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methods must be adopted, and M. DELAMBRE has resorted to those which he had employed in the constrution of his tables of this planet: but for the other new plenets, viz. Ceres, Juno, Pallas, and Vesta, he makes use of the elegant method of M. Gauss, which he illustrates by a numerical example in all its detail. His history of these discoveries, which have nearly doubled the limits of the solar system, is highly interesting. He shews, beyond a doubt, that Meyer had in 1756 observed the planet Uranus, but considered it only as a small star, and as such placed it in his catalogue : this observation is of course extremely valuable in determining the elements of its orbit; and the author has not failed to avail himself of so favourable a circumstance. The chapter closes with a synoptic table of the elements of the planets, and a general view of the solar system ; viz. the sidereal revolutions; semi-axes, major and minor ; excentricities; inclinations ; greatest, least, and mean distances from the sun and earth ; apparent diameters ; masses, densities, &c. &c. This table, as being the most recent and doubtless the most correct of any yet published, we could have wished to have presented to our readers, if it had been .consistent with the plan of a Review : but, that not being the case, we must content ourselves with exhibiting a few of the principal formula whence the computations have been made.

• The semi-axes major of the orbits have been computed from the movement of the planets in a given time, by the laws of Kepler ; or Tather from the formula,

mean mot. of earth va mean motion of the planet =

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v representing the sum of the masses of the sun and planet,

or: y = M + m = m (1 + M): but the fraction being very small, and uncertain, it may be omitted. If we take unity to represent the mass of the sun, and m that of the planet, then u = 1 tim; and the mean motion being generally z = -e sin. x, we have, when = - 360°, %= = 3600 - e sin. 360° = 360° = 25, T representing the semi-circumference. Hence the sidereal revolution

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that is, the law of Kepler ; which, it thus appears, is not rigorously correct, since it supposes all the planets to be of equal magnitude.

• The same law will apply to the different satellites which revolve about the same planet. Let t be the time of the revolution of one of these satellites, a" its mean distance from the planet, and m' the mass of the planet, which here answers to the sun in the preceding case ;

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calling the mass of the sun unity.

• From this formula, the masses of those planets are determined which have satellites revolving about them; and the masses of the others are found from the perturbations which they produce in the motion of the earth or other planet.'

In order to estimate the space through which a heavy body falls in a second, at the surface of any of the planets, we have the formula: g d m

where g represents the space through which a heavy body falls in one second at the surface of the earth; d, the diameter, and y, the mass, of the earth; and D and m the diameter and mass of the planet. If the two former be taken each equal to 1, then the formula becomes s= 8 : This, being applied to the sun, whose diameter is 111.74 times and its mass 329630 times those of the earth, gives 129.53 metres, or 398.74 French feet, for the space through which a heavy body would fall at its surface in i".

Volume III. contains eleven chapters, on the stations and retrogradations of the planets ; on the diurnal revolutions of the sun and planets ; on the aberration of the stars, and their annual parallax ; on the nutation of the earth's axis ; on the displacement of the ecliptic, and divers motions of the stars ; on comets ; on satellites ; on the magnitude and figure of the earth; on nautical astronomy; on projections; and on the calendar. - In the first chapter, are given general formula and tables of retrogradation for all the planets, which agree perfectly with observation; and which, therefore, offer a farther opportunity of drawing a comparison between the three systems of Ptolemy, Tycho, and Copernicus. In the deterApp. REV. VOL. LXXVI.

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mination of the diurnal revolutions of the sun and planets, from observations of spots on their discs, we have seven different methods of making the required deductions, viz. those of Boscovich, Pézénas, and Cagnoli, by the method of the minimum squares; by trigonometry; the same abridged, and by a new analytical method ; and an application of these principles to the rotation and libration of the moon, and to the ring of Saturn, with formulæ for computing all these phænomena. The chapter on comets is another of those in which the author exhibits the great resources of his analysis, and his profound knowlege of astronomy. Besides a detail of many different methods, viz. by Olbers, Lagrange, Laplace, and Legendre, M. DELAMBRE gives also one of his own for determining all the elements of a cometary orbit, from three observations only; with the application of it in numbers to certain supposititious observations, and to others drawn from the known elements of the comet of 1759, and general formulæ of correction for any number of observations. This chapter is terminated by two general and extensive tables of the parabolic motion of comets, the one according to the form proposed by La Caille, and the other agreeably to the idea of Barker. The latter form has been generally preferred by recent astronomers, but M. DELAMBRE thinks that it is far less commodious than the former ; in fact he has proved it to be so, by a comparison of the two tables with a numerical example; and these tables, which occupy more than 40 pages, have been computed by the author de novo from certain formulæ exhibited in the body of the chapter.

