PROOFS
OF THE
THEORY OF THE EARTH
ARTICLE I.
Of the Formation of Planets.
NATURAL history being our subject, we would willingly dispense with astronomical observations. But, as the Earth is so nearly related to the heavenly bodies, and as observations of this kind illustrate more fully those doctrines we have already advanced, it is necessary to give some general ideas of the formation, motion, and figure of the earth, and other planets.
The earth is a globe of about 3000 leagues in diameter; it is situated 30 million of leagues from the sun, round which it revolves in 365 days. The annual revolution is the effect of two forces; the one may be considered as an impulse from right to left, or from left to right; the [59] other as an attraction from above downwards, or from below upwards, to a common centre. The direction and quantity of these forces are combined, and so nicely adjusted, that they produce a uniform motion in an ellipse approaching to a circle. Like the other planets, the earth is opaque, throws out a shadow, and reflects the rays of the sun, about which it revolves in a time proportioned to its relative distance and density. It likewise revolves about its own axis in 24 hours; and its axis is inclined to the plane of its orbit 66 ½ degrees. Its figure is that of a spheroid, the two axes of which differ from each other about 165th part; and it revolves round the shortest axis.
These are the principal phaenomena of the earth, the results of discoveries made by means of geometry, astronomy, and navigation. It is unnecessary here to enumerate the proofs and observations by which these facts have been established. We shall continue our remarks to such objects as are still doubtful; and shall therefore proceed to give our ideas concerning the formation of planets, and the changes they have undergone, previous to their arriving at the state in which we now perceive them. To the many systems and hypotheses that have been framed concerning the formation of the earth, and the different states it has passed through, we may be allowed to add our own conjectures, especially as we are determined to support them with a su- [60] perior degree of probability; and we are the more encouraged to deliver our notion on this subject, because we hope to enable the reader to distinguish between an hypothesis which consists only of possibilities, and a theory supported by facts; between a system, such as we are about to give, of the formation and primitive state of the earth, and a physical history of its real condition, which has been giving in the preceding discourse.
Galileo having traced the laws of falling bodies, and Kepler having observed, that the areas which the principal planets describe in moving round the sun, and those of the satellites round the planets to which they belong, were proportioned to the periods of their revolutions, and that these periods were as the square roots of the cubes of their distances from the sun, or from the principal planets. Newton discovered that the power of gravity extended to the moon, and retained it in its orbit; that the force of gravity diminished in exact proportion to the squares of the distances, and, consequently, that the moon is attracted by the earth; that the earth, and all planets, are attracted by the sun; and, in general, that all bodies which revolve about a centre, and describe areas proportioned to the periods of their revolution, are attracted by that luminary. Gravity, therefore, is a general law of nature. The planets, comets, the sun, the earth, are all subject to its laws; and it is the force of that harmony which prevails in the universe. Nothing [61] in physics is better established than the existence of this power in every material body. Repeated experience has confirmed the effects of its influence, and the labour and ingenuity of geometers have determined its quantity and relations.
This general law being once discovered, the effects of it would be easily explained, if the action of those bodies which produce them were not too complicated. A slight view of the solar system will convince us of the difficulties which attend this subject. The principal planets are attracted by the sun, the sun by the planets, the satellites by their principal planets, and each planet attracts all the others, and is attracted by them. All these actions and re-actions vary according to the quantities of matter and the distances, and give rise to great inequalities, and even irregularities. How are so many relations to be combined and estimated? Among such a number of objects, how is it possible to trace any individual? These difficulties, however, have been surmounted; the reasonings of theory have been confirmed by calculation; every observation has produced a new demonstration; and the systematic order of the universe is now laid open to every man who is able to distinguish truth from error.
The force of impulsion, or what is commonly called the centrifugal force, is still unknown; [62] but it affects not the general theory. It is evident, that, as the attractive force continually draws all the planets towards the sun, they would fall in a perpendicular line into that luminary, if they were not kept at a distance by some other power, forcing them to move in a straight line. If, again, this impulsive force were not counteracted by that of attraction, all the planets would fly off in the tangents of their respective orbits. This progressive or impulsive force was unquestionably at first communicated to the planets by the Supreme Being. But, in physical subjects, we ought, as much as possible, to avoid having recourse to supernatural causes; and, I imagine, a probable reason may be assigned for the impulsive force of the planets, which will be agreeable to the laws of mechanics, and not more surprising than many revolutions that must have happened in the universe.
The sphere of the sun’s attraction is not limited by the orbits of the planets, but extends to an indefinite distance, always decreasing according as the squares of the augmented distances. The comets, it is evident, which escape our sight in the heavenly regions, are, like the planets, subject to the attraction of the sun, and by it their motions are regulated. All these bodies, the directions of which are so various, move round the sun, and describe areas proportioned to their periods, the planets in ellipses, more or less circular, and the comets, in narrow ellipses of vast [63] extent. The motions, therefore, both of planets and comets, are regulated by impulsive and attractive forces continually acting upon them, and obliging them to describe curves. But it is worthy of remark, that comets run through the system in all directions; that the inclinations of the planes of their orbits are so very different, that though, like the planets, they be subject to the law of attraction, they have nothing in common with regard to their progressive or impulsive motions, but appear, in this respect, to be absolutely independent of each other. The planets, on the contrary, move round the sun in the same direction, and nearly in the same plane, the greatest inclination of their planes not exceeding 7 ½ degrees. This similarity in the position and motion of the planets indicates, that their impulsive or centrifugal forces must have originated from one common cause.
