the subject of aberration, completely overthrows this theory, and establishes, beyond a doubt, the earth's annual motion in its orbit. 4. Precession. The intersection of the Equator and Ecliptic, has a slow annual retrograde motion of 50" nearly. This causes the pole of the equator to describe a circle about the pole of the ecliptic; and hence arise errors in declination and right ascension, which require computation. The precession was first remarked by Hipparchus, who discovered it by comparing his own observations with the more antient ones of T'imocharis and Aristillus. 5. Lastly, Nutation. While Bradley was engaged in his inquiry into the aberration, he observed small inequalities in the precession of the equinox, and in the mean obliquity of the ecliptic, to which, accounting for them by conceiving the axis of the earth to have an oscillatory motion, he gave the name of Nutation. This inequality affects all the heavenly bodies; and, when used as a correction, their places are found to agree much more accurately with observation, than when it is not applied. To the discussion and explanation of these Corrections, eight chapters are devoted-which, however, is no more than their consequence, and the important theories connected with them, absolutely require. We next come to the Solar Theory, in which the most material discussion is, the determination of the Sun's place by what is called Kepler's Problem. Kepler was one of those rarely gifted men, whom Nature has given to the world, to enlarge the boundaries of science-to enrich it by his discoveriesand to lay the foundation of systems, which the labours of future philosophers might ripen to maturity. The friend and disciple of Tycho Brahé, he had the advantage of a constant residence with that great practical astronomer, during the latter years of his life and at his death, he obtained the accumulated mass of observations, which the incessant labour of one-and-twenty years at his Observatory, in the little island of Huon, had enabled him to collect. These observations formed, in fact, the groundwork of Kepler's discoveries; and the great services they were thus the means of rendering to astronomy, sufficiently atone for the erroneous ideas they led Tycho to adopt, in his misconceived system of the universe. In the hands of Kepler, they produced the three most important discoveries which have ever been made in natural science. He began his inquiries respecting the form of the planets' orbits, conceiving, with Copernicus, that they moved in circles with an uniform motion; and by a most fortunate chance he fixed upon Mars, as the planet whose motions he should first investigate. His choice of Mars was fortunate, inasmuch as the orbit of this planet is one of the most. eccentric in the system; so that the inequalities, and consequently the laws of its motion, were more easily detected. He soon perceived, that supposing the orbit to be circular, the sun was not situated in the centre, as had been supposed, but in some intermediate point between the centre and circumference. To discover this point, that is, to find the eccentricity of the orbit, was his next inquiry. He proceeded by tentative methods, of the most laborious kind; he made no less than seventy suppositions before he got one to agree with observation. Having determined the eccentricity, he proceeded to compare the latitudes, in opposition, and the longitudes out of opposition, computed upon his hypothesis, and those found by observation. A very marked difference between them, led him to suspect that the erfor was in his hypothesis, and not in the inaccuracy of Tycho's observations: He then conjectured, that the orbit of Mars was not a circle; but, undismayed by want of success, he resolved to give it another and a fuller trial, upon a different plan. He observed two positions of the carth when Mars was in the same part of his orbit, he then found the difference of the longitudes of the Sun and Mars;-and thence, by a trigonometrical calculation, ascertained the distance of Mars from the Sun. In this manner he observed three distances; and then calculated the same three distances on his hypothesis of the circular orbit, and compared them with the observed distances: But here, as in his former process, the difference was so great, as to compel him altogether to abandon the supposition, that the orbit of Mars was a circle. The result of his attempts, however, was such, that he was persuaded the orbit did not materially differ from that form. It must therefore be an oval; * and if so, there was no figure so probable as an ellipse, having the sun in one of the foci. Upon this hypothesis, which certainly was not the result of chance as some have been hardy enough to assert, he again calculated the three distances, and found they agreed most accurately with ob servation. The orbit of Mars being thus determined, he naturally imagined, that the other planets described similar orbits about the sun. Applying the same tests, his conjecture was verified, and the great and important truth was at last established, * Orbita planetæ non est circulus, sed ingrediens ad latera utraque paulatim, iterumque ad circuli amplitudinem in perigo exiens, cujusmodi figuram itineris ovalem, appellitant. De Motibus Stella Martis. p. 213. that the planets revolve in elliptic orbits of small eccentricity, having the sun situated in one of the foci. His next object was to find an area of the ellipse proportional to the time-(he had already proved, that areas described by a line drawn from the sun to a planet, were proportional to the times of description); and this is what is called Kepler's Problem. The accurate solution is by no means easy. Mr Woodhouse has given two methods;-in the first, he has deduced equations from which an accurate solution may be obtained, the further investigation of which is reserved for the second volume of this work ;-the other is an approximate method, considerably casier—and although it does not give a complete solution, it is sufficiently accurate for the purposes of the practical astronomer. But before this problem can be used in determining the sun's place, it is necessary that the position of the apsides of the sun's orbit be known. Our attention is next directed to the longitude and progression of the Aphelion; and the method of finding these is that given by Lacaille. Mr Woodhouse next illustrates, by an example, the manner of determining the Sun's longitude from Solar Tables, constructed by means of Kepler's Problem; and shows, that the result differs from the Sun's longitude, as expressed in the Nautical Almanack, by a small error of 47". Hence Kepler's Problem will not alone suffice to determine