One of the most remarkable books of the month is The Logic and Utility of Mathematics, by Charles Davies, LL.D., published by Barnes and Co. It is not intended as a treatise on any special branch of mathematical science, and demands for its full appreciation a general acquaintance with the leading methods and routine of mathematical investigation. To those who have a natural fondness for this pursuit, and enjoy the leisure for a retrospect of their favorite studies, the present volume will possess a charm, not surpassed by the fascinations of a romance. It is an elaborate and lucid exposition of the principles which lie at the foundation of pure mathematics, with a highly ingenious application of their results to the development of the essential idea of Arithmetic, Geometry, Algebra, Analytic Geometry, and the Differential and Integral Calculus. The work is preceded by a general view of the subject of Logic, mainly drawn from the writings of Archbishop Whately and Mr. Mill, and closes with an essay on the utility of mathematics. Some occasional exaggerations, in presenting the claims of the science to which his life has been devoted, must here be pardoned to the professional enthusiasm of the author. In general, the work is written with singular circumspection; the views of the best thinkers on the subject have been thoroughly digested, and are presented in an original form; every thing bears the impress of the intellect of the writer; his style is for the most part chaste, simple, transparent, and in admirable harmony with the dignity of the subject, and his condensed generalizations are often profound and always suggestive.
The Gallery of Illustrious Americans, edited by C. Edwards Lester, Esq. has reached its seventh number, which contains a portrait and biographical sketch of the distinguished ornithologist, J. J. Audubon. The engraving presents a delightful view of the intellectual and expressive features of the veteran forester, savan, and artist, while the sketch by Mr. Lester gives a rapid and satisfactory summary of the principal incidents in his adventurous life. The daguerreotypes by Brady, and the lithographs by D'Avignon, throughout this series, are highly creditable specimens of their respective arts. The biographical notices are carefully written and beautifully printed. The previous numbers embrace Taylor, Calhoun, Webster, Wright, Clay, and Fremont—and that our readers may form some idea of the striking fidelity of the Portraits, we present, in a previous page, the well-known likeness of our late President, copied on wood by Lossing, from the first number of the work.
A. Hart, Philadelphia, has reprinted from the English edition, The Phantom World, from the French of Calmet, with a Preface and Notes by Rev. Henry Christmas, giving a general survey of the history and philosophy of spirits, apparitions, ghosts, elves, fairies, spooks, bogles, bugaboos, and hobgoblins. It will probably meet with an extensive circulation in these days when Connecticut divines are haunted by infernal visits, and the Rochester sibyls are on exhibition in New York.
Dies Boreales, or Christopher Under Canvas, is republished from Blackwood's Magazine in a neat edition, by A. Hart, Philadelphia, and will meet with a warm reception from the innumerable admirers of the noble, eloquent, impassioned, kaleidoscopic, frisky, and genial old Christopher.
Among the valuable scientific serials now issuing from the New York press, is The Dictionary of Mechanics, Engine Works, and Engineering, edited by Oliver Byrne, and published by D. Appleton and Co. Of this work we have thirteen numbers, which bring the subjects, in alphabetical order, to the article on "Etching," the last number completing the elaborate description of the "Steam Engine," which in itself forms a treatise on a leading branch of practical science, and may be commended in high terms to the attention both of the general reader and the professional engineer. It is rarely that such a mass of important information is condensed into so lucid and pleasing a form, attractive no less by the clearness of its scientific details, than by the bright picture which it gives of the progress of the useful arts in modern times.
Another work, of similar value, is A Treatise on Marine and Naval Architecture, by John W. Griffiths, a serial which has reached its seventh number, and has elicited the warmest encomiums from distinguished constructors and engineers. The style is a fine model of scientific discussion, presenting the first principles of naval architecture with precision, compactness, and simplicity, abounding with graphic descriptive details, and preserving a spirited freedom and boldness in the most intricate and difficult expositions. The superior character of its contents, with the low price at which it is afforded, will insure it a wide circulation among American mechanics, who can not fail to gain both a pecuniary and an intellectual advantage from its perusal.
Specimens of the Bridges, Viaducts, &c., on the United Slates Railroads, by George Duggin, deserves an honorable place by the side of the two preceding serials, as an important contribution to the science of civil engineering in this country. The sixth number has already made its appearance, being the commencement of an elaborate treatise on Bridge-building, illustrated with sketches of the most remarkable specimens in this branch of architecture. The multiplicity of works like those we have just alluded to, and the great and instant popularity which they attain, present a cheering proof of the prevalence of scientific curiosity, and of the mental activity which leads to thorough investigation, among the leading artisans of the United States.
The Second Book in Greek, by John M'Clintock, published by Harper and Brothers, is the complement to the previous volume, entitled First Book in Greek, which, as a practical manual in this branch of philology, has elicited the warmest approbation of judicious teachers. Dr. M'Clintock has brought the resources of a ripe and generous scholarship to the preparation of this work, which, with the other volumes of his Elementary Series in Greek and Latin, is a highly honorable proof of his sound learning and correct taste. The present work gives a full view of the Greek Syntax, with copious illustrations, and extracts from Xenophon's Anabasis, Homer, Anacreon, and sentences from the Greek Dramatists. Its peculiar merit consists in the progressive manner in which the various difficulties of Greek combination are unfolded, the pupil being thus led forward, by a natural sequence, to a mastery of the complicated idioms of the language, and trained imperceptibly to a perception of its rich and wonderful beauties.
Lea and Blanchard, Philadelphia, have republished Impressions and Experiences of the West Indies and North America in 1849, by Robert Baird, an intelligent Scotchman, apparently of the legal profession, but with little of the talent essential to the composition of a popular book of travels. His remarks on the United States are in a more discriminating tone than is often attained by English tourists, but the whole tone of the volume is, for the most part, so prosy and commonplace as to make its perusal an intolerable bore.
Tallis, Willoughby, and Company are publishing a beautifully embellished edition of The Life of Christ, by the Rev. John Fleetwood, with original illustrations by Warren, who has attained a distinguished reputation, as a delineator of Oriental scenery, characters, and costumes. It is to be completed in twenty-five parts, of which two have been issued, in a style of elegant typography, highly creditable to the taste and enterprise of the publishers. The biography of the Saviour by Dr. Fleetwood is written with decorum and gravity, reproducing the consecutive events of the sacred narrative in symmetrical order, and presenting with becoming reserve, such moral reflections as are naturally suggested by the different topics of the sublime history. The work is happily distinguished from several recent attempts on similar themes, by its freedom from the ambitious and disgusting pretension of dressing up the severe simplicity of the Oriental writers in the tawdry and finical robes of modern rhetoric.