ARTICLE I. ON THE FORMATION OF THE PLANETS.

Our subject being Natural History, we would willingly dispense with astronomical observations; but as the nature of the earth is so closely connected with the heavenly bodies, and such observations being calculated to illustrate more fully what has been said, it is necessary to give some general ideas of the formation, motion, figure of the earth and other planets.

The earth is a globe of about three thousand leagues diameter; it is situate one thousand millions of leagues from the sun, around which it makes its revolution in three hundred and sixty-five days. This revolution is the result of two forces; the one may be considered as an impulse from right to left, or from left to right, and the other an attraction from above downwards, or beneath upwards, to a common centre. The direction of these two forces, and their quantities, are so nicely combined and proportioned, that they produce an almost uniform motion in an ellipse, very near to a circle. Like the other planets the earth is opaque, it throws out a shadow; it receives and reflects the light of the sun, round which it revolves in a space of time proportioned to its relative distance and density. It also turns round its own axis once in twenty-four hours, and its axis is inclined 66-1/4 degrees on the plane of the orbit. Its figure is spheroidical, the two axes of which differ about 160th part from each other, and the smallest axis is that round which the revolution is made.

These are the principal phenomena of the earth, the result of discoveries made by means of geometry, astronomy, and navigation. We shall not here enter into the detail of the proofs and observations by which those facts have been ascertained, but only make a few remarks to clear up what is still doubtful, and at the same time give our ideas respecting the formation of the planets, and the different changes thro' which it is possible they have passed before they arrived at the state we at present see them.

There have been so many systems and hypotheses framed upon the formation of the terrestrial globe, and the changes which it has undergone, that we may presume to add our conjectures to those who have written upon the subject, especially as we mean to support them with a greater degree of probability than has hitherto been done: and we are the more inclined to deliver our opinion upon this subject, from the hope that we shall enable the reader to pronounce on the difference between an hypothesis drawn from possibilities, and a theory founded in facts; between a system, such as we are here about to present, on the formation and original state of the earth, and a physical history of its real condition, which has been given in the preceding discourse.

Galileo having found the laws of falling bodies, and Kepler having observed that the area described by the principal planets in moving round the sun, and those of the satellites round the planets to which they belong, are proportionable to the time of their revolutions, and that such periods were also in proportion to the square roots of the cubes of their distances from the sun, or principal planets. Newton found that the force which caused heavy bodies to fall on the surface of the earth, extended to the moon, and retained it in its orbit; that this force diminished in the same proportion as the square of the distance increased, and consequently that the moon is attracted by the earth; that the earth and planets are attracted by the sun; and that in general all bodies which revolve round a centre, and describe areas proportioned to the times of their revolution, are attracted towards that point. This power, known by the name of GRAVITY, is therefore diffused throughout all matter; planets, comets, the sun, the earth, and all nature, is subject to its laws, and it serves as a basis to the general harmony which reigns in the universe. Nothing is better proved in physics than the actual existence of this power in every material substance. Observation has confirmed the effects of this power, and geometrical calculations have determined the quantity and relations of it.

This general cause being known, the effects would easily be deduced from it, if the action of the powers which produce it were not too complicated. A single moment's reflection upon the solar system will fully demonstrate the difficulties that have attended this subject; the principal planets are attracted by the sun, and the sun by the planets; the satellites are also attracted by their principal planets, and each planet attracts all the rest, and is attracted by them. All these actions and reactions vary according to the quantities of matter and the distances, and produce great inequalities and irregularities. How is so great a number of connections to be combined and estimated? It appears almost impossible in such a crowd of objects to follow any particular one; nevertheless those difficulties have been surmounted, and calculation has confirmed the suppositions of them, each observation is become a new demonstration, and the systematic order of the universe is laid open to the eyes of all those who can distinguish truth from error.

We feel some little stop, by the force of impulsion remaining unknown; but this, however, does not by any means affect the general theory. We evidently see the force of attraction always draws the planets towards the sun, they would fall in a perpendicular line, on that planet, if they were not repelled by some other power that obliges them to move in a straight line, and which impulsive force would compel them to fly off the tangents of their respective orbits, if the force of attraction ceased one moment. The force of impulsion was certainly communicated to the planets by the hand of the Almighty, when he gave motion to the universe; but we ought as much as possible to abstain in physics from having recourse to supernatural causes; and it appears that a probable reason may be given for this impulsive force, perfectly accordant with the law of mechanics, and not by any means more astonishing than the changes and revolutions which may and must happen in the universe.

The sphere of the sun's attraction does not confine itself to the orbs of the planets, but extends to a remote distance, always decreasing in the same ratio as the square of the distance increases; it is demonstrated that the comets which are lost to our sight, in the regions of the sky, obey this power, and by it their motions, like that of the planets, are regulated. All these stars, whose tracts are so different, move round the sun, and describe areas proportioned to the time; the planets in ellipses more or less approaching a circle, and the comets in narrow ellipses of a great extent. Comets and planets move, therefore, by virtue of the force of attraction and impulsion, which continually acting at one time obliges them to describe these courses; but it must be remarked that comets pass over the solar system in all directions, and that the inclinations of their orbits are very different, insomuch that, although subject like the planets to the force of attraction, they have nothing in common with respect to their progressive or impulsive motions, but appear in this respect independent of each other: the planets, on the contrary, move round the sun in the same direction, and almost in the same plane, never exceeding 7-1/2 degrees of inclination in their planes, the most distant from their orbits. This conformity of position and direction in the motion of the planets, necessarily implies that their impulsive force has been communicated to them by one and the same cause.

