which they were produced, the one from the other, will have the twofold advantage of presenting a grand totality of important truths, and the true method to be pursued in the investigation of the laws of Mature: this is the object which I propose to myself in the present undertaking.'

The work is divided into chapters. The 1st discusses the diurnal motions of the heavens; in which the phenomena that ordinarily present themselves are noted and explained. This chapter merits the highest praise for the ease of its style, for its perspicuity, and for its arrangement. Chapter II. trests on the Sun, and his proper motion, and is equally meritorious. Chapter III. on Fime, and its measure. Here the author treats of the new division; and, speaking of the necessity of fixing a proper æra, he says

It is desirable that all people should adopt one and the same za, independant of moral revolutions, and founded solely on astronomical phænomena. The origin of this æra might be fixed in the year in which the apogee of the solar orbit coincided with the solar solstice, which ascends as high as the year 1250. This origin might be tax in the instant of the mean vernal equinox, which in this year 2L

hours

swers to the 5th of March, 5. 3676, at Paris. The universi meridian, where the origin of the terrestial longitudes might be fixed, would be that of the place which reckoned midnight at the same isstant, and which is to the cast of Paris 135°. 2965. If, after a long series of years, the origin of the ara became uncertain, it would Li difficult to find it by the sole movement of the apogee, on account of the slowness and the inequalities of this movement: but all uncer tainty respecting this origin, and the position of the universal meridian, will be removed when it is remembered that, at the moment of the mean equinox, the mean longitude of the moon was 143 - 7714Thus what is arbitrary in the origin of time, and in that of the te restial longitudes, might be made to disappear. In adopting afterward the intercalation, and the preceding division of the year, and . that of the month and day, the calendar would be formed in the nat natural and most simple manner that can be devised, for inhabitants on this side of the equator.'

Chap. IV. On the Moon's mean motion; her phases and eclipses.

Chap. V. Of the planets; particularly Mercury and Venus. Chap. VI. Of Mars. VII. Of Jupiter and his satellites. VIII. Of Saturn, his satellites and ring. IX. Of Uranus and his satellites. X. Of Comets. XI. Of Stars, and their mo tions. XII. Of the figure of the Earth, and the variation of gravity at its surface. In this chapter, the new system of weights and measures is explained with great perspicuity, ard justified; and we only omit to give an extract of the author's clear and forcible reasoning, because we recollect that the

system has already been presented to the public in Mr. Nicholson's valuable Journal: see M. R. July, p. 301 & seq. Chap. XIII. Of the flux and reflux of the Sea. XIV. Of the terrestial Atmosphere, and astronomical Refractions.

'The Second Book treats on the real motions of the heavenly bodies. Chap. I. Of the movement of the Earth's rotation. Chap. II. Of the motion of the planets about the Sun. III. Of the motion of the Earth about the Sun. The second and third of these chapters deserve notice as specimens of luminous and forcible argumentation. We shall give an extract from the

latter.

Now, shall we suppose the sun to be accompanied by planets and satellites in motion round the earth; or shall we make the earth move, as the planets, round the sun? The appearances of the heavenly motions are the same in the two hypotheses: but the second ought to be preferred, for the following considerations.

The masses of the sun, and of several of the planets, being considerably greater than the mass of the earth; it is much more simple to make the latter revolve about the sun, than to put in motion round it the whole solar system. What complication in the heavenly motions does the immobility of the carth induce? How rapid must be the motion which we must then attribute to Jupiter, to Saturn almost ten times more distant from the sun, to the planet Uranus still more distant; when they are made to move, each year, about us, and at the same time about the sun? This complication, and this rapidity of motion, disappear by the motion of the earth's translation; a motion conformable to the general law, according to which the small heavenly bodies revolve round the large bodies to which they are near.