That part which relates to the magnitude and figure of the earth is principally extracted from the “ Base du Systéme Métrique décimal,except that the historical portion is here given in more detail, with some new formulæ relative to the uncertainties which still attend this interesting problem, regarding both the compression and the probable irregularities of the terrestrial meridians. In his history of the different geodetic operations that have been performed, or which are still carTying on, M. DELAMBRE manifests (as indeed he does throughout the whole treatise,) that his liberality is worthy of his talents. We discover in no part of his work that spirit of jealousy and national rivalry, which has too often perverted and misrepresented historical facts; he examines dispassionately the merits and demerits of every point that comes under his investigation, whether it concerns himself or any other author ; and, in all cases, he reasons with coolness and decides with justice. In this spirit, he has adverted to the paper which appeared in the Philosophical Transactions for 1812, by which

it was attempted to be shewn that an error of aboạt 5" must have been made in the English survey at the station of Arbury, hill.

He admits that a correction of s" at that station would render the subdivisions of the arc more analogous to other modern measures : but then, he observes, it remains to conceive how the beautiful sextant of Ramsden, of which the error was nothing or constant at the extremities, could have an error of 5" at the intermediate station, Whether these anomalies proceed from the instrument or from local inequalities, (a point which does not appear to be yet well decided,) it will always happen in operations of this kind that we have no security except in arcs of great extent, such as that which goes from Dunkirk to Barcelona, or Formentera ; where the error, whatever may be the cause, is divided over a long interval. In small and contiguous arcs, the inevitable errors of observation will have too great an influence on the result to throw any light on the question of terrestrial compression.'

In the article on nautical astronomy, the author has collected the most important methods, and those which are intitled to the greatest confidence; and he has drawn together the formulæ which he had at different times published on this subject in the Connaissance des Tems. In the chapter on projections, we find every thing that is necessary for the construction of celestial charts, and charts of eclipses ; and, in the article relative to the calendar, every thing which this subject offers that is truly curious or useful. The author, however, has since made some emendations to this article in the Connaissance des Tems for 1817.

We have endeavoured, in the preceding pages, to give as clear and detailed sketch of this important work as we could render compatible with the plan of our Review, and throughout we have had the satisfaction of applauding its general arrangement and execution : we are sorry, therefore, in conclusion, to be under the necessity of mentioning one important defect, which will not fail to strike any person who

undertake to read it with attention. We allude to the extraordinary number of press-errors, which would be alone sufficient to condemn any book of less pretensions than the present; and, even in this, they will doubtless be considered as forming a great deduction from the general merits of the treatise.

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ART. XV. Vie Politique, &c. ; i... The Political Life of all the

Deputies to the National Convention, during and subsequent to : the Revolution ; a Work in which it is proved that on the Trial of

Louis XVI. the Punishment of Death was in fact rejected by a Majority of six Votes. By M. R. Author of the Address of Louis ÁVI., from the Abode of the Blessed, to his august Brother Louis XVIII., on the Entrance of the latter into the

Tuileries. 8vo. Pp. 439. Paris. 1814. This is a kind of biographical dictionary of the leading men

in the French Revolution, on a plan similar to the larger work so well known under the title of Biographie Moderne. The names of the deputies are given in alphabetical order; and the account of each consists chiefly in mentioning the place which he represented, and the part which he took on points of importance, particularly on the trial of Louis XVI.: with the date of any remarkable speech made by the member in question, and the time at which his party was overset and he himself doomed to political insignificance, or to terminate his career on the scaffold. The compiler seldom aims at reflection or disquisition, but is generally contented with giving a short narrative of the particulars which we have specified, and a few others peculiar to the individual. In political feeling, he is, or professes to be, an adherent of the Bourbons. We select some statements relative to actors of considerable importance in the revolutionary drama, which may serve to convey an idea of the plan of the work.

Carnot and Sieyès have been sometimes compared: but we were always in the habit of considering them in a very different light, the former being more of a man of business, and the latter more of a philosopher; and, although Carnot appeared to co-ope. rate for a season with the worst part of the revolutionists, his conduct never discovered so much finesse and dissimulation as that of the unbelieving member of the church.

Carnot was born at Nolay in Burgundy, of a family of the middle rank, and was early placed in an Engineer-corps, where the Prince of Condé soon took notice of him on account of the extent of his attainments. When he was a captain in the engineers, the Revolution burst forth, and excited all his ardour. He was nominated, in 1791, a deputy to the legislature by the department of the Pas de Calais, and he was subsequently a member of the Convention; in which capacity he voted for the King's death, and against an appeal to the people. He became afterward the director of the military operations of France; and if we can overlook his vote on the King's trial, and the character of the system to which for a time he gave his support, we must consider him as greatly instrumental in the aggrandizement of France and the success of her arms. After the 9th of Thermidor, he brought forwards charges against Carrier and I

Tureau,

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