May it not be imagined, with some degree of probability, that a comet falling into the body of the sun, will displace and separate some parts from the surface, and communicate to them a motion of impulsion, insomuch that the planets may formerly have belonged to the body of the sun, and been detached therefrom by an impulsive force, and which they still preserve.

This supposition appears to be at least as well founded as the opinion of Leibnitz, who supposes that the earth and planets had formerly been suns; and his system, of which an account will be given in the fifth article, would have been more comprehensive and more agreeable to probability, if he had raised himself to this idea. We agree with him in thinking that this effect was produced at the time when Moses said that God divided light from darkness; for, according to Leibnitz, light was divided from darkness when the planets were extinguished; but in our supposition there was a real physical separation, since the opaque bodies of the planets were divided from the luminous matter which composes the sun.

This idea of the cause of the impulsive force of the planets will be found much less objectionable, when an estimation is made of the analogies and degrees of probability, by which it may be supported. In the first place, the motion of the planets are in the same direction, from West to East, and therefore, according to calculation, it is sixty-four to one that such would not have been the case, if they had not been indebted to the same cause for their impulsive forces.

This, probably, will be considerably augmented by the second analogy, viz. that the inclination of the planes of the orbits do not exceed 7-1/2 degrees; for, by comparing the spaces, we shall find there is twenty-four to one, that two planets are found in their most distant places at the same time, and consequently ⁵, or 7,692,624 to one, that all six would by chance be thus placed; or, what amounts to the same, there is a great degree of probability that the planets have been impressed with one common moving force, and which has given them this position. But what can have bestowed this common impulsive motion, but the force and direction of the bodies by which it was originally communicated? It may therefore be concluded, with great probability, that the planets received their impulsive motion by one single stroke. This likelihood, which is almost equivalent to a certainty, being established, I seek to know what moving bodies could produce this effect, and I find nothing but comets capable of communicating a motion to such vast bodies.

By examining the course of comets, we shall be easily persuaded, that it is almost necessary for some of them occasionally to fall into the sun. That of 1680 approached so near, that at its perihelium it was not more distant from the sun than a sixteenth part of its diameter, and if it returns, as there is every appearance it will, in 2255, it may then possibly fall into the sun; that must depend on the rencounters it will meet with in its road, and of the retardment it suffers in passing through the atmosphere of the sun[78:A].

We may, therefore, presume with the great Newton, that comets sometimes fall into the sun; but this fall may be made in different directions. If they fall perpendicular, or in a direction not very oblique, they will remain in the sun, and serve for food to the fire which that luminary consumes, and the motion of impulsion which they will have communicated to the sun, will produce no other effect than that of removing it more or less, according as the mass of the comet will be more or less considerable; but if the fall of the comet is in a very oblique direction, which will most frequently happen, then the comet will only graze the surface of the sun, or slightly furrow it; and in this case it may drive out some parts of matter to which it will communicate a common motion of impulsion, and these parts so forced out of the body of the sun, and even the comet itself, may then become planets, and turn round this luminary in the same direction, and in almost the same plane. We might perhaps calculate what quantity of matter, velocity, and direction a comet should have, to impel from the sun an equal quantity of matter to that which the six planets and their satellites contain; but it will be sufficient to observe here, that all the planets, with their satellites, do not make the 650th part of the mass of the sun,[79:A] because the density of the large planets, Saturn and Jupiter, is less than that of the sun; and although the earth be four times, and the moon near five times more dense than the sun, they are nevertheless but as atoms in comparison with his extensive body.

However inconsiderable the 650th part may be, yet it certainly at first appears to require a very powerful comet to separate even that much from the body of the sun; but if we reflect on the prodigious velocity of comets in their perihelion, a velocity so much the greater as they approach nearer the sun; if, besides, we pay attention to the density and solidity of the matter of which they must be composed, to suffer, without being destroyed, the inconceivable heat they endure; and consider the bright and solid light which shines through their dark and immense atmospheres, which surround, and must obscure them, it cannot be doubted that the comets are composed of extremely solid and dense matters, and that they contain a greater quantity of matter in a small compass; that consequently a comet of no extraordinary bulk may have sufficient weight and velocity to displace the sun, and give a projectile motion to a quantity of matter, equal to the 650th part of the mass of this luminary. This perfectly agrees with what is known concerning the density of planets, which always decreases as their distance from the sun is increased, they having less heat to support; so that Saturn is less dense than Jupiter, and Jupiter much less than the earth; therefore if the density of the planets be, as Newton asserts, proportionable to the quantity of heat which they have to support, Mercury will be seven times more dense than the earth, and twenty-eight times denser than the sun; and the comet of 1680 would be 28,000 times denser than the earth, or 112,000 times denser than the sun, and by supposing it as large as the earth, it would contain nearly an equal quantity of matter to the ninth part of the sun, or by giving it only the 100th part of the size of the earth, its mass would still be equal to the 900th part of the sun. From whence it is easy to conclude, that such a body, though it would be but a small comet, might separate and drive off from the sun a 900th or a 650th part, particularly if we attend to the immense velocity with which comets move when they pass in the vicinity of the sun.

