Laplace, in effect, has devoted a chapter of his splendid work to an examination of the oscillations which the attractive force of the moon is capable of producing in our atmosphere. It results from these researches, that, at Paris, the lunar tide produces no sensible effect upon the barometer. The height of the tide, obtained by the discussion of a long series of observations, has not exceeded two-hundredths of a millimetre, a quant.i.ty which, in the present state of meteorological science, is less than the probable error of observation.
The calculation to which I have just alluded, may be cited in support of considerations to which I had recourse when I wished to establish, that if the moon alters more or less the height of the barometer, according to its different phases, the effect is not attributable to attraction.
No person was more sagacious than Laplace in discovering intimate relations between phenomena apparently very dissimilar; no person showed himself more skilful in deducing important conclusions from those unexpected affinities.
Towards the close of his days, for example, he overthrew with a stroke of the pen, by the aid of certain observations of the moon, the cosmogonic theories of Buffon and Bailly, which were so long in favour.
According to these theories, the earth was inevitably advancing to a state of congelation which was close at hand. Laplace, who never contented himself with a vague statement, sought to determine in numbers the rapid cooling of our globe which Buffon had so eloquently but so gratuitously announced. Nothing could be more simple, better connected, or more demonstrative, than the chain of deductions of the celebrated geometer.
A body diminishes in volume when it cools. According to the most elementary principles of mechanics, a rotating body which contracts in dimensions ought inevitably to turn upon its axis with greater and greater rapidity. The length of the day has been determined in all ages by the time of the earth"s rotation; if the earth is cooling, the length of the day must be continually shortening. Now there exists a means of ascertaining whether the length of the day has undergone any variation; this consists in examining, for each century, the arc of the celestial sphere described by the moon during the interval of time which the astronomers of the existing epoch called a day,--in other words, the time required by the earth to effect a complete rotation on its axis, the velocity of the moon being in fact independent of the time of the earth"s rotation.
Let us now, after the example of Laplace, take from the standard tables the least considerable values, if you choose, of the expansions or contractions which solid bodies experience from changes of temperature; search then the annals of Grecian, Arabian, and modern astronomy for the purpose of finding in them the angular velocity of the moon, and the great geometer will prove, by incontrovertible evidence founded upon these data, that during a period of two thousand years the mean temperature of the earth has not varied to the extent of the hundredth part of a degree of the centigrade thermometer. No eloquent declamation is capable of resisting such a process of reasoning, or withstanding the force of such numbers. The mathematics have been in all ages the implacable adversaries of scientific romances.
The fall of bodies, if it was not a phenomenon of perpetual occurrence, would justly excite in the highest degree the astonishment of mankind.
What, in effect, is more extraordinary than to see an inert ma.s.s, that is to say, a ma.s.s deprived of will, a ma.s.s which ought not to have any propensity to advance in one direction more than in another, precipitate itself towards the earth as soon as it ceased to be supported!
Nature engenders the gravity of bodies by a process so recondite, so completely beyond the reach of our senses and the ordinary resources of human intelligence, that the philosophers of antiquity, who supposed that they could explain every thing mechanically according to the simple evolutions of atoms, excepted gravity from their speculations.
Descartes attempted what Leucippus, Democritus, Epicurus, and their followers thought to be impossible.
He made the fall of terrestrial bodies depend upon the action of a vortex of very subtle matter circulating around the earth. The real improvements which the ill.u.s.trious Huyghens applied to the ingenious conception of our countryman were far, however, from imparting to it clearness and precision, those characteristic attributes of truth.
Those persons form a very imperfect estimate of the meaning of one of the greatest questions which has occupied the attention of modern inquirers, who regard Newton as having issued victorious from a struggle in which his two immortal predecessors had failed. Newton did not discover the cause of gravity any more than Galileo did. Two bodies placed in juxtaposition approach each other. Newton does not inquire into the nature of the force which produces this effect. The force exists, he designates it by the term attraction; but, at the same time, he warns the reader that the term as thus used by him does not imply any definite idea of the physical process by which gravity is brought into existence and operates.