May we not conjecture, that a comet falling into the body of the sun might drive off some parts from its surface, and communicate to them a violent impulsive force, which they still retain? This conjecture appears to be as well founded as that of Mr Leibnitz, which supposed the earth and planets to have formerly been suns; and his system, of which an abridgement will be given in art. V. would have been more comprehensive, and more consonant to probability, if it had embraced the above idea. We agree with him, that this effect was produced at [64] the time when God is said by Moses to have separated the light from darkness; for, according to Leibnitz, the light was separated from the darkness when the planets were extinguished. But, on our supposition, there was a real physical separation; because the opaque bodies of the planets were detached from the luminous matter of which the sun is composed.*
This notion concerning the cause of the centrifugal force of the planets will appear to be less exceptionable, after we have collected the analogies, and estimated the degrees of probability by which it may be supported. We shall first mention, that the motion of the planets have one common direction, namely, from west to east. By the doctrine of chances, it is easy to demonstrate, that this circumstance makes it as 64 to 1, that the planets could not all move in the same direction, if their centrifugal forces had not proceeded from the same cause.
This probability will be greatly augmented, if we take in the similarity in the inclinations of the planes of their orbits, which exceed not 7 ½ degrees; for, by calculations it has been discovered, that it is 24 to 1 against any two planets being found, at the same time, in the most distant parts of their orbits; and, consequently, 245, or 7692624 to 1, that this effect could not [65] be produced by accident; or, what amounts to the same, there is this great degree of probability, that the planets have been impressed with one common moving force, from which they have derived this singular position. But nothing could bestow this common centrifugal motion, excepting the force and direction of the bodies by which it was originally communicated. We may, therefore, conclude, that all the planets have probably received their centrifugal motion by one single stroke. Having established this degree of probability, which almost amounts to a certainty, I next inquire what moving bodies could produce this effect; and I can find nothing but comets capable of communicating motion to such vast masses.
Upon examining the course of comets, it is easy to believe that some of them must occasionally fall into the sun. The comet 1680 approached so near, that, at its perihelion, it was not more distant from the sun than a sixteenth part of its diameter; and, if it returns, which is extremely probable, in the year 2255, it may then fall into the sun. This must depend upon the accidents it meets with in its course, and the retardations it suffers in passing through the sun’s atmosphere.*
We may, therefore, presume, with the great Newton, that comets sometimes fall into the sun. But they may fall in different directions. [66] If they fall perpendicularly, or in a direction not very oblique, they will remain in the body of the sun, serve the purposes of feuel [sic], and, by their impulse, remove the sun from his place, in proportion to the quantity of matter they contain.* But, if a comet falls in a very oblique direction, which will most frequently happen, it will only graze the surface, or penetrate to no great depth. In this case, it may force its way past the sun, detach certain portions of his body, to which it will communicate a common impulsive motion; and these portions pushed off from the sun, and even the comet itself, may turn planets, which will revolve round this luminary in the same direction, and nearly the same plane. A calculation, perhaps, might be made of the quantity of matter, velocity, and direction, a comet ought to have, in order to force from the sun masses equal to those which compose the six planets and their satellites. But it is sufficient here to observe, that the whole planets, with their satellites, make not a 650th part of the sun’s mass;+ for, although the density of Saturn and Jupiter be less than that of the sun, and though the earth be four times, and the moon near five times more dense than the sun; yet they are only atoms when compared to his immense volume. [67]
It must be acknowledged, that, although a 650th part of a whole may seem inconsiderable, it would require a very large comet to detach this part from the sun. But, if we consider the prodigious rapidity of comets in their perihelion, the near approach they make to the sun; the density and the strong cohesion of parts necessary to sustain, without destruction, the inconceivable heat they undergo; and the solid and brilliant nucleus which shines through their dark atmospheres; it cannot be doubted that comets are composed of matters extremely dense and solid; that they contain, in small limits, a great quantity of matter; and, consequently, that a comet of no enormous size may remove the sun from its place, and give a projectile motion to a mass of matter equal to the 650th part of his body. This remark corresponds with what we know concerning the respective densities of the planets, which always decrease in proportion to their distances from the sun, having less force of heat to resist. Accordingly, Saturn is less dense than Jupiter, and Jupiter much less than the earth. Thus, if the density of the planets, as Newton alledges, be in proportion to the quantity of heat they support, Mercury will be seven times denser than the earth, and 28 times denser than the sun, and the comet 1680 28,000 times more dense than the earth, or 112,000 times denser than the sun. Now, supposing the quantity of matter in this comet to be equal to a [68] ninth part of the sun, or, allowing it to e only 100dth part of the bulk of the earth, its quantity of matter would still be equal to a 900dth part of the sun: Hence a body of this kind, which would be but a small comet, might push off from the sun a 900dth or a 650th part, especially when the amazing rapidity of comets, in their perihelion, is taken into the calculation.
