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 Europe5, 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.