Besides this, the conformity between the density of the matter of the planets, that of the sun deserves some attention. It is well known, that, both on and near the surface of the earth, there are some matters 14 or 1500 times denser than others. The densities of gold and air are nearly in this relation. But the internal parts of the earth and planets are composed of a more uniform matter, whose comparative density varies much less; and the conformity in the density of the planets and that of the sun is such, that of 650 parts which compose the whole of the matter of the planets, there are more than 640 of the same density as the matter of the sun, and only ten parts out of these 650 which are of a greater density, for Saturn and Jupiter are nearly of the same density as the sun, and the quantity of matter which these planets contain, is at least 64 times greater than that of the four inferior planets, Mars, the Earth, Venus, and Mercury. We must therefore admit, that the matter of which the planets are generally composed is nearly the same as that of the sun, and that consequently the one may have been separated from the other.

But it may be said, if the comet, by falling obliquely on the sun, drove off the matter which compose the planets, they, instead of describing circles of which the sun is the centre, would, on the contrary, at each revolution, have returned to the same point from whence they departed, as every projectile would which might be thrown off with sufficient force from the surface of the earth, to oblige it to turn perpetually: for it is easy to demonstrate that such, in that instance, would be the case, and therefore that the projection of the planets from the sun cannot be attributed to the impulsion of a comet.

To this I reply, that the matter which composes the planets did not come from the sun, in ready formed globes, but in the form of torrents, the motion of the anterior parts of which were accelerated by that of the posterior; and that the attraction of the anterior parts also accelerated the motion of the posterior, and that this acceleration produced by one or other of these causes, or perhaps by both, might be so great as to change the original direction of the motion occasioned by the impulse of the comet, from which cause a motion has resulted, such as we at present observe in the planets; especially when it is considered the sun is displaced from its station by the shock of the comet. An example will render this more reasonable; let us suppose, that from the top of a mountain a musket ball is discharged, and that the strength of the powder was sufficient to send it beyond the semi-diameter of the earth, it is certain that this ball would pass round the earth, and at each revolution return to the spot from whence it had been discharged: but, if instead of a musket-ball, we suppose a rocket had been discharged, wherein the action of the fire being durable, would greatly accelerate the motion of impulsion; this rocket, or rather the cartouch which contained it, would not return to the same place like the musket-ball, but would describe an orbit, whose perigee would be much farther distant from the earth, as the force of acceleration would be greater, and have changed the first direction.

Thus, provided there had been any acceleration in the motion of impulsion communicated to the torrent of matter by the fall of the comet, it is probable that the planets formed in this torrent, acquired the motion which we know they have in the circles and ellipsis of which the sun is the centre and focus.

The manner in which the great eruptions of volcanos are made, may afford us an idea of this acceleration of motion. It has been remarked that when Vesuvius begins to roar and eject the inflamed matter it contains, the first cloud has but a small degree of velocity, but which is soon accelerated by the impulse of the second; the second by the action of a third, and so on, until the heavy mass of bitumen, sulphur, cinders, melted metal, and huge stones, appear like massive clouds, and although they succeed each other nearly in the same directions, yet they greatly change that of the first, and drive it far beyond what it would have reached of itself.

In answer to this objection, it may be further observed, that the sun having been struck by the comet, received a degree of motion by the impulse, which displaced it from its former situation; and that although this motion of the sun is at present too little sensible for the notice of astronomers, nevertheless it may still exist, and the sun describe a curve round the centre of gravity of the whole system and if this is so, as I presume it is, we see perfectly that the planets, instead of returning near the sun at each revolution, will, on the contrary, have described orbits, the points of the perihelion of which will be as far distant from the sun, as it is itself from the place it originally occupied.

It may also be said, that if this acceleration of motion is made in the same direction, no change in the perihelion will be produced: but can it be thought that in a torrent, the particles of which succeed each other, there has been no change of direction; it is, on the contrary, very probable that a considerable change did take place, sufficient to cause the planets to move in the course they at present occupy.

It may be further urged, that if the sun had been displaced by the shock of a comet, it would move uniformly, and that hence this motion being common to the whole system, no alteration was necessary; but might not the sun before the shock have had a motion round the centre of the cometry system, to which primitive motion the stroke of the comet may have added or diminished? and would not that fully account for the actual motion of the planets?

If these suppositions are not admitted, may it not be presumed, that in the stroke of the comet against the sun, there was an elastic force which raised the torrent above the surface of the sun, instead of directly impelling it? which alone would be sufficient to remove the perihelion, and give the planets the motion they have retained. This supposition is not without probability, for the matter of the sun may possibly be very elastic, since light, the only part of it we are acquainted with, seems, by its effects, to be perfectly so. I own that I cannot say whether it is by the one or the other of these reasons, that the direction of the first motion of the impulse of the planets has changed, but they suffice to shew that such an alteration is not only possible but even probable, and that is sufficient for my purpose.