The correspondence between the density of the whole planets, and that of the sun, deserves also to be noticed. Upon and near the surface of the earth, there are substances 1400 or 1500 times denser than others; the densities of air and gold are nearly in this proportion. But the interior parts of the earth and planets are more uniform, and differ little with regard to density; and the correspondence in the density of the planets and that of the sun is so great, that, out of 650 parts, which comprehends the whole density of the planets, there are more than 640 nearly of the same density with the solar matter; and there are only ten of those 650 that are of a superior density; for the density of Saturn and Jupiter is nearly the same with that of the sun; and the quantity of matter in those two planets is at least 64 times greater than what is contained in the four inferior planets, Mars, the Earth, Venus, and Mercury. We may, therefore, conclude, that, in general, the matter of the planets is very nearly of the same kind with the solar matter, and, of course, that [69] the former may have been separated from the latter.
To this theory, it may be objected, that, if the planets had been driven off from the sun by a comet, in place of describing circles round him, they must, according to the law of projectiles, have returned to the same place from whence they had been forced; and, therefore, that the projectile force of the planets cannot be attributed to the impulse of a comet.
I reply, that the planets issued not from the sun in the form of globes, but in the form of torrents, the motion of whose anterior particles behoved [sic] to be accelerated by those behind, and the attraction of the anterior particles would also accelerate the motion of the posterior; and that this acceleration, produced by one or both of these causes, might be such as would necessarily change the original motion arising from the impulse of the comet, and that, from this cause, might result a motion similar to what takes place in the planets, especially when it is considered, that the shock of the comets removes the sun out of its former station. This reasoning may be illustrated by an example. Suppose a musket-ball discharged from the top of a mountain, and that the force of the powder was sufficient to push it beyond a semidiameter of the earth, it is certain that this ball would revolve round the earth, and return at every revolution to the place from whence it had been discharged. But, [70] instead of a musket-ball, if a rocket were employed, the continued action of the fire would greatly accelerate the original impulsive motion. This rocket would by no means return to the same point, like the ball; but, caeteris paribus, would describe describe an orbit, the perigee of which would be more or less distant from the earth in proportion to the greatness of the change produced in its direction by the accelerating force of the fire. In the same manner, if the original projectile force impressed by the comet on the torrent of solar matter was accelerated, it is probable, that the planets formed by this torrent acquired their circular or elliptical movements around the sun.
The appearance exhibited in great eruptions from volcano’s may give some idea of this acceleration of motion. When Vesuvius begins to groan and throw out inflamed matter, it has been often remarked, that the motion of the cloud first ejected is slower than the succeeding ones, and that they go on increasing in celerity, till at last sulphur [sic], lava, melted metal, and huge stones are thrown up; and that, though these observe nearly the same direction, they alter considerably that of the first cloud, and elevate it to a greater height than it would otherwise have reached.* [71]
The objection will be still farther obviated, if it is considered, that the impulse of the comet must, in some degree, have communicated a motion to the sun, and removed it from its former situation; and that, although this motion may now be so small as to escape the notice of astronomers, it may still, however, exist, and make the sun describe a curve round the center of gravity of the system. If this be allowed, as I presume it will, the planets, instead of returning to the sun’s body, would describe orbits, the perihelions of which would be as distant from the sun as the space which he presently occupies is distant from his original station.
It may be further objected, that, if motion be accelerated in the same direction, no change in the perihelion could take place. But, is it credible, that no change of direction can happen in a torrent whose particles succeed each other? On the contrary, it is extremely probable, that a change was actually produced sufficient to cause the planets move [sic] in their present orbits.
It may still be objected, that, if the situation of the sun had been changed by the shock of a comet, it would move uniformly; and, of course, this motion being common to the whole system, no alteration would be effected. But, previous to the shock, might not the sun move round [72] the centre of the cometary system; and might not this primary motion be augmented or diminished by the stroke of the comet? Is not this sufficient to account for the actual motion of the planets?
If none of these suppositions be admitted, may it not be presumed, that the elasticity of the sun might elevate the torrent above his surface, in place of pushing it directly forward? This of itself would be sufficient to remove the perihelion, and endow the planets with their present movements. Neither is this supposition destitute of foundation: The solar matter may be exceedingly elastic; since light, the only part of it we are acquainted with, seems, by its effects, to be perfectly elastic. I acknowledge that I cannot determine which of the causes above assigned has actually produced an alteration in the projectile force of the planets; but they at least show that such a change is not only possible, but probable; and this is enough for my present purpose.