The analogy of the earth to the planets confirms this motion. As to Jupiter, it revolves round itself, and is accompanied by a satellite. An observer, at the surface of Jupiter, would deem the solar system in motion round him; and the greatness of this planet would render this illusion less probable than in the case of the earth. Is it not natural to think that the motion of this system, about us, is probably only an appearance? Let us in imagination. transport ourselves to the surface of the sun, and thence contemplate the earth and the planets. All these bodies will to us appear moving from west to east; and this identity of direction indicates the motion of the earth: but what proves it evidently, is the law which exists between the times of the planets' revolutions and their distances from the sun. They revolve round him so much the more slowly, as they are more removed and regulated by this law, that the squares of the times of their revolutions are as the cubes of their mean distances. According to this remarkable law, the duration of the carth's revolution, when it is supposed to move round the sun, ought to be precisely that of the sidereal year. Is not this an incontestable proof that the earth revolves like all the planets, and is subjected to the same laws?

In other respects, would it not be strange to suppose the terrestial globe scarcely sensible to sight from the sun, fixed in the M m 3 midst

midst of planets moving round this star, which itself would revolve with them about the earth? Ought not the force, which, in order to retain the planets in their respective orbits round the sun, balances their centrifugal force,-ought it not to act equally on the earth, and the earth to oppose to this action the same centrifugal force? Thus the consideration of the heavenly motions observed from the sun leaves no doubt of the earth's real motion:-but the observer, placed on it, has an additional sensible proof of this motion, in the phænomenon of the aberration of light, which is a necessary consequence of it — We now proceed to develope this phænomenon.'

The author then gives the history of the discovery of the propagation of light, and of the aberration of the fixed stars; after which, he thus continues his argument for the truth of the Copernican system:

The consideration of the celestial motions conducts us then to displace the earth from the centre of the world, where we suppose i to be, misled by appearances, and by the propensity which man has to consider himself as the principal object in Nature. The globe which he inhabits is a planet moving round an axis of its own, and round the sun. In viewing it under this aspect, all the phænomena are explained in the most simple manner; the laws of the heavenly motions are uniform; and all analogies are observed. Like Jupiter, Saturn, and Uranus, the earth is attended with a satellite; it revolves round itself, as do Venus, Mars, Jupiter, Saturn, and probably the other planets; it borrows, as they do, its light from the sun, and revol a round the sun, observing the same direction and laws. In fine, the idea of the motion of the earth unites in its favour, simplicity, ana logy, and generally all that characterises the true system of Nature. In following it in its consequences, we shall see the celestial pheno mena referred, even in their minutest details, to one law alone, of which they become the necessary developements. Thus will the carth's motion acquire all the certainty of which physical truths are susceptible; and which results, whether we consider the great nur ber and variety of the phænomena explained, or the simplicity of the laws from which they are made to depend. No branch of naturd knowlege unites in a higher degree these advantages, which the system of the world, grounded on the earth's motion, possesses. This motion enlarges the universe in our eyes; to measure the distances of the heavenly bodies, it affords us an immense base, the diameter of the earth's orbit. By its means, the dimensions of the planetary orbits have been exactly determined. Thus, the earth's motion, which by the illusions to which it gave rise, during a long period, retarded the knowlege of the real motions of the planets, has at length made them known to us, with greater precision than we had been placed in the focus of these motions. Nevertheless, the annual parallax of the stars, or the angle under which the diameter of the earth's orbit would be seen from their centre, is insensible, ard does not amount to six seconds, even in those sta.s which by ther superior brightness apear most near to us: there stars are t... et the least a hundred thousand times more distant than the sun.

So

prodigious

prodigious a distance, joined to their brightuess, is a sufficient proof that they do not, like the planets and the satellites, derive their light from the sun, but that they shine with their own light, and are as so many suns scattered in the immensity of space, which may be the foci of planetary systems. In fact, it is sufficient to place ourselves on the nearest of these stars, in order to see the sun only as a luminous star, whose diameter is less than the thirtieth part of a second.