The force of attraction being once admitted as a fact, Newton studies it in all terrestrial phenomena, in the revolutions of the moon, the planets, satellites, and comets; and, as we have already stated, he deduced from this incomparable study the simple, universal, mathematical characteristics of the forces which preside over the movements of all the bodies of which our solar system is composed.
The applause of the scientific world did not prevent the immortal author of the _Principia_ from hearing some persons refer the principle of gravitation to the cla.s.s of occult qualities. This circ.u.mstance induced Newton and his most devoted followers to abandon the reserve which they had hitherto considered it their duty to maintain. Those persons were then charged with ignorance who regarded attraction as an essential property of matter, as the mysterious indication of a sort of charm; who supposed that two bodies may act upon each other without the intervention of a third body. This force was then either the result of the tendency of an ethereal fluid to move from the free regions of s.p.a.ce, where its density is a maximum, towards the planetary bodies around which there exists a greater degree of rarefaction, or the consequence of the impulsive force of some fluid medium.
Newton never expressed a definitive opinion respecting the origin of the impulse which occasioned the attractive force of matter, at least in our solar system. But we have strong reasons for supposing, in the present day, that in using the word _impulse_, the great geometer was thinking of the systematic ideas of Varignon and Fatio de Duillier, subsequently reinvented and perfected by Lesage: these ideas, in effect, had been communicated to him before they were published to the world.
According to Lesage, there are, in the regions of s.p.a.ce, bodies moving in every possible direction, and with excessive rapidity. The author applied to these the name of ultra-mundane corpuscles. Their totality const.i.tuted the gravitative fluid, if indeed, the designation of a fluid be applicable to an a.s.semblage of particles having no mutual connexion.
A single body placed in the midst of such an ocean of movable particles, would remain at rest although it were impelled equally in every direction. On the other hand, two bodies ought to advance towards each other, since they would serve the purpose of mutual screens, since the surfaces facing each other would no longer be hit in the direction of their line of junction by the ultra-mundane particles, since there would then exist currents, the effect of which would no longer be neutralized by opposite currents. It will be easily seen, besides, that two bodies plunged into the gravitative fluid, would tend to approach each other with an intensity which would vary in the inverse proportion of the square of the distance.
If attraction is the result of the impulse of a fluid, its action ought to employ a finite time in traversing the immense s.p.a.ces which separate the celestial bodies. If the sun, then, were suddenly extinguished, the earth after the catastrophe would, mathematically speaking, still continue for some time to experience its attractive influence. The contrary would happen on the occasion of the sudden birth of a planet; a certain time would elapse before the attractive force of the new body would make itself felt on the earth.
Several geometers of the last century were of opinion that the force of attraction is not transmitted instantaneously from one body to another; they even a.s.signed to it a comparatively inconsiderable velocity of propagation. Daniel Bernoulli, for example, in attempting to explain how the spring tide arrives upon our coasts a day and a half after the sizygees, that is to say, a day and a half after the epochs when the sun and moon are most favourably situated for the production of this magnificent phenomenon, a.s.sumed that the disturbing force required all this time (a day and a half) for its propagation from the moon to the ocean. So feeble a velocity was inconsistent with the mechanical explanation of attraction of which we have just spoken. The explanation, in effect, necessarily supposes that the proper motions of the celestial bodies are insensible compared with the motion of the gravitative fluid.
After having discovered that the diminution of the eccentricity of the terrestrial orbit is the real cause of the observed acceleration of the motion of the moon, Laplace, on his part, endeavoured to ascertain whether this mysterious acceleration did not depend on the gradual propagation of attraction.
The result of calculation was at first favourable to the plausibility of the hypothesis. It showed that the gradual propagation of the attractive force would introduce into the movement of our satellite a perturbation proportional to the square of the time which elapsed from the commencement of any epoch; that in order to represent numerically the results of astronomical observations it would not be necessary to a.s.sign a feeble velocity to attraction; that a propagation eight millions of times more rapid than that of light would satisfy all the phenomena.