Without farther insisting on the objections that may be made against my hypothesis, or the analogical proofs that might be brought in support of it, I shall prosecute my subject, and draw the proper conclusions. Let us first examine what might happen to the planets, and particularly to the earth, when they were impressed with their projectile forces, and what was their state after their separation from the body of the [73] sun. A projectile motion having been communicated by the stroke of a comet, to a quantity of matter equal to 650th part of the sun’s mass, the light particles would separate from the dense, and, by their mutual attractions, form globes of different solidities. Saturn being composed of the largest and lightest part, would be removed to the greatest distance from the sun; Jupiter, being denser than Saturn, would have a nearer station; and so of the rest. The largest and least solid planets are most distant, because they received a greater projectile force than the smaller and denser; for the projectile force being proportioned to the surfaces to which it is applied, the same stroke would make the larger and lighter parts of the solar matter move with more rapidity tha n the smaller and heavier. The parts, therefore, which differed in density would separate from each other in such a manner, that, if the density of the solar matter be equal to 100, that of Saturn will be equal to 67, of Jupiter, = 94 ½ , of Mars, = 200, of the Earth, = 400, of Venus, = 800, of Mercury, = 2800. But, as the attractive force acts not in proportion to the surface, but to the quantity of matter, it would retard the progress of the more dense parts of the solar matter; and it is for this reason that we find the most dense planets nearest the sun, and which move round him with more rapidity than those that are more distant, and less dense. [74]
The density and projectile motion of Saturn and Jupiter , the two largest planets in the system, have the most exact proportion. The density of Saturn is to that of Jupiter as 67 to 94 ½, and their velocities are nearly as 88 2/3 to 120 1/72, or as 67 to 90 11/16. How rarely do pure conjectures correspond so exactly to the phaenomena of nature? It is true, according to this relation between the celerity and density of the planets, the density of the earth ought not to exceed 206 7/18, instead of 400, which is its real density; hence it may be supposed, that the earth has now double its original density. With regard to the other planets, Marx, Venus, and Mercury, as their densities are only conjectural, we know not whether this circumstance would confirm or weaken our hypothesis. Newton says, that the densities of the planets are proportioned to the degrees of heat they are exposed to; and, it is in consequence of this idea, that we have mentioned Mars as being one time less dense that eh earth, Venus one tijme, Mercury seven times, and the comet 1680, 28,000 times denser than the earth. But, if we attend to Saturn and Jupiter, the two principal planets, we will find, that this supposed proportion between the densities of the planets, and the heat they sustain, is not well founded: For, according to this hypothesis, the density of Saturn would be as 4 7/18, and that of Jupiter ads 14 17/22, instead of the proportions of 67 and 94 ½; differences so great as [75] to destroy the principles upon which they are founded. Thus, notwithstanding the regard due to the conjectures of Newton, I cannot help thinking that the densities of the planets have a nearer relation to their celerities than to the degrees of heat to which they are exposed. This, indeed, is only a final cause, but the other is a physical relation, the exactness of which is remarkable in Saturn and Jupiter. It is, however, certain, that the density of the earth, instead of being 206 7/8, is 400; and consequently, the earth must have suffered a condensation in the proportion of 206 7/8 to 400.
But, have the condensations of the planets no relation to the quantity of solar heat they sustain? In that case, Saturn, which is at the greatest distance from the sun, would have suffered little or no condensation; and Jupiter would be condensed from 99 11/16 to 94 ½. Now, the sun’s heat in Jupiter being to his heat in the earth as 14 17/22 to 400, their condensation ought to be in the same proportion. Thus, if Jupiter be condensed as 90 11/16 to 94 ½, the earth, if it had been in the orbit of Jupiter, as 400 to 14 1722, the quantity of condensation it would have undergone in the orbit of Jupiter must be multiplied by the proportion of 400 to 14 17/22, which will give nearly 234 1/8 for the condensa- [76] tion the earth must have received. The density of the earth was 206 7/8; by adding its acquired condensation, its actual density will be 400 7/8, which is nearly the same with 400, its real density determined by the moon’s parallax. With regard to the other planets, I pretend not to give exact proportions, but only approximations, tending to show, that their densities have a strong connection with the celerity of their motions in their respective orbits.
The comet, by falling obliquely on the sun, as mentioned above, must have forced off from his surface a quantity of matter equal to a 650th part of his body. This matter being in a liquid state, would at first form a torrent, of which the largest and rarest parts would fly to the greatest distances; the smaller and more dense, having received only an equal impulse, would remain nearer the sun; his power of attraction would operate upon all the parts detached from his body, and make them circulate round him; and, at the same time, the mutual attraction of the particles of matter would cause all the detached parts to take on the form of globes, at different distances from the sun, the nearer moving with greater rapidity in their orbits than the more remote.
But, to this it may be objected, that, if the planets had been detached from the sun, they must have been burning and luminous, not cold and opaque bodies; nothing can have less re- [77] semblance to a globe of fire than a globe composed of earth and water; and, by comparison, the matter of the earth is totally different from that of the sun.
It may be replied to this objection, that the matter changed its form upon its separation, and that the fire, or light, was extinguished by the projectile motion communicated by the stroke. Besides, may it not be supposed, that the sun, or a burning star, moving with a rapidity equal to that of the planets, would soon be extinguished; and that this may be the reason why all the luminous, or burning stars, are fixed, and with out motion; and why those called new stars, which have probably changed their stations, are frequently extinguished and disappear? To confirm this remark, comets, when in their perihelia, ought to be inflamed even to their center; but they never become luminous stars; they only emit a burning vapour, a considerable portion of which they leave behind them in their course.
