was nearly balanced by another in his data, in taking the moon's disturbing force considerably greater than its true value. Several other astronomers and mathematicians have since written upon this subject with various success. Bevis, Silvabella, Walmsey, Milner, Simpson, Landen, La Lande, and Robertson, have not proceeded upon correct principles. Several of them, like La Lande, adopted Simpson's erroneous method. D'Alembert, rather vexed to find La Lande had placed his solution upon a par with Simpson's, remarked, with some testiness; 'Le fameux problême de la Précession des équinoxes, dont J'ai donné le premier la solution en 1749, a été depuis bien ou mal résolu par beaucoup d'autres Géometres. M. de la Lande, dans un vaste Recueil qu'il a publié sous le titre d'Astronomie, n'ayant pas distingué celles de ces solutions, qui sont défecteuses d'avec celles qui ne le sont pas, s'est contenté de les indiquer toutes in globo, et de dire qu'elles ne sont pas d'accord.' Dr Horsley, in his edition of Newton's works, adopts the prudent course of not expressing his opinion, and though fond of giving his own notes, and in many cases where no commentary was necessary, in the part treating of the precession, he very unceremoniously turns the reader over to Euler and Simpson, not wishing to decide upon so difficult a point.*

The theory of the tides, first explained by Newton, and afterwards by Maclaurin and Bernoulli, in their prize papers of 1740, has been fully examined by Laplace, in the fourth book of his Mécanique Céleste, and in a paper published in the Memoirs of the Academy of Arts and Sciences of Paris, for 1818. In these works he fully analyses all the effects of the change of distances, declinations, velocities or elongations of the sun and moon, and compares his theory with the observations made at Brest, during two successive periods of six and eight years; giving analytical formulas for computing the times of the tides, their heights, and all the effects arising from the change of situation and distances of the sun and moon; the whole subject being treated very much in detail, and in a satisfactory manner.

*The following is Dr Horsely's note;

Quem tamen longè alium invenerunt viri permagni Eulerus et Simpsonus nostras; quos velim Lector consulas. Ipse nil definio.

Before closing this review, it may not be amiss to mention a few of the most noted works on astronomy, in which the state of the science, as it now exists, may be found. The Astronomie by La Lande, in 3 vols. 4to, third edition, 1792,* is complete up to the time of its publication. It contains a description of astronomical instruments, and the methods of reducing the observations, an account of the most noted European observatories, a good treatise of spherics, with most of the formulas, used in astronomical calculations, and a collection of tables of the motions of all the planets, particularly Delambre's of the Sun, Saturn, Jupiter and its Satellites. This was the standard work to which astronomers referred for nearly half a century; nothing so complete had ever before been published. It contains a number of things that might as well have been omitted, but it is an extremely useful and interesting work for astronomers. Without having mathematical talents of the first order, La Lande, by his great zeal and devotion to astronomy, did much for its improvement. All parts of that science, which required no more than an accurate knowledge of spherics, and the elementary calculations of the perturbations of the motions of the planets, by their mutual attractions, were quite within the compass of his abilities; but when he attempted to explain and calculate the forces, which cause the precession of the equinoxes and the change of the inclinations of the lunar orbit, he laid himself open to the sneers of those, who, like D'Alembert, were offended with his excessive egotism. This foible in La Lande's character was carried to a great excess. It is to be seen in his Bibliographie, at every moment. In mentioning the year 1732, he remarks, 'Cette année, qui est celle de ma naissance, est remarquable pour l'astronomie.' In speaking of his astronomy he says, 'il a été utile en formant presque tous les astronomes qui existent actuellement.' He could bear the most fulsome flattery. His bust, made of Carrarian marble, having been placed in an Italian observatory, mention was made of it in a printed letter, in which it was called il dio dell' astronomia, (the God of Astronomy.) He thought the compliment rather extravagant, but was, notwithstanding,

*There was also a fourth volume relative to the tides at Brest, which was not republished with the third edition.

very much delighted with it. This weakness was, however, useful to astronomy. It induced him to keep up a correspondence with men of science in all parts of the world, and made him, for many years, the centre of information on all astronomical subjects.

The Complete System of Astronomy,' by Professor Vince, in 3 vols. 4to, 1797, 1799, and 1808, contains much useful matter, but it must be acknowledged, that it bears many marks of a crude compilation, particularly in the tables, in some of which the anomaly is counted from the aphelion, in others from the perihelion, some have all the corrections additive, others not; being copied from the works of La Lande, Delambre, and Burg, in the forms in which they were published, without taking the trouble to make much alteration, except in adapting them to the meridian of Greenwich. This mixture of different forms and systems, in the same collection of tables, may frequently lead to error, and it is to be regretted that Professor Vince did not adopt some fixed plan, and carry it fully through. The ease with which the use of the signs plus and minus is avoided in the solar tables, published by Delambre, and in those of Jupiter and Saturn, by Bouvard, makes the defect of Professor Vince's tables very apparent. Several parts of the translation of the introduction to his copy of Burg's tables are difficult to understand, without referring to the original work published by Delambre, the translation being quite imperfect and filled with errors.