accurately the sun's place. The above error will require a correction ;-and this is supplied by investigating the inequalities of the Earth's motion, produced by the disturbing forces of the sun and moon. We have then to consider these bodies, whose masses are known, projected from given points, in given directions and with given velocities, and gravitating to one another with forces that are directly as their masses, and inversely as the squares of their distances, to trace the orbits they describe, and to find their positions at any given time. This is no other than the celebrated problem of the Three Bodies; and so great is its difficulty, that the highest refinements of modern analysis, have hitherto been inadequate to furnish a general and complete solution. The problem of Two Bodies gravitating to one another, was fully solved by Newton; but when he attempted, by a similar process, to find the place of a body attracted by one, and at the same time disturbed by another body, the instruments he employed were insufficient to combat the extreme difficulties of the case. His inquiries, however, were not altogether fruitless; he detected five very remarkable inequalities in the Moon's motion, which he explained by the disturbing force of the Sun; and his theories, verified by the researches of succeeding mathematicians, and by methods of calculation essentially different from those which he employed, create in us the greatest astonishment, that a man, by the force of his single genius,-no way benefited by the speculations of those who went before him,-no way assisted by the efforts of his cotemporaries-should have made such progress in a science so abstruse.. To estimate his merit,' as Mr Woodhouse tells us, we must take science as he found it, and as he left it. He did not merely add to, or beautify a system. Newton's merit was more than that of having left marble what he found brick: For he laid the very foundations of Physical Astronomy, and furnished the materials and means of putting them together.' The investigation of these different inequalities, as well as those which arise from the disturbing forces of the planets, do not belong to Plane Astronomy. The inquiry is therefore reserved for the second volume. The Planetary succeeds the Solar theory. In this the heliocentric and geocentric longitudes and latitudes of the planets, and their periods, are fully discussed. This is followed by the Lunar theory, which, in our opinion, ought to have preceded it. The inequalities affecting the earth's orbit, and those affecting the moon's, are so intimately connected in the problem of the Three Bodies, that the Solar and Lunar theories should not have been separated. Moreover, this is the arrangement which is followed in the second volume of this work. The eclipses of the sun and moon, too, would have fallen better in with this order, and the simplicity of the whole been more completely preserved. This volume concludes with the various methods of finding latitudes and longitudes. Among these, the very useful way of determining the longitude of a ship at sea, by the distance of the Moon from the Sun, or from a fixed star, is explained at some length. Borda's formula for correcting that distance, by making allowance for the effects of parallax and refraction, is also given here. We have insensibly protracted our remarks upon this volume so much, that we shall have less room to give to the second volume than we could have wished. But we cannot close this, without a singleremark upon Mr Woodhouse's language throughout the whole book. In a subject like Plane Astronomy, where there is less of mathematical reasoning, and more of familiar explanation, it is most essential that such explanations be given in a full and distinct, but at the same time in as concise and compendious a manner as possible. Mr Woodhouse seems to have been so well aware of the first requisites, that the necessity of the others has altogether escaped him. He endeavours, at Bb VOL. XXXI. NO, 62. all times, to be so lucid, that his explanations, like cross lights thrown upon a picture, tend only to perplex the subject; and, by bewildering our intellects, prevent us from obtaining any clear or distinct notions respecting it. We have not room to give many extracts to instance this obscurity of style-but they occur perpetually. We open the book at random, (at the ninth page, for example), where Mr Woodhouse is instructing us respecting the motion of the sun:-It is thus announced- The Sun has evidently a proper and peculiar motion. He moves towards the stars that set after him, and from the stars that rise before him. In other words, amongst the fixed stars he moves from the west towards the east; that is to say, to a spectator in our hemisphere facing the south, from the right hand to the left.' Add to this, that the sun appears to us to move from east to west; and we venture to affirm, that the generality of readers, upon perusing the above explanation, will exclaim, Then, in the name of all that is lucid, how does the sun move?' Mr Woodhouse seems also to labour under a perpetual apprehension lest the proportion of the lines in his figures, not being always accurately kept, should lead his readers into error, or weaken the vigour of his demonstrations. His concern about this mistake seems quite disproportionate to the danger; and the earnestness with which he cautions the reader against it, seems to us sometimes ludicrous. We come now to the second volume-containing Physical Astronomy, in which Mr Woodhouse appears to much greater advantage. The principal objects of inquiry are, the Solution of the Problem of the Three Bodies, and the Investigation of the Motions and Perturbations of the Principal Planets. Some other inquiries relating to this subject are slightly entered into, and many wholly omitted. Indeed, from the size of this volume, it is impossible that the greater part of this extensive subject could be contained in it. But the topics we have mentioned are very fully discussed, and the investigations carried on, as far as is requisite for the purposes of this work. It is admirably adapted to be a stepping-stone to the Méchanique Céleste of La Place; but it is not intended to be a complete system in itself, nor are its processes pursued to that degree of accuracy necessary for the construction of Lunar or Planetary tables. But we must object to its being called an Elementary Treatise. The theories it contains are of a very abstruse and complicated nature in themselves; and, even to understand the language in which they are explained, requires a considerable knowledge of the principles of the Calculus, and no small degree of proficiency in its |