Page 291, line 17, from the bottom, after the word attended, insert to. 33, for Holyohe read Holyoke. 292, 292, 293, 295, 295, 295, 296, 296, 297, 299, 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. was removed from office in 1816; and the Rev. Francis Brown was appointed in his place. By some legislative transaction the College has become a University, and President Wheelock was reinstated in office; but has since died. 43, The Rev. Mr. Anderson and the Rev. Samuel Austin, D. D. are the only persons who have presided in the college at Burlington; and the Rev. Jeremiah Atwater, D. D. and the Rev. Henry Davis, D. D. at the college of Middlebury, in the state of Vermont. 22, omit and the Rev. John Mason D. D. The Rev. John M. Mason, D. D. was lately Provost, or the first instructor of that college, while the Rev. William Harris, D. D. was the nominal President, or sleeping partner. 31, The Rev. Jonathan Edwards, D. D. (son of the great metaphysician, who was nothing more than the Rev. Jonathan Edwards, A. M.) was the first President of Union College, the Rev. John B. Smith, D. D. the second, &c. 18, for Fenley read Finley. 42, The President of Hampden-Sidney College, the Rev. Moses Hoge, D. D. is also Professor of the Theological Seminary of the Synod of Virginia. But the College and the Seminary are distinct institutions. The Theological Seminary has been aided,' not by the General Assembly of the Presbyterian church,' which would not encourage any rival to that at Princeton, but by the abovementioned Synod. 300, 39, The Rev. Dr. Maxcy is president, we believe, of South Carolina College; and we are certain, that the Rev. Robert H. Chapman, D. D. (and not Dr. M.) is President of the University of North Carolina. 13, from the bottom, for continuations read combinations. 9, for of read half. 314, 233, 338, In our present 370, 372, 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 proois ought to be carried to such a length, that no desideratum 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 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. The work is not a mere compilation. The subjects treated of are necessarily much the same with those which may be found in other writers; but the arrangement, the language, and the examples, are wholly our author's. And if clearness of method, a judicious selection of materials, and perspicuity and neatness of expression, be regarded as furnishing any claims to originality, we think Professor Day is, in no common degree, entitled to the character of an original author.-The general principles, which are printed in a distinct character, and are designed to be committed, possess a degree of brevity, clearness, and precision, which we have seen in no other mathematical work. His illustrations are generally somewhat diffuse; but uniformly luminous, and adapted to the capacity of the learner. He appears to us to possess, in a degree unusual in men of profound science, the power of placing himself in the attitude of a learner, of feeling his difficulties, and of hitting on the most happy expedients for removing them. When an obstacle is to be removed, the most advantageous position is assumed, and the lever uniformly applied at the right spot. As examples of this fortunate mode of illustration, we might refer our readers, among many others, to the distinction given between positive and negative quantities, to the explanation of the reduction of a problem to the language of Algebra,-to the remarks on the reduction of affected quadratics,-to the illustration of mathematical infinity, or, in the last Number, to the view given of the principles of Mercator's chart. Here, if the adept in science finds nothing absolutely new, he will at least find known truths placed in a stronger light, and happier attitude. In regard to his illustrations, our author has taken for his model the familiar, diffuse manner of Euler and Lacroix, rather than the concise, abridged mode of the English writers. The reasons which have induced him to carry his explanations to a greater length than most elementary writers have done, may be found in the Preface to the Algebra. Although they appear, on the whole, sufficient, this method is liable to an objection which our author has not noticed. He has, indeed, furnished us with a highway up the difficult ascents of mathematical science; in travelling which the student of ordinary talents and diligence will find little to impede his progress: But some may question whether an obstacle occasionally left to be removed by his own exertions,— a step in the ascent required to be dug by his own labour,— will not ultimately contribute to accelerate his march. Admitting that 'hours may be spent, in supplying an explanation, |