But, without dwelling any longer on the objections which might be made, I shall pursue the subject, and draw the fair conclusions on the proofs which analogies might furnish in favour of my hypothesis: let us, therefore, first see what might happen when these planets, and particularly the earth, received their impulsive motion, and in what state they were after having been separated from the sun. The comet having, by a single stroke, communicated a projectile motion to a quantity of matter equal to the 650th part of the sun's mass, the light particles would of course separate from the dense, and form, by their mutual attraction, globes of different densities: Saturn being composed of the most gross and light parts, would be the most remote from the sun: Jupiter being more dense than Saturn, would be less distant, and so on. The larger and least solid planets are the most remote, because they received an impulsive motion stronger than the smallest, and more dense: for, the force of impulsion communicating itself according to the surface, the same stroke would have moved the grosser and lighter parts of the matter of the sun with more velocity than the smallest and more weighty; a separation therefore will be made of the dense parts of different degrees, so that the density of the sun being equal to 100, that of Saturn will be equal to 67, that of Jupiter to 94-1/2, that of Mars to 200, that of the Earth to 400, that of Venus to 800, and that of Mercury to 2800. But the force of attraction not communicating like that of impulsion, according to the surface, but acting on the contrary on all parts of the mass, it will have checked the densest portions of matter; and it is for this reason that the densest planets are the nighest the sun, and turn round that planet with greater rapidity than the less dense planets, which are also the most remote.

Jupiter and Saturn, which are the largest and principal planets of the solar system, have retained the relation between their density and impulsive motions, in the most exact proportions; the density of Saturn is to that of Jupiter as 67 to 94-1/2 and their velocities are nearly as 88-2/3 to 120-1/72, or as 67 to 90-11/16; it is seldom that pure conjectures can draw such exact relations. It is true, that by following this relation between the velocity and density of planets, the density of the earth ought to be only as 206-7/18, and not 400, which is its real density; from hence it may be conceived, that our globe was formerly less dense than it is at present. With respect to the other planets, Mars, Venus, and Mercury, as their densities are known only by conjecture, we cannot be certain whether this circumstance will destroy or confirm our hypothesis. The opinion of Newton is, that density is so much the greater, as the heat to which the planet is exposed is the stronger; and it is on this idea that we have just said that Mars is one time less dense than the Earth, Venus one time, Mercury seven times, and the comet in 1680, 28,000 times denser than the earth: but this proportion between the density of the planets and the heat which they sustain, seems not well founded, when we consider Saturn and Jupiter, which are the principal objects; for, according to this relation between the density and heat, the density of Saturn would be about 4-7/18, and that of Jupiter as 14-17/22, instead of 67 and 94-1/2, a difference too great to be admitted, and must destroy the principles upon which it was founded. Thus, notwithstanding the confidence which the conjectures of Newton merit, I can but think that the density of the planets has more relation with their velocity than with the degree of heat to which they are exposed. This is only a final cause, and the other a physical relation, the preciseness of which is remarkable in Jupiter and Saturn: it is nevertheless true, that the density of the earth, instead of being 206-7/8, is found to be 400, and that consequently the terrestrial globe must be condensed in this ratio of 206-7/8 to 400.

But have not the condensations of the planets some relation with the quantity of the heat of the sun which they sustain? If so, Saturn, which is the most distant from that luminary, will have suffered little or no condensation; and Jupiter will be condensed from 90-11/16 to 94-1/2. Now the heat of the sun in Jupiter being to that of the sun upon the earth as 14-17/22 are to 400, the condensations ought to be in the same proportion. For instance, if Jupiter be condensed, as 90-11/16 to 94-1/2, and the earth had been placed in his orbit, it would have been condensed from 206-7/8 to 215-990/1451, but the earth being nearer the sun, and receiving a heat, whose relation to that which Jupiter receives is from 400 to 14-17/22, the quantity of condensation it would have experienced on the orbit of Jupiter by the proportion of 400 to 14-17/22, which gives nearly 234-1/3 for the quantity which the earth would be condensed. Its density was 206-7/8, by adding the quantity of its acquired condensation, we find 400-7/8 for its actual density, which nearly approaches the real density 400, determined to be so by the parallax of the moon. As to other planets, I do not here pretend to give exact proportions, but only approximations, to point out that their densities have a strong relation to their velocity in their respective orbits.

The comet, therefore, by its oblique fall upon the surface of the sun, having driven therefrom a quantity of matter equal to the 650th part of its whole mass; this matter, which must be considered in a liquid state, will at first have formed a torrent, the grosser and less dense parts of which will have been driven the farthest, and the smaller and more dense, having received only the like impulsion, will remain nearest its source; the force of the sun's attraction would inevitably act upon all the parts detached from him, and constrain them to circulate around his body, and at the same time the mutual attraction of the particles of matter would form themselves into globes at different distances from the sun, the nearest of which necessarily moving with greater rapidity in their orbits than those at a distance.