In a medium which has little resistance, I acknowledge, that fire may subsist, although the burning body be moved with great rapidity. It must likewise be acknowledged, that what I have said applies only to those stars which disappear for ever, not to those that appear and disappear at stated intervals, without changing their situations in the heavens. Of these Maupertuis, in his discourse on the figure of the stars, has given a most satisfactory account. But those [78] which have appeared, and then vanished for ever, must unquestionably have been extinguished either by the quickness of their motion, or some other cause. There is not a single example of a luminous star revolving round another; and not one of the sixteen planets which revolve round the sun have any light in themselves.
Farther, fire, in small masses, cannot subsist so long as in large ones. The planets would burn a considerable time after they issued from the sun; but, at length, would extinguish for want of combustible matter. For the same reason, the sun itself will be extinguished; but at a period as much beyond that which extinguished the planets, as the quantity of matter in the sun exceeds that of the planets. However this may be, the separation of the planets from the sun, by the shock of a comet, appears sufficient to account for their extinction.
The earth and planets, when they issued from the sun, were totally composed of liquid fire; in which state they would continue no longer than the violence of the heat that kept them in fusion. But this heat would gradually decay from the moment they left the sun. During their fluid state, they necessarily assumed circular figures; and their diurnal motion would elevate their equators, and flatter their poles. I agree with M. Leibnitz,* that this figure corresponds [79] so exactly with the laws of hydrostatics, that the earth and planets must necessarily have bee nonce in a state of fluidity occasioned by fire; and consequently, that the interior parts of the earth must be composed of vitrified matter, of which sand, free-stone, granite, and perhaps clay, are fragments, or scoriae.
It is therefore extremely probable, that the planets were originally parts of the sun separated by a stroke which communicated to them a projectile motion; and that their different distances proceeded solely from the difference of their densities. To compleat this theory, it only remains to account for the diurnal motion of the planets, and the origin of their satellites; and this, instead of adding fresh difficulties, will tend greatly to confirm my hypothesis: For rotation, or what is called diurnal motion, entirely depends on the obliquity of the stroke; an oblique impulse on the surface of a body necessarily gives it a rotatory motion. If the body which receives the impulse by homogeneous, the rotatory motion will always be equal and uniform; but it will be unequal, if the body consist of heterogeneous parts, or of parts different in density. Hence we may conclude, that the matter of each planet is homogeneous, because the diurnal motion of each is uniformly performed in the same time; and this circumstance is an additional proof, that portions of different densities were originally separated from the sun. [80]
But the obliquity of the stroke might be so great as to throw off small quantities of matter from the principal planet, which would necessarily move in the same direction. These parts, by mutual attraction, would reunite, according to their densities, at different distances from the planet, follow its course round the sun, and at the same time revolve about the body of the planet, nearly in the plane of its orbit. It is easy to perceive that the portions we mean are the satellites: Thus the formation, position, and motion of the satellites correspond, in the most perfect manner, with our theory; for they all move in the same direction, and in concentric circles round their principal planets, and nearly in the plane of their orbits. All these common effects, depending on an impulsive force, must have proceeded from a common cause, which was a projectile force communicated to them by the same oblique stroke. This account of the motion and formation of the satellites will be strongly supported, if the other circumstances and phaenomena attending them be duly weighted. Those planets that are furnished with satellites, move quickest round their axes. The revolution of the earth is quicker than that of Mars, in the proportion nearly of 24 to 15; the earth has a satellite, and Mars has none; Jupiter, whose diurnal motion is 500 or 600 times more rapid than that of the earth, has four satellites; and it is extremely probable, that Saturn, who [81] has five satellites and a ring, revolves much more quickly than Jupiter.
We may even conjecture, with some probability, that the plane of the equator of Saturn’s ring is nearly the same with that of the planet; for, supposing, according to the preceding theory, the obliquity of the impulse which put Saturn in motion to have been very great, his diurnal motion would at first be in proportion to the excess of the centrifugal force above that of gravity, and, of course, a considerable quantity of matter would be thrown off from his equatorial regions, and necessarily assume the figure of a ring, the plane of which would be nearly the same with that of his own equator. This quantity of matter detached from the equatorial regions of Saturn, must have flattened the equator of that planet; which is the reason why, notwithstanding him to revolve round his axis, the diameters of Saturn are not so unequal as those of Jupiter, which differ from each other more than an eleventh part.
Though this theory of the formation of the planets and their satellites appears to be extremely probable; yet, as every man has his own standard of estimating probabilities of this nature, and as this standard varies according to the different capacities of combining analogies more or less remote, I pretend not to convince those who are unwilling to believe. I have offered those [82] ideas to the public, not only because I though them rational, and calculated to unravel a subject upon which, however important, nothing has hitherto been written; but because the impulsive motion of the planets gives rise to numberless phaenomena in the universe, which admit not of an explanation by gravity alone. To those who may be disposed to deny the possibility of my theory, I would propose the following queries:
1. Is it not natural to image, that a moving body has received its motion from the impulse of some other body?
2. When several bodies move in the same direction, is it not exceedingly probable, that they received this direction from a single stroke, or, at least, from strokes every way similar?
