The Correspondent; consisting of Letters, Moral, Political, and Literary, between eminent Writers in France and England; and designed by presenting to each Nation a faithful Picture of the other, to enlighten both to their True Interests, promote a mutual good understanding between them, and render Peace the Source of a common Prosperity, No. I. London. 1817. Longman and Co. 8vo. pp. 156. The object of this publication is more than sufficiently explained in the title-page. It is to appear at intervals of two months; and to be published simultaneously, in London and in Paris, in the respective languages of the two countries. The London Editor is Dr. John Stoddart, who was formerly a zealous advocate of the French Revolution,-but has since changed his politics, and is understood to be the conductor of the newspaper, called The Times. We are told in the Introduction, (which, by the way, is a very silly rhapsody about, we suspect the writer did not know himself,) that the plan has long been in contemplation, and that the several writers have entered into an agreement of contributing their quotas. There are sixteen Articles in the first Number-six English and ten French; from nearly all of which we have derived a good deal of pleasure. They are chiefly of a political nature; though there is one pretty long Letter, (by Mr. Southey, we suppose from the signature, R. S.) which gives an entertaining account of John Wesley, the founder of the Methodistical Sect. We think the Letter On the Affairs of Spain is the best English Article--and that respecting the Royalists of Brittany the best of the French. Our readers, however, will shortly have an opportunity of judging for themselves; as we understand it is in contemplation to republish the work in this country. They will find a good deal of illiberality among some of the articles; but it is mixed up with so many new facts, that its offensiveness is pretty much neutralized. We are afraid, indeed, that strict impartiality is not to be one of its characteristics; but, if the several writers will only give us the facts, we care very little for the reflections, which they smuggle in along with them. A new application of IRON in the streets of the metropolis has, for some weeks, excited considerable attention. Instead of paving the streets with stone, it is proposed to pave them with squares pieces of cast-iron, suitably shaped, roughted, and dove-tailed. The experiment has already been tried on the south side of Blackfriars-bridge, and has so far succeeded, that we learn it is intended to pave some streets in the city in this manner, under the auspices of the patriotic Lord Mayor, and to begin with Woodstreet. As we presume there can be no doubt but this plan will answer, we may congratulate the despairing iron-masters and their workmen on a new market for iron; and all large towns, on an immense saving of expense in paving their streets with stones, and on a great diminution in the dust and dirt which now arise from their friction and wear. It is computed that an iron pavement, well adjusted, will endure for twenty years in a great thoroughfare; whereas, it is too well known that a stone pavement requires repairs and re-adjusting two or three times in the year, and renewing every three or four years. The pieces laid down in Blackfriars'-road resemble a batch of eight or nine rolls, as taken from the oven, and they are united like the parts of a dissected map, without interstices or even palpable joints. During many weeks, under every kind of load, and the roughest usage, the firmness of this mass has been undisturbed, and no doubt remains of the success of the experiment. Besides this new and extensive application of Iron, another has presented itself in the Colonnades of the Opera-house, which instead of being composed of the perishable materials of stone, wood, or plaster brick, have been cast in iron; and recommend themselves to admiration, not less by their beauty and precision than by the defiance they set to the ravages of time. Page 291, line 17, from the bottom, after the word attended, insert tø. 292, 292, 293, 295, 295, 295, 296, 296, 297, 300, 314, 233, 338, In our present 370, 372, 33, for Holyoke read Holyoke. 38, for Rev. Thomas Kirkland, read Rev. John T. Kirkland, D. D. LL. D. 22, omit with. 14, omit Rev. Samuel Davis. The Rev. Henry Davis, D. D. was elected president, but declined accepting the office. 27, for two read three. The Hon. John Wheelock, LL D. 43, The Rev. Mr. Anderson and the Rev. Samuel Aus- 18, for Fenley read Finley. 16, after the word three insert the word hundred. 18, from the bottom, for charges read changes. 4, from the bottom, for interpretable read uninterpretable. THE ANALECTIC MAGAZINE. JUNE, 1817. ART. I.-A Course of Mathematics, adapted to the Metho of Instruction in the American Colleges. By Jeremiah Ďay, Professor of Mathematics and Natural Philosophy, in Yale College. Parts I, II, III, and IV, including Algebra, Logarithms and Trigonometry, Navigation and Surveying. New-Haven. 