Although the true cause of the acceleration of the moon is now well known, the ingenious calculation of which I have just spoken does not the less on that account maintain its place in science. In a mathematical point of view, the perturbation depending on the gradual propagation of the attractive force which this calculation indicates has a certain existence. The connexion between the velocity of perturbation and the resulting inequality is such that one of the two quant.i.ties leads to a knowledge of the numerical value of the other. Now, upon a.s.signing to the inequality the greatest value which is consistent with the observations after they have been corrected for the effect due to the variation of the eccentricity of the terrestrial orbit, we find the velocity of the attractive force to be fifty millions of times the velocity of light!
If it be borne in mind, that this number is an inferior limit, and that the velocity of the rays of light amounts to 77,000 leagues (192,000 English miles) per second, the philosophers who profess to explain the force of attraction by the impulsive energy of a fluid, will see what prodigious velocities they must satisfy.
The reader cannot fail again to remark the sagacity with which Laplace singled out the phenomena which were best adapted for throwing light upon the most obscure points of celestial physics; nor the success with which he explored their various parts, and deduced from them numerical conclusions in presence of which the mind remains confounded.
The author of the _Mecanique Celeste_ supposed, like Newton, that light consists of material molecules of excessive tenuity and endued in empty s.p.a.ce with a velocity of 77,000 leagues in a second. However, it is right to warn those who would be inclined to avail themselves of this imposing authority, that the princ.i.p.al argument of Laplace, in favour of the system of emission, consisted in the advantage which it afforded of submitting every question to a process of simple and rigorous calculation; whereas, on the other hand, the theory of undulations has always offered immense difficulties to a.n.a.lysts. It was natural that a geometer who had so elegantly connected the laws of simple refraction which light undergoes in its pa.s.sage through the atmosphere, and the laws of double refraction which it is subject to in the course of its pa.s.sage through certain crystals, with the action of attractive and repulsive forces, should not have abandoned this route, before he recognized the impossibility of arriving by the same path, at plausible explanations of the phenomena of diffraction and polarization. In other respects, the care which Laplace always employed, in pursuing his researches, as far as possible, to their numerical results, will enable those who are disposed to inst.i.tute a complete comparison between the two rival theories of light, to derive from the _Mecanique Celeste_ the materials of several interesting relations.
Is light an emanation from the sun? Does this body launch out incessantly in every direction a part of its own substance? Is it gradually diminishing in volume and ma.s.s? The attraction exercised by the sun upon the earth will, in that case, gradually become less and less considerable. The radius of the terrestrial orbit, on the other hand, cannot fail to increase, and a corresponding effect will be produced on the length of the year.
This is the conclusion which suggests itself to every person upon a first glance at the subject. By applying a.n.a.lysis to the question, and then proceeding to numerical computations, founded upon the most trustworthy results of observation relative to the length of the year in different ages, Laplace has proved that an incessant emission of light, going on for a period of two thousand years, has not diminished the ma.s.s of the sun by the two-millionth part of its original value.
Our ill.u.s.trious countryman never proposed to himself any thing vague or indefinite. His constant object was the explanation of the great phenomena of nature, according to the inflexible principles of mathematical a.n.a.lysis. No philosopher, no mathematician, could have maintained himself more cautiously on his guard against a propensity to hasty speculation. No person dreaded more the scientific errors which the imagination gives birth to, when it ceases to remain within the limits of facts, of calculation, and of a.n.a.logy. Once, and once only, did Laplace launch forward, like Kepler, like Descartes, like Leibnitz, like Buffon, into the region of conjectures. His conception was not then less than a cosmogony.
All the planets revolve around the sun, from west to east, and in planes which include angles of inconsiderable magnitude.
The satellites revolve around their respective primaries in the same direction as that in which the planets revolve around the sun, that is to say, from west to east.
