MATHEMATICS.

Airy.-Works by SIR G. B. AIRY, K. C.B., Astronomer Royal :

ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the UniverWith Diagrams. Crown 8vo. cloth. 5s. 6d.

sities.

It is hoped that the methods of solution here explained, and the instances exhibited, will be found sufficient for application to nearly all the important problems of Physical Science, which require for their complete investigation the aid of Partial Differential Equations.

ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS. Crown 8vo. cloth. 6s. 6d.

In order to spare astronomers and observers in natural philosophy the confusion and loss of time which are produced by referring to the ordinary treatises embracing both branches of probabilities (the first relating to chances which can be altered only by the changes of entire units or integral multiples of units in the fundamental conditions of the problem; the other concerning those chances which have respect to insensible gradations in the value of the element measured), the present tract has been drawn. up. It relates only to errors of observation, and to the rules, derivable from the consideration of these errors, for the combination of the results of observations.

Airy (G. B.)-continued.

UNDULATORY THEORY OF OPTICS. Designed for the Use of Students in the University. New Edition. Crown 8vo. cloth. 6s. 6d.

The undulatory theory of optics is presented to the reader as having the same claims to his attention as the theory of gravitation: namely, that it is certainly true, and that, by mathematical operations of general elegance, it leads to results of great interest. This theory explains with accuracy a vast variety of phenomena of the most complicated kind. The plan of this tract has been to include those phenomena only which admit of calculation, and the investigations are applied only to phenomena which actually have been observed.

ON SOUND AND ATMOSPHERIC VIBRATIONS. With the Mathematical Elements of Music. Designed for the Use of Students of the University. Second Edition, Revised and Enlarged. Crown 8vo. 95.

This volume consists of sections, which again are divided into numbered articles, on the following topics: General recognition of the air as the medium which conveys sound; Properties of the air on which the formation and transmission of sound depend; Theory of undulations as applied to sound, &c.; Investigation of the motion of a wave of air through the atmosphere; Transmission of waves of soniferous vibrations through dif ferent gases, solids, and fluids; Experiments on the velocity of sound, &c.; On musical sounds, and the manner of producing them; On the elements of musical harmony and melody, and of simple musical composition; On instrumental music; on the human organs of speech and hearing.

A TREATISE OF MAGNETISM.

Designed for the use of

Students in the University. Crown 8vo. 9s. 6d.

As the laws of Magnetic Force have been experimentally examined with philosophical accuracy, only in its connection with iron and steel, and in the influences excited by the earth as a whole, the accurate portions of this work are confined to the investigations connected with these metals and the earth. The latter part of the work, however, treats in a more general way of the laws of the connection between Magnetism on the other hand and Galvanism and Thermo-electricity on the other. The work is divided into Twelve Sections, and each section into numbered articles, each of which states concisely the subject of the following paragraphs.

Airy (Osmund).

A TREATISE ON GEOMETRICAL OPTICS. Adapted for the use of the Higher Classes in Schools. By OSMUND AIRY, B.A., one of the Mathematical Masters in Wellington College. Extra fcap. 8vo. 3s. 6d.

“This is, I imagine, the first time that any attempt has been made to adapt the subject of Geometrical Optics to the reading of the higher classes in our good schools. That this should be so is the more a matter for remark, since the subject would appear to be peculiarly fitted for such an adaptation. I have endeavoured, as much as possible, to avoid the example of those popular lecturers who explain difficulties by ignoring them. But as the nature of my design necessitated brevity, I have omitted entirely one or two portions of the subject which I considered unnecessary to a clear understanding of the rest, and which appear to me better learnt at a more advanced stage."—AUTHOR'S PREFACE. "This book," the ATHENÆUM says, "is carefully and lucidly written, and rendered as simple as possible by the use in all cases of the most elementary form of investigation."

Bayma.-THE ELEMENTS OF MOLECULAR MECHA-
NICS. By JOSEPH BAYMA, S. J., Professor of Philosophy,
Stonyhurst College. Demy 8vo. cloth.
IOS. 6d.
Of the Twelve Books into which the present treatise is divided, the first
and second give the demonstration of the principles which bear directly on
the constitution and the properties of matter. The next three books contain
a series of theorems and of problems on the laws of motion of elementary
substances. In the sixth and seventh, the mechanical constitution of mole-
cules is investigated and determined: and by it the general properties of
bodies are explained. The eighth book treats of luminiferous æther. The
ninth explains some special properties of bodies. The tenth and eleventh
contain a radical and lengthy investigation of chemical principles and
relations, which may lead to practical results of high importance. The
twelfth and last book treats of molecular masses, distances, and powers.