It results from the immense distance of the stars, that their mo. tions in right ascension and declination are only appearances produced by the motion of the earth's axis of rotation:-but some stars appear to have real and proper motions; and it is probable that they are all in motion, as the sun is; which carries along with him, through space, the entire system of planets, comets, and satellites; in the same manner in which each planet draws his satellites along with him in his motion round the sun,'

Chap. IV. Of the appearances which belong to the motion of the Earth. V. Of the figure of the orbits of the Planets, and the laws of their motion about the Sun. VI. Of the figure of the orbits of the Comets, and the laws of their motion about the Sun. VII. Of the laws of the motions of Satellites about their Planets.

In the Third Book, we have the author's comment on the laws of motion; and here again we think it proper to give an extract but it will be short:

From amid the infinite variety of phænomena, which follow one another on the earth in continual succession, philosophers have at length discovered the small number of general laws which matter obeys in its motions. To these laws, every thing in Nature is submissive; from them, every thing is derived, as necessarily as the res turn of seasons; and the curve described by the lightest atom, which the winds seem to carry at the caprice of chance, is regulated as certainly as the planetary orbits. It should seem that the importance of these laws, on which we perpetually depend, ought to have exeited curiosity in every period of time but that indifference, which is too common to the human mind, kept them concealed until the commencement of the last century; an epoch in which Galileo laid the foundations of the science of motion, by his discoveries con, cerning the fall of bodies. Geometricians, in following the route of this great man, have at length reduced all mechanics to certain ge neral formulas, so exact and comprehensive, that nothing is wanting to them except the perfection of analysis.

We have next a chapter on Forces, and their composition. This is followed by another on the motion of a material point; a chapter pregnant with just observatious and luminous reasoning. We come then to remarks on the equilibrium of a system of bodies; and a chapter on the Equilibrium of Fiuids. Here the author, speaking of the Forces vives, and the principle of the least action, is led to offer the following remarks on the doctrine of final causes: • Many

Mm 4

Many philosophers, struck with the order which reigns in Na ture, and with the fecundity of her means in the production of phanomena, have imagined that she always arrives at its end by the most simple ways. In extending these views to mechanics, they have inquired what was the economy which Nature proposed to her self, in the employment of forces. After many fruitless trials, they have at length ascertained that, among all the curves which can be described by a body moving from one point to another, that is always selected to be described, in which the integral of the product of the mass of the body, by its velocity and the element of the curve, is a minimum; so that, the velocity of a body moving in a curve surface, and unsolicited by any force, being constant, it proceeds from one point to another by the shortest line. The preceding tegral has been called the action of a body; and the reunion of like integrals relative to each body of a system has been named the action of a system. The economy of Nature consists, then, according to these philosophers, in sparing this action, so that it may be the least possible; it is this which constitutes the principle of the least action.

This principle, examined thoroughly, is only a carious result of the primordial laws of motion; laws which, as it has appeared, are the most simple and natural that can be imagined; and which, on that account, seem to flow from the very essence of matter :-but, as all the laws which are mathematically possible offer aualagous results, it ought not to be elevated to the dignity of a final cause; and, far from having given birth to the laws of motion, it has not beca even accessory to their discovery; without which it would be still a subject of dispute, what was to be understood by the least action of Nature.'

In Vol. II. Chap. III. the author explains the perturbations of the elliptical motion of the planets. In Chap. IV. on the perturbations of the elliptical motions of comets, he thus digresses into an account of the effects which probably would be produced by the shock of a comet :

To the terrors inspired by the appearance of comets, has suc ceeded the apprehension that, out of the vast number of those which traverse in every direction the planctary system, some one should overthrow the earth :-but they pass so rapidly by us, that the effects of their attraction are not to be dreaded. It is only by striking against the earth, that they can here produce disastrous ravages: but this shock, although possible, is probable in a very slight degree during the course of a century. That two bodies, so small when com. pared with the immensity of space in which they move, should im pinge against each other, requires a concurrence of circumstances so extraordinary, that we are not warranted in entertaining on this head any reasonable fear. Nevertheless, the small probability of such a shock, by accumulating during a long series of ages, may become considerable. It is easy to represent the effects of this shock on the earth. The axis and the motion of rotation changed; the scas aban"doning their antient beds, in order to precipitate themselves towards the new equator great numbers of men and animals, overwhelmed in