of which are beneficially felt at the present hour. Admission to the School was equivalent to a provision in the public service; hence it was an object of ambition to all ranks and as no other title than the possession of knowledge was recognised, it could select its pupils from among the whole youth of France. The great abundance of candidates allowed the standard of previous acquirement to be fixed high; and a rigorous examination sternly excluded all whose insufficient progress indicated inferior talent or power of application, on the principle that the public ought not to be charged with the instruction of those whose education, however desirable to their families, could be productive of no advantage to the state. Thus an adequate degree of talent on the part of the pupils was secured, and no means were omitted, which an enlightened direction could suggest, to ensure its complete development. In the list of the professors, the most essential agents in such institutions, were included the names of the illustrious Lagrange, Laplace, Monge, Berthollet, and others now associated with the scientific glory of their country. The effect was what might be anticipated: almost every man of scientific eminence in France, who has come forward during the last thirty years, has been indebted to the Polytechnic School for his instruction and future success. Although its original regulations have been deviated from, and there is reason to apprehend that it has become an engine of patronage in the hands of a minister of state, it still possesses enough of the fresh

ness and vigour of youth to exercise a powerful influence on the national science and education.

Although the habits and prejudices of this country are opposed to establishments on the plan of the Polytechnic School, many of its most valuable improvements might be adopted with great advantage, were it possible to overcome that tenacious adherence to established modes which characterises the public instruction in this country through all its departments. A modern education embraces a wide range; it is consequently impossible to enter profoundly into any particular branch, at least within the time which young men not destined to follow a learned profession, can devote to the acquisition of general knowledge. The object, therefore, which ought to be steadily kept in view, is to impart such instruction as will enable an attentive student to peruse with advantage the best works that have been composed on such special subjects as his peculiar avocations may make it desirable he should be acquainted with, and thereby give him the means of afterwards perfecting himself in his profession. Unless this object is accomplished, his time, however sedulously he may have been employed, has been consumed to little advantage; and if, when his course is completed, he takes up an intelligent French work on a professional subject, and finds himself stopt at the very first page because he is unable to decipher the Algebra, his education is obviously still to begin. Now we fear that this is what must take place in almost every instance. Euclid and the Conic Sections are desirable acquisitions; but without other aids, without some knowledge of Algebra beyond Simple Equations, they will no more enable any one to read a page of Poisson, or Francoeur, or Dupin, than to calculate from a Peruvian Quipo or a Chinese Swan-Pan. While the elements are so little adapted to the actual state of science, it is not to be wondered at that our public schools should send forth so few.proficients in Analysis.

ART. XI.-Monuments des Arts du Dessin chez les Peuples tant Anciens que Modernes, recueillis par le Baron Vivant Denon, Ancien Directeur-General des Musées de France, pour servir à l'Histoire des Arts; lithographiés par ses soins et sous ses yeux. Décrits et expliqués par Amaury Duval, Membre de I'Institut. 4 tom. folio. Paris. 1829.

THE General History of the Fine Arts comprehends not only a critical description of the most important works of art, arranged in classes to assist the memory, and to enable the mind of the reader to embrace the whole subject, which is the direct object of that department of history, but also an account of the taste, the

manners, the religion and the genius of various nations at different periods of their existence, and indeed of the prosperity and happiness of the human race, with which the origin, progress and decay of art are intimately connected. The vast extent of these indirect objects would render the task of executing such a history one of almost infinite labour, for the great works of art are so numerous, that a bare description of them would alone demand considerable time and talent, and much diligence. It is certain that no complete history has hitherto been produced, and we may reasonably doubt whether the whole life, and the entire mental powers, of a single individual would be sufficient to detail fully and philosophically the immense mass of facts: if, however, such a historian should arise, or, which seems more probable and practicable, if a writer possessed of the rare qualifications that are requisite for the due performance of the arduous duty, should separate a portion from the entire mass, and attempt to handle it in the elaborate style of workmanship that the matter deserves, the materials are wanting that would enable him to execute in a satisfactory manner the office of Historian of the Fine Arts. Investigations have been pursued in some directions with great activity and brilliant success, but in others little has yet been effected: of certain objects valuable and extensive collections have been already formed; others have either been neglected, or the endeavours of the curious have been frustrated by untoward accidents: many learned and elaborate volumes have discussed largely various topics connected with art, and have accumulated important facts; but much is still desired, to fill up that scheme and system of the whole subject, which the lover of these engaging pursuits chalks out to assist and regulate his own studies. The Baron Denon has contributed largely on other occasions to extend our acquaintance with works of art, and these posthumous volumes form a considerable addition to his former good deeds, and would alone entitle him to a distinguished place amongst the benefactors to the fund of humane and elegant knowledge.

We will first say a few words about M. Denon himself, and then proceed to offer some observations on the present work. A short prefatory memoir, "Notice sur la Vie et les Ouvrages, &c." is prefixed to the first volume. This distinguished person, however, was so well known, that it is unnecessary to repeat, even in an abridged form, the events of his life, and the history of his labours in literature and virtù; we will only mention, therefore, two matters that are new and curious, which we have learned from this short notice. It is accompanied by some letters from Voltaire to M. Denon, which were never before published; and although their contents are not altogether creditable to the person



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