But another objection may be started, and it may be said, if the matter which composes the planets had been separated from the sun, they, like him, would have been burning and luminous bodies, not cold and opaque, for nothing resembles a globe of fire less than a globe of earth and water; and by comparison, the matter of the earth and planets is perfectly different from that of the sun?

To this it may be answered, that in the separation the matter changed its form, and the light or fire was extinguished by the stroke which caused this motion of impulsion. Besides, may it not be supposed that if the sun, or a burning star, moved with such velocity as the planet, that the fire would soon be extinguished; and that is the reason why all luminous stars are fixed, and that those stars which are called new, and which have probably changed places, are frequently extinguished and lost? This remark is somewhat confirmed by what has been observed in comets; they must burn to the centre when they pass to their perihelium: nevertheless they do not become luminous themselves, they only exhale burning vapours, of which they leave a considerable part behind them in their course.

I own, that in a medium where there is very little or no resistance, fire may subsist and suffer a very great motion without being extinguished: I also own, that what I have just said extends only to the stars which totally disappear, and not to those which have periodical returns, and appear and disappear alternately without changing place in the heavens. The phenomena of these stars has been explained in a very satisfactory manner by M. de Maupertuis, in his discourse on the figures of the planets. But the stars which appear and afterwards disappear entirely, must certainly have been extinguished, either by the velocity of their motion, or some other cause. We have not a single example of one luminous star revolving round another; and among the number of planets which compose our system, and which move round the sun with more or less rapidity, there is not one luminous of itself.

It may also be added, that fire cannot subsist so long in the small as in large masses, and that the planets must have burnt for some time after they were separated from the sun, but were at length extinguished for want of combustible matter, as probably would be the sun itself, and for the same reason; but in a length of time as far beyond that which extinguished the planets, as it exceeds in quantity of matter. Be this as it may, the matter of which the planets are formed being separated from the sun, by the stroke of a comet, that appears a sufficient reason for the extinction of their fires.

The earth and planets at the time of their quitting the sun, were in a state of total liquid fire; in this state they remained only as long as the violence of the heat which had produced it; and which heat necessarily underwent a gradual decay: it was in this state of fluidity that they took their circular forms, and that their regular motions raised the parts of their equators, and lowered their poles. This figure, which agrees so perfectly with the laws of hydrostatics, I am of opinion with Leibnitz, necessarily supposes that the earth and planets have been in a state of fluidity, caused by fire, and that the internal part of the earth must be a vitrifiable matter, of which sand, granite, &c. are the fragments and scoria.

It may, therefore, with some probability, be thought that the planets appertained to the sun, that they were separated by a single stroke, which gave to them a motion of impulsion, and that their position at different distances from the sun proceeds only from their different densities. It now only remains, to complete this theory, to explain the diurnal motion of the planets, and the formation or the satellites; but this, far from adding difficulties to my hypothesis, seems, on the contrary, to confirm it.

For the diurnal motion, or rotation, depends solely on the obliquity of the stroke, an oblique impulse therefore on the surface of a body will necessarily give it a rotative motion; this motion will be equal and always the same, if the body which receives it is homogeneous, and it will be unequal if the body is composed of heterogeneous parts, or of different densities; hence we may conclude that in all the planets the matter is homogeneous, since their diurnal motions are equal, and regularly performed in the same period of time. Another proof that the separation of the dense or less dense parts were originally from the sun.

But the obliquity of the stroke might be such, as to separate from the body of the principal planet a small part of matter, which would of course continue to move in the same direction; these parts would be united, according to their densities, at different distances from the planet, by the force of their mutual attraction, and at the same time follow its course round the sun, by revolving about the body of the planet, nearly in the plane of its orbit. It is plain, that those small parts so separated are the satellites: thus the formation, position, and direction of the motions of the satellites perfectly agree with our theory; for they have all the same motion in concentrical circles round their principal planet; their motion is in the same direction, and that nearly in the plane of their orbits. All these effects, which are common to them, and which depend on an impulsive force, can proceed only from one common cause, which is, impulsive motion, communicated to them by one and the same oblique stroke.

What we have just said on the cause of the motion and formation of the satellites, will acquire more probability, if we consider all the circumstances of the phenomena. The planets which turn the swiftest on their axis, are those which have satellites. The earth turns quicker than Mars in the relation of about 24 to 15; the earth has a satellite, but Mars has none. Jupiter, whose rapidity round its axis is five to six hundred times greater than that of the earth, has four satellites, and there is a great appearance that Saturn, which has five, and a ring, turns still more quickly than Jupiter.

It may even be conjectured with some foundation, that the ring of Saturn is parallel to the equator of the planet, so that the plane of the equator of the ring, and that of Saturn, are nearly the same; for by supposing, according to the preceding theory, that the obliquity of the stroke by which Saturn has been set in motion was very great, the velocity around the axis will, at first, have been in proportion as the centrifugal force exceeds that of gravity, and there will be detached from its equator and neighbouring parts, a considerable quantity of matter, which will necessarily have taken the figure of a ring, whose plane must be nearly the same as that of the equator of the planet; and this quantity of matter having been detached from the vicinity of the equator of Saturn, must have lowered the equator of that planet, which causes that, notwithstanding its rapidity, the diameters of Saturn cannot be so unequal as those of Jupiter, which differ from each other more than an eleventh part.