8vo. 1814-1817, IN Na work, like that which we here announce, designed merely to conduct the student through the elements of mathematical science, and adapted, in its extent, to the circumstances of our public seminaries, original matter is not to be expected. The writer will have met every reasonable demand, if he has succeeded in abridging and arranging the materials furnished by original authors, in such a manner as is best fitted to secure the interest, and accelerate the pro gress, of the pupil. As the primary object of the mathematical course, in a system of collegiate studies, it not so much to form professed mathematicians as to discipline the intellectual faculties,-to fix the attention,-to sharpen the inventive powers, and to inspire the student with the love of truth, a compilation for this purpose ought to be chiefly of the scientific cast, and to deliver general principles, rather than practical details. While the successive principles of the science are unfolded in their natural order, and each is established on its proper evidence, without anticipating truths which are to be afterwards proved, the illustrations and proofs ought to be carried to such a length, that no desidera tum shall be left, which ordinary talents and perseverance are inadequate to supply. A style ought to be adopted, which, if destitute, as it must necessarily be, of rhetorical ornament, shall nevertheless interest those who are sensible 56 VOL. IX. to the charms of neatness and precision, and which shall tend to promote a taste for the more chastened and durable beauties of composition. Those general principles and rules which are to be committed to memory, ought to be expressed with the utmost perspicuity and brevity; while a more diffuse and familiar manner, adapted to the capacity of the learner, is best suited to the object of particular illustrations. A system of mathematics, conducted agreeably to these principles, has always been wanting in the public seminaries of our country. In many of them, independent treatises, by different authors, are still used, for the different departments of mathematical study. As these separate treatises, in general, are written without reference to the peculiar wants of a public seminary, and are equally designed for the general scholar, and the practical mathematician, the use of them cannot but be attended with inconvenience. Besides containing many things, considered individually, which are aside from the object of a collegiate course, they do not, taken collectively, form the system that is wanted. In some cases, they interfere with each other; in others, what is taken for granted by the author of a subsequent branch has not been proved by the author of the preceding; and, in no case, can that system of reference be kept up, from one department to another, which can alone give them the character of a coherent body of science. Those institutions in this country, which have adopted a single system, have, we believe, generally given the preference to that of President Webber. This compilation, although not destitute of merit, we must think, with many others who have used it, to be but imperfectly adapted to the purposes for which it was made. Not to mention that it contains numerous errors, some of which are of the most palpable nature, its method is too involved, its omissions are too numerous, and clearness of style is too little regarded, to present the elements of science to the student, in the most attractive form. The illustrations contained in the notes are often loose, often obscure, and very often anticipative of principles, with which the reader must be supposed to be unacquainted. Nor is it sufficiently copious for the present advancing state of science in our literary institutions. Besides containing nothing on the elements of the Fluxional Calculus, there are many topics in the other departments, particularly in Algebra and Trigonometry, which, although strictly elementary, and practically important, are passed over in silence.. The system of Dr. Hutton, although it contains a fund of valuable matter, and deserves one of the foremost places on the shelves of the professed mathematician; yet, as an elementary work for schools, is liable to similar objections with that of Webber; for which, indeed, it afforded a large share of the materials. It is likewise too much shaped to the course of instruction in the military school, for which it was originally designed, to be adapted to the wants of public seminaries at large. The joint compilation of Wood and Vince, however well it may be calculated for an English university, is certainly ill fitted for the use of American colleges. The several topics are discussed with a degree of brevity which renders them obscure to the learner; while the variety of matter introduced is much greater than can be consistently attended to, in our public institutions. In Wood's Algebra, for instance, not less than seventy pages are devoted to the general theory of equations,-a subject by no means elementary, and little connected with the subsequent parts of the course. Among the writings of English mathematicians, we have read none with greater interest than those of Simpson. His arrangement is natural, and his style is easy and pure. His works, however, when taken together, by no means form a complete system. His own investigations, which he often introduces, and which enhance the value of his works to the advanced student, unfit them for the use of the learner. Little more than half of his Algebra, and not half of his Fluxions, could be read, with advantage, by a class of students at college. We congratulate our readers, and the public seminaries of our country, therefore, on the appearance of the fourth Part of a work which is so well adapted, as that of Professor Day, to the satisfaction of their wants. Our readers scarcely need to be reminded, that the first Part, containing Algebra, the second, treating of Logarithms and Trigonometry, and the third, on Mensuration, have already appeared, at considerably distant intervals. Although it is more than two years since the publication of this work commenced, we shall avail ourselves of the opportunity presented by the appearance of the present number, on Surveying and Navigation, to take a retrospect of the whole work, in this stage of its progress. We do this the rather, because the length of time which has elapsed since the publication of the earlier parts of it, will enable us to speak with more confidence of its merits, from having observed its success in practice. |