Beasley.-AN ELEMENTARY TREATISE ON PLANE
TRIGONOMETRY. With Examples. By R. D. BEASLEY,
M.A., Head Master of Grantham Grammar School. Third
Edition, revised and enlarged. Crown 8vo. cloth.
This treatise is specially intended for use in schools. The choice of matter
has been chiefly guided by the requirements of the three days' examination

3s. 6d.

at Cambridge. About four hundred examples were added to the second edition, mainly collected from the Examination Papers of the last ten In this edition several new articles have been added, the examples have been largely increased, and a series of Examination Papers appended.

years.

Blackburn

(Hugh). — ELEMENTS OF PLANE TRIGONOMETRY, for the use of the Junior Class of Mathematics in the University of Glasgow. By HUGH BLACKBURN, M. A., Professor of Mathematics in the University of Glasgow. Globe 8vo. Is. 6d.

The author having felt the want of a short treatise to be used as a Text-Book after the Sixth Book of Euclid had been learned and some knowledge of Algebra acquired, which should contain satisfactory demonstrations of the propositions to be used in teaching Junior Students the solution of Triangles, and should at the same time lay a solid foundation for the study of Analytical Trigonometry, thinking that others may have felt the same want, has attempted to supply it by the publication of this little work.

Boole.-Works by G. BOOLE, D.C.L., F.R.S., Professor of Mathematics in the Queen's University, Ireland.

A TREATISE ON DIFFERENTIAL EQUATIONS. New and Revised Edition. Edited by I. TODHUNTER. Crown 8vo. cloth. 145.

Professor Boole has endeavoured in this treatise to convey as complete an account of the present state of knowledge on the subject of Differential Equations as was consistent with the idea of a work intended, primarily, for elementary instruction. The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connection with the methods and processes of his previous course. A treatise incomparably superior to any other elementary book on the same subject with which we are acquainted."-PHILOSOPHICAL MAGAZINE.

A TREATISE ON DIFFERENTIAL EQUATIONS. Supplementary Volume. Edited by I. TODHUNTER. Crown 8vo. cloth. 8s. 6d.

Boole-continued.

This volume contains all that Professor Boole wrote for the purpose of enlarging his treatise on Differential Equations.

THE CALCULUS OF FINITE DIFFERENCES. Crown 8vo. cloth. IOS. 6d. New Edition, revised by J. F. MOULTON. In this exposition of the Calculus of Finite Differences, particular attention has been paid to the connection of its methods with those of the Differential Calculus—a connection which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to Professor Boole's Treatise on Differential Equations. "As an original book by one of the first mathematicians of the age, it is out of all comparison with the mere second-hand compilations which have hitherto been alone accessible to the student."-PHILOSOPHICAL MAGAZINE.

Brook - Smith

(J.)-ARITHMETIC IN THEORY AND PRACTICE. By J. BROOK-SMITH, M.A., LL.B., St. John's College, Cambridge; Barrister-at-Law; one of the Masters of Cheltenham College. Complete, Crown 8vo. 4s. 6d. Part I. 3s. 6d.

Writers on Arithmetic at the present day feel the necessity of explaining the principles on which the rules of the subject are based, but few as yet feel the necessity of making these explanations strict and complete. If the science of Arithmetic is to be made an effective instrument in developing and strengthening the mental powers, it ought to be worked out rationally and conclusively; and in this work the author has endeavoured to reason out in a clear and accurate manner the leading propositions of the science, and to illustrate and apply those propositions in practice. In the practical part of the subject he has advanced somewhat beyond the majority of preceding writers; particularly in Division, in Greatest Common Measure, in Cube Root, in the Chapters on Decimal Money and the Metric System, and more especially in the application of Decimals to Percentages and cognate subjects. Copious examples, original and selected, are given. "This strikes us as a valuable Manual of Arithmetic of the Scientific kind. Indeed, this really appears to us the best we have seen." -LITERARY CHURCHMAN. This is an essentially practical book, providing very definite help to candidates for almost every kind of competitive examination."-BRITISH QUARTERLY.

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