However great the probability of what I have advanced on the formation of the planets and their satellites may appear to me, yet, every man has his particular measurement, to estimate probabilities of this nature; and as this measurement depends on the strength of the understanding to combine more or less distant relations, I do not pretend to convince the incredulous. I have not only thought it my duty to offer these ideas, because they appear to me reasonable, and calculated to clear up a subject, on which, however important, nothing has hitherto been written, but because the impulsive motion in the planets enter at least as one half of the composition of the universe, which gravity alone cannot unfold. I shall only add the following questions to those who are inclined to deny the possibility of my system.

1. Is it not natural to imagine, that a body in motion has received that motion by the stroke of another body?

2. Is it not very probable, that when many bodies move in the same direction, that they have received this direction by one single stroke, or by many strokes directed in the same manner?

3. Is it not more probable that when many bodies have the same direction in their motion, and are placed in the same plane, that they received this direction and this position by one and the same stroke, rather than by a number?

4. At the time a body is put in motion by the force of impulsion, is it not probable that it receives it obliquely, and, consequently, is obliged to turn on its axis so much the quicker, as the obliquity of the stroke will have been greater? If these questions should not appear unreasonable, the theory, of which we have presented the outlines, will cease to appear an absurdity.

Let us now pass on to something which more nearly concerns us, and examine the figure of the earth, on which so many researches and such great observations have been made. The earth being, as it appears by the equality of its diurnal motion and the constancy of the inclination of its axis, composed of homogeneous parts, which attract each other in proportion to their quantity of matter, it would necessarily have taken the figure of a globe perfectly spherical, if the motion of impulsation had been given it in a perpendicular direction to the surface; but this stroke having been obliquely given, the earth turned on its axis at the moment it took its form; and from the combination of this impulsive force, the attraction of the parts, there has resulted a spheroid figure, more elevated under the great circle of rotation, and lower at the two extremities of the axis, and this because the action of the centrifugal force proceeding from the diurnal rotation must diminish the action of gravity. Thus, the earth being homogeneous, and having received a rotative motion, necessarily took a spheroidical figure, the two axes of which differ a 230th part from each other. This may be clearly demonstrated, and does not depend on any hypothesis whatever. The laws of gravity are perfectly known, and we cannot doubt that bodies attract each other in a direct ratio of their masses, and in an inverted ratio, at the squares of their distances; so likewise we cannot doubt, that the general action of any body is not composed of all the particular actions of its parts. Thus each part of matter mutually attracts in a direct ratio of its mass and an inverted ratio of its distance, and from all these attractions there results a sphere when there is no rotatory motion, and a spheroid when there is one. This spheroid is longer or shorter at the two extremities of the axis of rotation, in proportion to the velocity of its diurnal motion, and the earth has then, by virtue of its rotative velocity, and of the mutual attraction of all its parts, the figure of a spheroid, the two axes of which are as 229 to 230 to one another.

Thus, by its original constituent, by its homogeneousness, and independent of every hypothesis from the direction of gravity, the earth has taken this figure of a spheroid at its formation, and agreeable to mechanical laws: its equatorial diameter was raised about 6-1/2 leagues higher than under the poles.

I shall dwell on this article, because there are still geometricians who think that the figure of the earth depends upon theory, and this from a system of philosophy they have embraced, and from a supposed direction of gravity. The first thing we have to demonstrate is, the mutual attraction of every part of matter, and the second the homogeneousness of the terrestrial globe; if we clearly prove, that these two circumstances are really so, there will no longer be any hypothesis to be made on the direction of gravity: the earth will necessarily have the figure Newton decided in favour of, and every other figure given to it by virtue of vortexes or other hypotheses, will not be able to subsist.

It cannot be doubted, that it is the force of gravity which retains the planets in their orbits; the satellites of Saturn gravitate towards Saturn, those of Jupiter towards Jupiter, the Moon gravitates towards the Earth: and Saturn, Jupiter, Mars, the Earth, Venus, and Mercury, gravitate towards the Sun: so likewise Saturn and Jupiter gravitate towards their satellites, the Earth gravitates towards the Moon, and the Sun towards the whole of the planets. Gravitation is therefore general and mutual in all the planetary system, for action cannot be exercised without a re-action; all the planets, therefore, act mutually one on the other. This mutual attraction serves as a foundation to the laws of their motion, and is demonstrated to exist by its effects. When Saturn and Jupiter are in conjunction, they act one on the other, and this attraction produces an irregularity in their motion round the Sun. It is the same with the Earth and the Moon, they also mutually attract each other; but the irregularities of the motion of the Moon, proceeds from the attraction of the Sun, so that the Earth, the Sun, and the Moon, mutually act one on the other. Now this mutual attraction of the planets, when the distances are equal, is proportional to their quantity of matter, and the same force of gravity which causes heavy matter to fall on the surface of the Earth, and which extends to the Moon, is also proportional to the quantity of matter; therefore the total gravity of a planet is composed of the gravity of each of its parts; from whence all the parts of the matter, either in the Earth or in the planets, mutually attract each other and the Earth, by its rotation round its own axis, has necessarily taken the figure of a spheroid, the axes of which are as 229 to 230. The direction of the weight must be perpendicular to the Earth's surface; consequently no hypothesis, drawn from the direction of gravity, can be sustained, unless the general attraction of the parts of matter be denied; but the existence of this mutual attraction is demonstrated by observations, and the experiment of pendulums prove, that its extension is general; therefore we cannot support an hypothesis on the direction of gravity without going against experience and reason.