Notwithstanding these defects, the work is val e for its extensive compilation of tables of the moti the heavenly bodies, the catalogues of the fixeds, and the numerous auxiliary tables for facilitating most of the calculations of the practical astronomer.

The Astronomie Théorique et Pratique,' by Delambre, in 1814, 3 vols. 4to, is an excellent work, but deficient in tables. All the instruments are described with the most approved methods of rectification. One of his chapters contains a good treatise on spherical trigonometry and the differential analogies, so useful in all branches of astronomy. It abounds with numerous formulas for the calculation of the effects of refraction, parallax, aberration, nutation, &c. His demonstrations are easy to follow, being quite full, without

omitting the detail of any important part. He explains the formation of the tables of the sun, moon, planets, satellites, and catalogues of the fixed stars, and gives everything which can serve to show the present state of astronomy, excepting a good collection of tables of the motions of the heavenly bodies. To supply this deficiency a person, who owns this work, would do well to procure Zach's or Delambre's solar tables, and the tables of the Planets and Satellites, whose titles are mentioned at the beginning of this review.

The Elementi di Astronomia, published in 1819, at Padua, by Santini, in two quarto volumes, contains the most noted theorems in spherics, and the formulas generally used in calculations of astronomy, particularly, a detailed account of the methods of Olbers and Gauss for computing the orbits of comets or planets, with Burckhardt's tables of motion for a parabola, and Gauss's tables for an ellipsis or hyperbola. It is a much smaller work than those just mentioned, does not contain the description of astronomical instruments, has but few plates, and no tables of the motions of the heavenly bodies, but is a good work of its kind.

About the year 1798, Schubert published a system of astronomy in 3 vols. 4to, in the German language, and in 1804, 1810, a smaller one, entitled 'Populáre Astronomie,' in 3 vols. 8vo. Each volume of this latter work treats of a different division of the science, spherical, theoretical, and physical. It is executed in the best manner, and is well adapted to popular use. Within a short time he has reprinted his large treatise, in the French language, making many improvements in it, to adapt it to the present state of science, so that it may be considered as a new work. The well known talents of the author are a sure pledge of its excellence. Many other useful works on astronomy, of a more limited extent, might be mentioned, as those published by Biot, Woodhouse, Brinkley, and others, but the limits of this Review will not permit a full enumeration of them.

In several of these treatises an abridged history of astronomy is given, and the same is likewise to be found in various Cyclopedias and histories of the mathematics, as Montucla's, and Bossut's. There are, likewise, separate works on this subject, as Bailly's Histoire de l'Astronomie Ancienne et Moderne, some parts of which are beautiful, though he endea

vors, throughout the whole work, to support his fanciful theory of the antediluvian origin of the science. It has, however, been objected to Bailly, that he took too much pains to render his writings, on scientific subjects, elegant, and that he sometimes sacrificed the truth to his fondness for polished sentences and antitheses. Baron de Zach, in speaking of him, makes this remark, 'Les astronomes n'ont que trop justement reproché a leur malhereux confrère Bailly, d'avoir été grand phrasier, ainsi que D'Alembert et Condorcet. Il a souvent sacrifié la vérité à une tirade, à une antithèse.'

Delambre published in 2 vols. 4to, in 1817, his Histoire de l'Astronomie Ancienne, giving extracts from each author, which enable the reader to form a correct idea of the works of the most noted astronomers of antiquity. He has continued the subject in his Histoire de l'Astronomie du Moyen Age, in 1 vol. 4to, in 1819, and his Histoire de l'Astronomie Moderne, in 2 vols. 4to, in 1821, in which the same plan is pursued. This history is continued to the end of the seventeenth century, and is an excellent work. Delambre's labors were extremely useful to astronomy. The history just mentioned, in 5 vols. 4to, his astronomy in 3 vols. 4to, and the work on the measure of the arch of the meridian,* in 3 vols. 4to, form by no means, the greater part of his labors. His tables of the Sun, Jupiter, Saturn, and the Satellites of Jupiter, required several years' incessant application to complete them. He invented and simplified numerous useful formulas, and in almost everything he wrote, there was a great degree of method and elegance. As perpetual Secretary of the Institute, he made several annual reports, and delivered a number of eulogies on the deceased members, which deserve high commendation for their completeness and impartiality.

The history of the appearances of comets is given by Pingré, in his Cométographie, in 2 vols. 4to, which contains, also, a collection of tables and formulas, for computing their motions.

The periodical journals exclusively devoted to astronomy are numerous; as the Nautical Almanac, Connoissance des Tems, Bode's Jahrbuch, etc. The two last works contain numerous memoirs and accounts of discoveries, useful for a

* Several astronomers assisted in this measure, as Méchain, Arago, Biot, &c. but the account of their labors was drawn up by Delambre.