The planets and satellites which have been found to have a rotatory motion, turn also upon their axes from west to east. Finally, the rotation of the sun is directed from west to east. We have here then an a.s.semblage of forty-three movements, all operating in the same direction. By the calculus of probabilities, the odds are four thousand millions to one, that this coincidence in the direction of so many movements is not the effect of accident.
It was Buffon, I think, who first attempted to explain this singular feature of our solar system. Having wished, in the explanation of phenomena, to avoid all recourse to causes which were not warranted by nature, the celebrated academician investigated a physical origin of the system in what was common to the movements of so many bodies differing in magnitude, in form, and in distance from the princ.i.p.al centre of attraction. He imagined that he discovered such an origin by making this triple supposition: a comet fell obliquely upon the sun; it pushed before it a torrent of fluid matter; this substance transported to a greater or less distance from the sun according to its ma.s.s formed by concentration all the known planets.
The bold hypothesis of Buffon is liable to insurmountable difficulties.
I proceed to indicate, in a few words, the cosmogonic system which Laplace subst.i.tuted for that of the ill.u.s.trious author of the _Histoire Naturelle_.
According to Laplace, the sun was at a remote epoch the central nucleus of an immense nebula, which possessed a very high temperature, and extended far beyond the region in which Ura.n.u.s revolves in the present day. No planet was then in existence.
The solar nebula was endued with a general movement of revolution directed from west to east. As it cooled it could not fail to experience a gradual condensation, and, in consequence, to rotate with greater and greater rapidity. If the nebulous matter extended originally in the plane of the equator as far as the limit at which the centrifugal force exactly counterbalanced the attraction of the nucleus, the molecules situate at this limit ought, during the process of condensation, to separate from the rest of the atmospheric matter and form an equatorial zone, a ring revolving separately and with its primitive velocity. We may conceive that a.n.a.logous separations were effected in the higher strata of the nebula at different epochs, that is to say, at different distances from the nucleus, and that they give rise to a succession of distinct rings, included almost in the same plane and endued with different velocities.
This being once admitted, it is easy to see that the indefinite stability of the rings would have required a regularity of structure throughout their whole contour, which is very improbable. Each of them accordingly broke in its turn into several ma.s.ses, which were plainly endued with a movement of rotation, coinciding in direction with the common movement of revolution, and which in consequence of their fluidity a.s.sumed spheroidal forms.
In order, then, that one of those spheroids might absorb all the others belonging to the same ring, it will be sufficient to a.s.sign to it a ma.s.s greater than that of any other spheroid.
Each of the planets, while in the vaporous condition to which we have just alluded, would manifestly have a central nucleus gradually increasing in magnitude and ma.s.s, and an atmosphere offering, at its successive limits, phenomena entirely similar to those which the solar atmosphere, properly so called, had exhibited. We here witness the birth of satellites, and that of the ring of Saturn.
The system, of which I have just given an imperfect sketch, has for its object to show how a nebula endued with a general movement of rotation must eventually transform itself into a very luminous central nucleus (a sun) and into a series of distinct spheroidal planets, situate at considerable distances from each other, revolving all around the central sun in the direction of the original movement of the nebula; how these planets ought also to have movements of rotation operating in similar directions; how, finally, the satellites, when any of such are formed, cannot fail to revolve upon their axes and around their respective primaries, in the direction of rotation of the planets and of their movement of revolution around the sun.
We have just found, conformably to the principles of mechanics, the forces with which the particles of the nebula were originally endued, in the movements of rotation and revolution of the compact and distinct ma.s.ses which these particles have brought into existence by their condensation. But we have thereby achieved only a single step. The primitive movement of rotation of the nebula is not connected with the simple attraction of the particles. This movement seems to imply the action of a primordial impulsive force.
Laplace is far from adopting, in this respect, the almost universal opinion of philosophers and mathematicians. He does not suppose that the mutual attractions of originally immovable bodies must ultimately reduce all the bodies to a state of rest around their common centre of gravity.
