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