Let us now proceed to examine whether the matter of which the terrestrial globe is composed be homogeneous. I admit, that if it is supposed the globe is more dense in some parts than in others, the direction of gravity must be different from what we have just assigned, and that the figure of the Earth would also differ agreeable to those suppositions. But what reason have we to make these suppositions? Why, for example, should we suppose that the parts near the centre are denser than those which are more remote? Are not all the particles which compose the globe collected together by their mutual attraction? hence, each particle is a centre, and there is no reason to believe, that the parts which surround the centre are denser than those which are about any other point. Besides, if one considerable part of the globe was denser than another, the axis of rotation would be found near the dense parts, and an inequality would ensue in the diurnal revolution; we should remark an inequality in the apparent motion of the fixed stars; they would appear to move more quick or slow in the zenith, or horizon, according as we should be placed on the denser or lighter parts of the earth; and the axis of the globe no longer passing through the centre of gravity, would also very sensibly change its position: but nothing like this ever happens; on the contrary, the diurnal motion of the earth is equal and uniform. At all parts of the Earth's surface, the stars appear to move with the same velocity at all heights, and if there be any rotation in its axis, it is so trifling as to have escaped observation: it must therefore be concluded, that the globe is homogeneous, or nearly so in all its parts.

If the earth was a hollow and void globe, and the crust of which, for example, not more than two or three miles thick; it would produce these effects. 1. The mountains would be such considerable parts of the whole thickness of the crust, that great irregularities in the motions of the Earth would be occasioned by the attraction of the Moon and Sun: for when the highest parts of the globe, as the Cordeliers, should have the Moon at noon, the attraction would be much stronger on the whole globe than when she was in the meridian of the lowest parts. 2. The attraction of mountains would be much more considerable than it is in comparison with the attraction of the whole globe, and experiments made at the mountain of Chimboraco, in Peru, would in this case give more degrees than they have given seconds for the deviation of the plumb line. 3. The weight of bodies would be greater on the tops of high mountains than on the planes; so that we should feel ourselves considerably heavier, and should walk with more difficulty in high than in low places. These observations, with many others that might be added, must convince us, that the inner parts of the globe is not void, but filled with a dense matter.

On the other hand, if below the depth of two or three miles, the earth was filled with a matter much more dense than any known, it would necessarily occur, that every time we descended to moderate depths, we should weigh much more, and the motion of pendulums would be more accelerated than in fact they are when carried from an eminence into a plain: thus, we may presume that the internal part of the Earth is filled with a matter nearly similar to that which composes its surface. What may complete our determination in favour of this opinion is, that in the first formation of the globe, when it took its present spheroidical figure, the matter which composed it was in fusion, and, consequently, all its parts were homogeneous, and nearly equally dense. From that time the matter on the surface, although originally the same with the interior, has undergone a variety of changes by external causes, which has produced materials of such different densities; but it must be remarked, that the densest matters, as gold and metals, are also those the most seldom to be met with, and consequently the greatest part of the matter at the surface of the globe has not undergone any very great changes with relation to its density; the most common materials, as sand and clay, differ very little, insomuch, that we may conjecture, with great probability, that the internal part of the earth is composed of a vitrified matter, the density of which is nearly the same as that of sand, and that consequently the terrestrial globe in general may be regarded as homogeneous.

Notwithstanding this, it may be urged, that although the globe was composed of concentrical strata of different densities, the diurnal motion might be equally certain, and the uniform inclination of the axis as constant and undisturbed as it could be, on the supposition of its being composed of homogeneous matter. I acknowledge it, but I ask at the same time, if there is any reason to believe that strata of different densities do exist? If these conclusions be not rather a desire to adjust the works of Nature to our own ideas? And whether in physics we ought to admit suppositions which are not founded on observations or analogy?

It appears, therefore, that the earth, by virtue of the mutual attraction of its parts and its diurnal motion, assumed the figure of a spheroid; that it necessarily took that form from being in a state of fluidity; that, agreeable to the laws of gravity and of a centrifugal force, it could have no other figure: that in the moment of its formation as at present, there was a difference between the two diameters equal to a 230th part, and that, consequently, every hypothesis in which we find greater or less difference are fictions which merit no attention.

But it may be said, if this theory is true, and if 229 to 230 is the just relation of the axis, why did the mathematicians, sent to Lapland and Peru, agree to the relation of 174 to 175? From whence does this difference arise between theory and practice? And is it not more reasonable to give the preference to practice and measures, especially when we have been taken by the most able mathematicians of Europe[109:A], and with all necessary apparatus to establish the result.

