it is perhaps the leading characteristic of the following work, that, while it contains all the tables and rules for computation necessary for the practical seaman, it contains also the investigation of the rules, and the preparatory mathematical information necessary to make the investigations understood.

The introductory article on the Principles of Algebra is intended merely to enable the student to read, without difficulty, the analytical investigations in Plane and Spherical Trigonometry; and the spaces allotted to the other elementary branches of science have been in some degree proportioned to their relative importance. They will be found sufficient to serve the purpose for which they are chiefly intended, and perhaps also to excite that taste for demonstrative science which it ought to be one great object of mathematical instruction to superinduce.

The principal and most useful trigonometrical formulæ are written out in words, in the form of practical rules; and the whole of the work has been so arranged that the theoretical and the practical parts may he taught either separately or jointly; so that those who have not leisure, inclination, or talent, to master the theory, may content themselves with learning its practical application.

The principles of Navigation are explained at con

siderable length, and their application shown in the solution of a variety of problems in Plane, Parallel, Middle Latitude, and Mercator's Sailing, in keeping a Sea Journal, and the construction of Charts.

An investigation is given of the principles of the Quadrant, and other reflecting instruments for nautical observations. In teaching the practical use of these instruments, in our unsteady climate, opportunities sufficiently numerous for the student to exercise himself in observing, are not always to be obtained during the ordinary hours of school attendance; and this is particularly the case with respect to lunar distances. A convenient expedient for exercising young observers in the method of making this class of observations, is to make them observe the distance of the sun from his image, as reflected from a plane mirror, or a piece of polished glass. By placing the glass in different situations, the relative positions and distances of the sun and his image may be so varied, as to afford exercise in managing the instrument in every way in which it can be required to be held; and the distances may any time be made either increasing or decreasing, and to vary either quickly or slowly; so that the student may, in this way, be taught to observe in every variety of circumstances under which an actual observation can be taken.

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The practical solutions of the most useful problems. in Nautical Astronomy will, it is hoped, be found as simple as can be desired. The method of finding the latitude by double altitudes of the sun, is derived from a solution of the problem originally given by J. IVORY, Esq.; and the methods of clearing the lunar distance from the effects of parallax and refraction, are deduced from formula which were first investigated by that accomplished navigator the late J. DE MENDOZA RIOS.

The investigations which are given of the practical rules, will present no difficulty to those who understand the theory of Plane and Spherical Trigonometry as given in the preceding parts of the work; and the concluding Miscellaneous Nautical Problems will afford sufficient variety to guide the student in applying his knowledge of Spherics in the solution of any useful problem that can arise in actual practice.

Very great care has been bestowed on the Tables, and it is presumed that few errors of any practical importance will be found in them. The Tables of Figures have been stereotyped, which will ensure the continuance of whatever accuracy they at present possess, while it will admit the correction of any error that may hereafter be discovered. With respect to Tables, the work has one advantage which in schools will be found of considerable importance. It contains

every table requisite in solving the different examples; the necessary parts of the Nautical Almanac being given for the time to which the examples are fitted which require its aid. Another advantage which the work possesses in this respect, is of not less importance in practice. The tables of the sun's declination, right ascension, and the equation of time, here given, with the auxiliary table for reducing them to subsequent years, will enable the mariner to find his longitude with sufficient exactness by a chronometer for more than sixty years to come, without the aid of the Nautical Almanac.

A work from which any branch of science is intended to be taught should abound with practical examples; and the following work will in that respect be found to answer its object. The examples which require numerical computation are chiefly new; and in making such a multiplicity of calculations, it is very probable that a wrong figure may have sometimes passed unobserved, though it is believed that this can have happened but seldom.

For the elementary theorems in the different branches of science it would, in most instances, be difficult for the author to say to whom he is indebted; as they have long been the common property of every writer on those subjects. But in one instance he is under no

such difficulty; it is chiefly to the excellent collection of "Geometrical Problems," by Mr. BLAND, that he is indebted for the Examples for Exercise in Geometrical Investigation, and the solutions of these problems may be seen in Mr. BLAND'S volume.

In concluding, the author has only to add, that he has endeavoured to adapt his work at once "to Practice, and to the Purposes of Elementary Instruction;" how far his endeavours may be calculated to answer their intended purpose must be left with the public to determine.

ROYAL NAVAL ASYLUM, GREENWICH.

February 16, 1824,