3. When several bodies in motion have not only the same direction, but are placed in the same plane, it is not more natural to think that they received this direction and position from one impulse than from many?
4. Is it not probable, that a body put in motion by impulse, should receive it in an oblique direction; and consequently that it should be forced to move round its axis with a rapidity proportioned to the obliquity of the stroke? If these queries be not unreasonable, the theory of which we have given a sketch will no longer have the appearance of absurdity. [83]
Let us know proceed to a more interesting object; let us examine the figure of the earth, upon which so many inquiries and observations have been made. As it appears, from the equality of the earth’s diurnal motion, and the uniformity in the inclination of its axis, that it is composed of homogeneous parts which mutually attract each other in proportion to their quantities of matter; if its impulsive motion had been communicated in a direction perpendicular to its surface, it would necessarily have assumed the figure of a perfect sphere: But, having been struck obliquely, it moved round its axis at the instant it received its figure; and, from the combination of the projectile force and that of attraction, there resulted a spheroid figures, more elevated at the equator than at the poles; because the centrifugal force, arising from the diurnal rotation of the earth, must diminish the action of gravity, or that power which makes all the parts tend to the centre. Thus the earth, being composed of homogeneous parts, and having been endowed with a rotatory motion, must necessarily have assumed a spheroidal figure, the two axes of which differ from each other by a 230th part. To show that this is the real figure of the earth, we need not have recourse to hypotheses; it is capable of the clearest demonstration. The laws of gravitation are well known: That bodies attract each other di- [84] rectly as their quantities of matter, and inversely as the squares of their distances, admits not of a doubt. It can as little be doubted, that the total action of any body is composed of all the particular actions of its parts.
The parts of bodies are all mutually attracted in the above proportion; and all these attractions, when the body has no rotation, necessarily produce a sphere, and a spheroid, when the body is endowed with a rotatory motion. This spheroid is more or less flattened at the poles in proportion to the quickness of its diurnal motion; and the earth, in consequence of the celerity of its rotation, and the mutual attraction of its parts, has assumed the figure of a spheroid, of which the two axes are to one another as 229 to 230.
Thus the earth, at the time of its formation, from the original constitution and homogeneity of its parts, and independent of every hypothesis derived from the direction of gravity, took the figure of a spheroid; and, from the known laws of mechanics, its equatorial diameter was necessarily elevated about six leagues and a half more than its poles.
I shall dwell on the longer on this article, because there are some geometers, who, from a system of philosophy they have adopted, and from a supposed direction of gravity, still imagine that the figure of the earth depends upon theory. The first thing to be demonstrated is [85] the mutual attraction of the parts of matter; and the second, the homogeneity of the terrestrial globe. When these two facts are clearly proved, there will be no occasion to have recourse to any theory derived from the direction of gravity; because the earth’s figure, in this case, must necessarily be as Newton determined it; and all the other figures assigned to it in consequence of vortexes, and other hypotheses, can have no existence.
It will not be doubted, even by the most incredulous, that the planets are retained in their orbits by the power of gravity. The satellites of Saturn gravitate towards that planet, those of Jupiter towards Jupiter; the moon gravitates towards the earth; and Saturn, Jupiter, Mars, the Earth, Venus, and Mercury, gravitate towards the sun. In the same manner, Saturn, Jupiter, and the Earth, gravitate towards their respective satellites, and the sun gravitates towards the whole planets. Gravitation is therefore a general law, by which the whole planetary system is mutually affected; for action cannot exist without re-action. This mutual attraction of the planets is the law which regulates all their motions; and its existence is demonstrated by its effects. When Saturn and Jupiter are in conjunction, their mutual attraction produces an irregularity in their motion round the sun. The earth and the moon, also, mutually attract each other; but the irregularities in the moon’s mo- [86] tion proceed principally from the attraction of the sun; and hence the sun, the earth, and the moon, mutually act upon each other. Now, the reciprocal attraction of the planets, when the distances are equal, is proportioned to their quantities of matter; and the same power of gravity, which makes heavy bodies fall to the earth, and which extends as far as the moon, is likewise in proportion to the quantity of matter: The total gravity of a planet, therefore, is composed of the gravity of all its parts: Hence all the parts of matter, whether in the earth or planets, mutually attract each other; and, of course, the rotation of the earth round its axis must necessarily have bestowed on it the figure of a spheroid, the axes of which are as 229 to 230. But the direction of gravity must be perpendicular to the earth’s surface; and, consequently, unless the general and mutual attraction of the parts of matter be denied, no hypothesis derived from the direction of gravity can have any solid foundation. But this mutual attraction, as we have seen, is demonstrated by actual observation; and the experiments made by pendulums prove its universal extension. No hypothesis, therefore, founded on the direction of gravity, can be admitted, without contradicting both reason and experience.