To this I answer, that I have paid attention to the observations made at the equator and near the polar circle; that I have no doubt of their being exact, and that the earth may possibly be elevated an 175th part more at the equator than at the poles. But, at the same time, I maintain my theory, and I see clearly how the two conclusions may be reconciled. This difference is about four leagues in the two axes, so that the parts at the equator are raised two leagues more than they ought to be, according to my theory; this height answers exactly to the greatest inequalities on the surface of the globe, produced by the motion of the sea, and the action of the fluids. I will explain; it appears that when the earth was formed, it must necessarily have taken, by virtue of the mutual attraction of its parts, and the action of the centrifugal force, a spheroidical figure, the axes of which differ a 230th part: the original earth must have had this figure, which it took when it was fluid, or rather liquified by the fire; but after its formation the vapours which were extended and rarefied, as in the atmosphere and tail of a comet, became condensed, and fell on the surface in form of air and water: and when these waters became agitated by the flux and reflux, the matters were, by degrees, carried from the poles towards the equatorial parts; so that the poles were lowered about a league, and those of the equator raised in the same proportion; this was not suddenly done, but by degrees in succession of time; the earth being also exposed to the action of the winds, air, and sun; all these irregular causes concurred with the flux and reflux to furrow its surface, hollow it into valleys, and raise it into mountains; and producing other inequalities and irregularities, of which, nevertheless, the greatest thickness does not exceed one league at the equator; this inequality of two leagues, is, perhaps, the greatest which can be on the surface of the earth, for the highest mountains are scarce above one league in height, and there is much probability of the sea's not being more at its greatest depth. The theory is therefore true, and practice may be so likewise; the earth at first could not be raised above 6-1/2 leagues more at the equator than the poles, but the changes which have happened to its surface might afterwards raise it still more. Natural History wonderfully confirms this opinion, for we have proved in the preceding discourse that the flux and reflux, and other motions of the water, have produced mountains and all the inequalities on the surface of the globe, that this surface has undergone considerable changes, and that at the greatest depths, as well as on the greatest heights, bones, shells and other wrecks of animals, which inhabit the sea and earth, are met with.

It may be conjectured, from what has been said, that to find ancient earth, and matters which have never been removed from the spot in which they were first placed, we must dig near the poles, where the bed of the earth must be thinner than in the Southern climates.

On the whole, if we strictly examine the measures by which the figure of the earth is determined, we shall perceive this hypothesis enters into such determination; for it supposes the earth to have the figure of a regular curve, whereas from the constant changes the earth is continually undergoing from a variety and combination of causes, it is almost impossible that it should have retained any regular figure, and hence the poles might, originally, only be flattened a 230th part, as Newton says, and as my theory requires. Besides, although we had exactly the length of the degree at the polar circle and equator, have we not also the length of the degree as exactly in France? And the measure of M. Picard, has it not been verified? Add to this that the augmentation and diminution in the motion of the pendulum, do not agree with the result drawn from measurement, and that, on the contrary, they differ very little from the theory of Newton. This is surely more than is requisite to convince us that the poles are not flattened more than a 230th part, and that if there is any difference, it can proceed only from the inequalities, which the water and other external causes have produced on its surface; but these inequalities being more irregular than regular, we must not form any hypothesis thereon, nor suppose, that the meridians are ellipses, or any other regular curves. From whence we perceive, that if we should successively measure many degrees of the earth in all directions, we still should not be certain by that alone, of the exact situation of the poles, nor whether they were depressed more or less than the 230th part.

May it not also be conjectured, that if the inclination of the axis of the earth has changed, it can only be produced by the changes which have happened to the surface, since all the rest of the globe is homogeneous; that consequently this variation is too little sensible to be perceived by astronomers, and that if the earth is not encountered with a comet, or deranged, by any other external cause, its axis will remain perpetually inclined as it is at present, and as it has always been?

In order not to omit any conjecture which appears reasonable, may it not be said, that as the mountains and inequalities which are on the surface of the earth have been formed by the flux and reflux of the sea, the mountains and inequalities which we remark on the surface of the moon, have been produced by a similar cause? they certainly are much higher than those of the earth, but then her tides are also much stronger, occasioned by the earth's being considerably larger than the moon, and consequently producing her tides with a superior force; and this effect would be much greater if the moon had, like the earth, a rapid rotation; but as the moon presents always the same surface to the earth, the tides cannot operate but in proportion to the motion arising from her libration, by which it alternatively discovers to us a segment of its other hemisphere; this, however, must produce a kind of flux and reflux, quite different from that of our sea, and the effects of which will be much less considerable than if the moon had from its course a revolution round its axis, as quick as the rotation of the terrestrial globe.

I should furnish a volume as large as that of Burnet or Whiston's, if I were to enlarge on the ideas which arise in support of the above; by giving them a geometrical air, in imitation of the last author, I might add considerably to their weight; but, in my opinion, hypothesis, however probable, ought not to be treated with such pomposity; it being a dress which borders so much on quackery.

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