same title but of little more than half the size; and every reader will, we think, agree in the author's remark in his preface to the present publication, that instead of calling it a new edition he might have called it a new work. The second Volume was published in the year 1818, but we trust this circumstance need not prevent us from attempting to give some account of its valuable contents in conjunction with the later publication.

The primary object for which the work before us is des tined, is academical instruction. In its former state it was highly esteemed in reference to this purpose, and we understand has become the text book at the distinguished seat of science from which it emanates. Its appearance in an extended and improved form is cotemporary with the increased stimulus and facilities to the study of astronomy in that place, from the establishment of an observatory there, now nearly completed. Our author has extended his preface to introduce several judicious remarks on this topic. He seems particularly careful not to allow his readers to raise too high expectations of the benefits to accrue from such an establishment, whilst he points out the real advantages likely to attend it.

"Such institutions," he observes, "can hardly fail to augment science; they will do some good, although perhaps not all the good that is intended to be done by them."

The instruction of academical students in the use of instru- · ments, and in practical astronomy, he states to be one object, though a subordinate one, of this institution. "It is not however," he remarks," to be used as a kind of astronomical toy, and to become the mere resort of leisurely amateurs and random star-gazers." It is to the completion of a regular and systematic study of astronomy that the use of an observatory thus opened to the student is to tend. And it can hardly be doubted, that by thus combining experimental with theoretical instruction, much more will be effected than the mere perusal of the best works could, without such assistance, accomplish. It seems that in the new edition, or we might almost call it, new work which the author has now given to the public, he has had a special regard to preparing the student for a profitable use of the advantages thus to be opened to him. He has increased his work to nearly double its original size, chiefly by the introduction of much valuable information on the principles of the construction and use of astronomical instruments and again, by elucidating each chapter with extensive and appropriate examples. The numerous and well selected cases of actual observation, with which every part of this treatise is thus amply illustrated, will no doubt

make it doubly acceptable to those students who have the advantage of access to the instruments of an observatory; an advantage (as we have seen) shortly promised to the Cam bridge learners: and one which has been long accessible to those of the Sister University: but we cannot forbear remark. ing, with how little benefit. In the seat of Wallis, of Halley, and of Bradley, how little, even of their names is known. With one of the most splendid observatories in Europe,remarkably favoured by local circumstances, furnished with the best instruments, and, we may be allowed to add, presided over by a professor of the most unquestionable genius and attainments, how entirely insensible does this learned body seem to the advantages it possesses.

The very appearance of the observatory is such, that we cannot be surprised at the remark of a visitor on traversing its grass grown court and its chill and desolate halls, " Is any thing ever done here?" We would not be thought to insinuate any thing against the distinguished Radcliffian observer, it is well known that his excellent observations are indefatigably continued and regularly communicated to the Royal Society. Nor would we for a moment be thought to undervalue his admirable lectures, but what we cannot forbear remarking is, that with such inducements and advantages it should be an event of the most rare occurrence that a sufficient class is collected to attend those lectures: that when this does happen, the number is observed to diminish at each successive lecture,-as the subject becomes a little more complicated. And that as to fixing the truths of the science in the mind by actual practice with the instruments, the establishment (for any such good derived from it) might as well be a hundred miles distant. The fact is, it is in vain that at the observatory every explanation, encouragement, and invitation is afforded, if there be no corresponding stimulus in the schools; for there, under the present order of things, must be the primum mobile. If the work before us should become as much known and valued as it deserves to be, in Oxford, it will undoubtedly lead the way to many other improvements in the state of mathematical science and instruction in that seat of learning: the necessity for instance of an acquaintance with the higher analytics, in order to the complete study of these volumes, will lead to more enlarged views of mathematical study than are at present usually entertained there. We will not, however, digress any further on these points, but proceed to a slight sketch of the contents and nature of the work before us.

VOL. XX. AUGUST, 1823.

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The first few chapters of the work contain a general survey of the principal phenomena which it is the business of plane astronomy to investigate. In this part of the work elementary explanation is the principal object in view. The student is here made acquainted with the general features of those subjects which he is afterwards led to investigate in detail. The clearness with which the different subjects are elucidated, is such as we conceive can leave nothing to be desired even by the student of the most obtuse comprehension. The description of the appearances of the heavens, and of the imaginary lines and circles to which those appearances are referred, in order to be susceptible of accurate measure ́ment, are given in the most familiar form of illustration, and in a method totally devoid of all formality, and unnecessary and pedantic use of difficult terms. Those technical words, which it is necessary for the student to take out of their ordinary acceptations, and limit to the designation of some peculiar ideas belonging alone to the phenomena under his consideration, are not formally assembled in a list of definitions, with which the memory is apt to be burdened before the understanding has occasion to use them, but are introduced only when the explanation has arrived at that point where a fixed word is wanted as a term of reference, and where the student has become well acquainted with the thing before he learns the sign.