Let us now examine whether the parts composing the terrestrial globe be homogeneous. I acknowledge, that, if the globe be supposed to [87] consist of parts different in density, the direction of gravity would be different from that we have assigned, and that the earth’s figure would vary according to the different suppositions of this kind? Why, for example, do we suppose the parts near the center to be more dense than those more distant from it? Are not all the particles which compose the globe united by their mutual attraction? Every particle, therefore, is a centre; and there is no reason to believe that the parts which surround the centre are denser than those which surround any other point. Besides, if any considerable part of the earth were more dense than another, the axis of rotation would approach nearer that part, and create an inequality in the diurnal revolution of the globe: It would produce an inequality in the apparent motion of the fixed stars; they would appear to move more quickly or slowly in the zenith or horizon, according as we happened to be situated on the heavy or light parts of the earth; and the axis of the globe not passing through its centre of gravity, would make a perceptible change in its position. But nothing of this kind ever takes place. On the contrary, the diurnal revolution of the earth is equal and uniform. At every point of the earth’s surface, the stars appear to move with the same quickness; and, if there by any rotation in its axis, it is too inconsiderable [88] to attract observation. Hence it may be concluded, that all the parts of the globe are at least nearly homogeneous.
If the earth were hollow, the crust of which, for example, exceeded not three leagues in thickness, it would give rise to the following phaenomena. 1. The mountains would bear so great a proportion to the total thickness of the crust, that vast irregularities in the earth’s motion would be occasioned by the attraction of the moon and of the sun: When the moon was in the meridian of the more elevated parts, as the Cordeliers, her attraction upon the whole globe would be much greater, than when she was in the meridian of the lower parts. 2. the comparative attraction of the mountains would be greatly increased; and the experiments made on Mount Chimboraco in Peru, would have given more degrees in the deviation of the plumb line than they actually gave seconds. 3. The weight of bodies would be greater on the tops of mountains than in the plains; and men would find themselves more weighty, and would walk with more difficulty in high than in low grounds. These observations, and many others that might be made, should convince us, that the interior parts of the earth are not hollow, but that they are composed of matter of a considerable density.
If, on the other hand, the earth, at the depth of two or three leagues, consisted of matter [89] much denser than that we are acquainted with, upon descending even into ordinary pits, we should find ourselves considerably heavier; and the motion of pendulums would there be more accelerated than they actually are when brought down from a hill to a plain. Hence we may presume, that the interior parts of the earth consist of matter nearly similar to that on its surface. Of this, we will be still further convinced, if we consider, that the earth, at the time of its original formation, when it assumed its present spheroidal figure, was in a state of fusion, and, consequently, that all its parts were homogeneous, and nearly of equal density. The matter on the surface, though originally the same with that of the interior parts, has, in the revolutions of time, undergone many changes from external causes; and to these are to be ascribed the production of material so different in their densities. But it ought to be remarked, that the densest bodies, as gold, and other metals, are most rarely to be met with; and, consequently, that the greatest quantity of materials, at the surface, have suffered littler alteration with regard to density. The most common materials, indeed, as sand and clay, differ so little in density, that we may conjecture, with much probability, the internal parts of the earth to consist of a vitrified matter, the density of which is nearly equal to that of sand; and, consequently, [90] that the whole globe may be considered as one homogeneous mass.
But, it may be said, that, though the earth were composed of concentric beds, of different densities, the equality of its diurnal motion, and the uniform inclination of its axis, would remain equally undisturbed, as upon the supposition of its consisting wholly of homogeneous matter. This I allow; but I demand, at the same time, whether there be any reason for believing, that these beds of different densities really exist? Whether this method of solving difficulties be not an attempt to adjust the works of nature to our own imaginations? And whether suppositions, neither founded on observations nor analogy, ought to find admittance into physics?
It is, then, apparent, that the earth received its spheroidal figure in consequence of its diurnal motion, and the mutual attraction of its parts; that this figure necessarily resulted from the globe’s being in a liquid state; that, according to the laws of gravity and of a centrifugal force, it could not possibly assume any other figure; that, at the moment of its formation, the difference between its two diameters was, as at present, equal to 230th part; and, of course, that all other hypotheses which make this difference greater or less, are mere fictions, and deserve no attention. [91]
Perhaps it may be objected, that, if this theory be well founded, and if the proportion of the axes of the two diameters be as 229 to 230, how came the mathematicians sent to Lapland and Peru to concur in making it as 174 to 175? Why should such a difference subsist between practice and theory? And, is it not more reasonable to give the preference to actual measurement, especially when executed by the ablest mathematicians in Europe,* and furnished with all the necessary apparatus?
To this I reply, that I mean not to combat the observations made at the equator, and near the pole; that I doubt not of their exactness; and that the earth may actually be elevated a 175th part more at the equator than at the poles. Still, however, I maintain my theory; and I perceive clearly how it may be reconciled to practice. The difference between the two conclusions is about four leagues in the two axes. The equatorial regions are found to have an elevation of two leagues more than they ought to have by the theory. This heighth [sic] of two leagues corresponds exactly with the greatest inequalities which have been produced on the surface of the globe by the motion of the sea, and the action of fluids. This requires illustration. At the time of the earth’s formation, in consequence of the mutual attraction of its parts, and of its centrifugal force, it must have assumed a spheroidal [92] figure, with its axes different by a 230th part. This would be the real figure of the earth while it remained in a state of liquifaction [sic]. But, after cooling for some time, the rarified vapours, like those in the tail or atmosphere of a comet, would condense, and fall on the surface in the form of air and water; and, when these waters began to be agitated by a flux and reflux, sand, and other bodies, would be gradually transported from the poles towards the equatorial parts. This operation, when continued for some time, would necessarily sink the poles, and elevate the equator in the same proportion. The surface of the earth being likewise exposed to the winds, to the action of the air and of the sun; all these causes would concur with the tides in furrowing the earth, in scooping out vallies [sic], in elevating the mountains, and in producing other superficial irregularities, none of which, perhaps, exceed a league in thickness, even at the equator. This inequality of two leagues may be supposed to be the greatest that can take place on the surface; for the highest mountains exceed not a league in height; and the most profound parts of the ocean, it is probable, are not above a league in depth. Thus my theory perfectly coincides with practice. The earth’s equator could not, at first, be elevated more than six leagues and a half above the poles; but the changes produced on the surface might give it a still greater elevation. Natural history won- [93] derfully supports this opinion; for, in the preceding discourse, we have proved, that, from the tides and other motions of the waters, have proceeded mountains, and all the other inequalities on the surface of the globe; and that, at great depths, as well as upon the greatest heights, bones, shells, and other relicts [sic] of sea and land animals, have been discovered.
From what has been observed, it may be conjectured, that, in order to find primitive earth, and substances which have never been removed from their original stations, we must dig in countries near the poles, where the bed of unmoved earth will be thinner than in southern climates.
In fine, if the measurement by which the figure of the earth was determined be strictly scrutinized, we shall find that it is not altogether free from hypothetical reasoning: For it proceeded on the supposition that the earth was a regular curve: But, as the earth is liable to considerable and constant changes from a thousand causes, it is impossible that it could have retained any perfectly regular figure; and hence, agreeable to our theory, and the opinion of Newton, the poles might originally be only flattened a 230th part. Besides, though we had the exact length of a degree at the equator and polar circle, yet, have we not likewise the exact length of a degree in France? and the measures of M. Picard have never been confirmed. It may be [94] added, that the diminution and increase in the motion of the pendulum agree not with the conclusions drawn from measurement; and that, on the contrary, they correspond very nearly to the theory of Newton. These circumstances tend farther to convince us, that the poles are not depressed above a 230th part; and that, if there be any difference, it can proceed from nothing but the inequalities produced on the surface by the waters, and other external causes. But these inequalities are by no means so regular as to justify any hypothesis which supposes the meridians to be ellipses, or any other perfect curves. Hence it appears, that, though many degrees should be successively measured in different regions, we cannot, by that alone, ascertain the exact depression of the poles, nor determine how much it exceeds or falls short of a 230th part.
May we not likewise conjecture, that, if the inclination of the earth’s axis has been changed, this effect could not be produced but by the changes on the surface, since all the other parts are homogeneous; that this variation is, of course, too small to be perceived by astronomers; and that, if the earth be not disturbed by a comet, or some other external cause, its axis will for ever preserve its present and original inclination?
Not to omit any conjecture that seems reasonable, may we not suppose, that, as the mountains, and other inequalities on the surface of [95] the earth, have originated from the action of the tides, those which we perceive in the moon have been produced by a similar cause? The mountains of the moon are indeed higher than those of the earth; but her tides are likewise stronger; because the earth, the size of which is much larger, produces the tides of the moon with superior force. This effect would be greatly augmented, if the moon, like the earth, had a quick diurnal motion. But, as the moon uniformly presents the same face to the earth, the tides are raised only in proportion to the motion occasioned by her librations, which alternately expose to our view a small segment of her other hemisphere. This cause, however, must produce tides very different from those of our seas; and their effects will, of course, be much less considerable, than if the moon had possessed a diurnal revolution round her axis, equally quick as the rotation of the earth.
I should compose a volume equal to that of Burnet or Whiston, were I to extend the ideas presented by the above theory; and were I, in imitation of the last mentioned author, to clothe them in a geometrical dress, I might add considerably to their importance. But I have always thought, that hypotheses, however probable, deserve not to be treated so pompously; it is apt to give them the air of quackery and imposition. [96]
Notes
* If M. de Buffon had known, that the nucleus of the
sun was a solid and opaque matter, a discovery lately made by the ingenious Dr
Wilson of
* See Newt. Edit. 3. p. 525 [back to page 66].
* Quaer. Would not such an event, by augmenting the sun’s quantity of matter, and, consequently, his attractive power, produce other changes in the solar system? [Smellie’s note, back to page 67].
+ See Newt. P. 405 [back to page 67].
* This reasoning is ingenious; but its solidity is suspicious. The evomitions [sic] from volcano’s, and the elevation the matter acquires, are effects of successive impulses. The impulse from a [71] comet upon the sun must necessarily be single and instantaneous; which seems to weaken the analogy which the author means to establish [Smellie’s note; this note straddles pages 71-72, with the break coming where I indicated; back to page 71]
* Vid. Act. Erud. Lips. An. 1692 [back to page 79].
* M. de
Maupertuis, figure de la terre [back to page 92].