The explanation of the heavenly phenomena commences in the most simple and natural manner possible, not like many popular introductions where the first object presented to the contemplation of the student is nothing less than (as such works have it,)" the sun, a huge globe of fire in the centre, round which revolve the primary planets, in the following order," &c. a sort of description which it is utterly impossible the learner can connect with any appearances presented by the heavens to his eye. In the work before us, on the contrary, the first view of the subject is deduced from a simple inspection of the appearances which the sky presents on a clear evening, and the observations of the changes which take place in those appearances from hour to hour and from night to night. From this simple view by the most natural and gradual progress, the student is conducted to the consideration of the modes of measuring and estimating the apparent changes, and from thence to deduce a knowledge of the real nature of those changes, and of the mode in which they are brought about: to transfer in short the apparent positions of the heavenly bodies seen, as the eye refers them, upon an imaginary concave surface, to their real positions, as reasoning clearly indicates in the depths of space.

Having in the way of general illustration explained those points, such as the earth's and planet's motions, the seasons, phases of the moon, &c. which are perceptible without instrumental measurement, and having explained the nature of the principal phenomena, the author is next led to the examination of such subjects as require accurate instrumental determination, and to the investigation of the quantities of observed effects.

Here then, he is naturally brought to the description of the principal astronomical instruments. The object of their contrivance is, that of affording means for the determination of the position of a point in the imaginary surface of the heavens. Now such position is determined by the interseotion of lines in two directions, one being that of the terrestrial meridian, the other at right angles to it.

Astronomical instruments must therefore essentially be of two classes, adapted to these two sorts of measurement. A tube or telescope moveable accurately in the plane of the meridian, and capable of indicating with exactness the arc intercepted by the direction of a point in the heavens with that of a plumb-line, will afford the vertical measurements wanted. With respect to the second sort of measurement no such simple and obvious means are applicable. The consideration of time is introduced. And by means of a clock, regulated with the requisite exactness, and an instrument fixed with precision in the plane of the meridian the time of the passage of the point or body in question is determined, and hence its position in perpendicular distance from the meridian. And from this, combined with the former, its position on the supposed surface with respect to some assumed fixed point, is ascertained. Such may be considered the simple and fundamental principle of all astronomical observations. Simple, however, as this may appear in theory, the practical application of it involves the greatest difficulty. The most important parts of the different instrumental adjustments are treated with great clearness and ability in the fifth Chapter, and illustrated by well executed wood cuts. The most valuable illustration will however be found in the constant recurrence to actual examples. And the best directions are given throughout, by which the student may be guided in the still further and better elucidation of the subject by the practical trial of the use of the instruments; a mode of illustration more necessary and more efficacious perhaps in this, than in any other branch of science.

After the description and use of instruments, some of the. more simple phenomena observable by means of them are to

be described. Among these by a comparison of positions, as just described, from time to time are the various particulars of the Sun's motion, path, &c. determined, and the right ascensions, latitudes, and longitudes of the stars. These subjects being throughout explained by most copious examples.

At the ninth Chapter our author commences the " theory of corrections," which he first explains in a general and popular form, and afterwards proceeds to discuss in detail.

The apparent places of the fixed stars are the first to be determined with accuracy by such observations as we have alluded to, being those to which the situations of the moving bodies are referred, and by which intervals of time measured. Hence the most minute causes of error or discrepancy in such determinations will affect all subsequent ones. Repeated observation has pointed out many inequalities which cause the apparent places of stars to differ, sometimes from themselves, and always from their mean places: they are however minute, but not on that account the less important to be taken into consideration. Supposing all errors arising from instrumental inaccuracy to be got rid of, there will still remain several sources of inequality inherent in the nature of the observations. The investigation of the corrections for these inequalities, and the deduction of formulæ for computing them, are among the most important objects of plane astronomy, and will necessarily occupy a considerable space in every complete treatise on the science. They accordingly in the present work afford matter for about half the first part.

The formulæ, for some of these corrections depend entirely upon the investigation of the causes of the irregularities which give rise to them,--investigations which belong to the province of physical astronomy and which are not introduced into the first volume of the work, at least, in any degree of detail.

To continue our sketch, the second part of the work consists of the theory of the sun, the planets, and the moon.

From the results of observations the nature of the sun's apparent path is deduced, the mode of computing the obliquity of the ecliptic is hence investigated, and this important process being given, our author proceeds to consider the form of the sun's or earth's orbit, and the laws of its motion. Here then we are introduced to the wonderful discoveries of Kepler; for wonderful they may truly be called, as our author justly observes:

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These, like many other astronomical results, are now so familiar