He maintains, on the contrary, that three bodies, in a state of rest, two of which have a much greater ma.s.s than the third, would concentrate into a single ma.s.s only in certain exceptional cases. In general, the two most considerable bodies would unite together, while the third would revolve around their common centre of gravity. Attraction would thus become the cause of a sort of movement which would seem to be explicable solely by an impulsive force.
It might be supposed, indeed, that in explaining this part of his system Laplace had before his eyes the words which Rousseau has placed in the mouth of the vicar of Savoy, and that he wished to refute them: "Newton has discovered the law of attraction," says the author of _Emile_, "but attraction alone would soon reduce the universe to an immovable ma.s.s: with this law we must combine a projectile force in order to make the celestial bodies describe curve lines. Let Descartes reveal to us the physical law which causes his vortices to revolve; and let Newton show us the hand which launched the planets along the tangents of their orbits."
According to the cosmogonic ideas of Laplace, comets did not originally form part of the solar system; they are not formed at the expense of the matter of the immense solar nebula; we must consider them as small wandering nebulae which the attractive force of the sun has caused to deviate from their original route. Such of those comets as penetrated into the great nebula at the epoch of condensation and of the formation of planets fell into the sun, describing spiral curves, and must by their action have caused the planetary orbits to deviate more or less from the plane of the solar equator, with which they would otherwise have exactly coincided.
With respect to the zodiacal light, that rock against which so many reveries have been wrecked, it consists of the most volatile parts of the primitive nebula. These molecules not having united with the equatorial zones successively abandoned in the plane of the solar equator, continued to revolve at their original distances, and with their original velocities. The circ.u.mstance of this extremely rare substance being included wholly within the earth"s...o...b..t, and even within that of Venus, seemed irreconcilable with the principles of mechanics; but this difficulty occurred only when the zodiacal substance being conceived to be in a state of direct and intimate dependence on the solar photosphere properly so called, an angular movement of rotation was impressed on it equal to that of the photosphere, a movement in virtue of which it effected an entire revolution in twenty-five days and a half. Laplace presented his conjectures on the formation of the solar system with the diffidence inspired by a result which was not founded upon calculation and observation.[39] Perhaps it is to be regretted that they did not receive a more complete development, especially in so far as concerns the division of the matter into distinct rings; perhaps it would have been desirable if the ill.u.s.trious author had expressed himself more fully respecting the primitive physical condition, the molecular condition of the nebula at the expense of which the sun, planets, and satellites, of our system were formed. It is perhaps especially to be regretted that Laplace should have only briefly alluded to what he considered the obvious possibility of movements of revolution having their origin in the action of simple attractive forces, and to other questions of a similar nature.
Notwithstanding these defects, the ideas of the author of the _Mecanique Celeste_ are still the only speculations of the kind which, by their magnitude, their coherence, and their mathematical character, may be justly considered as forming a physical cosmogony; those alone which in the present day derive a powerful support from the results of the recent researches of astronomers on the nebulae of every form and magnitude, which are scattered throughout the celestial vault.
In this a.n.a.lysis, we have deemed it right to concentrate all our attention upon the _Mecanique Celeste_. The _Systeme du Monde_ and the _Theorie a.n.a.lytique des Probabilites_ would also require detailed notices.
The _Exposition du Systeme du Monde_ is the _Mecanique Celeste_ divested of the great apparatus of a.n.a.lytical formulae which ought to be attentively perused by every astronomer who, to use an expression of Plato, is desirous of knowing the numbers which govern the physical universe. It is in the _Exposition du Systeme du Monde_ that persons unacquainted with mathematical studies will obtain an exact and competent knowledge of the methods to which physical astronomy is indebted for its astonishing progress. This work, written with a n.o.ble simplicity of style, an exquisite propriety of expression, and a scrupulous accuracy, is terminated by a sketch of the history of astronomy, universally ranked in the present day among the finest monuments of the French language.
A regret has been often expressed, that Caesar, in his immortal _Commentaries_, should have confined himself to a narration of his own campaigns: the astronomical commentaries of Laplace ascend to the origin of communities. The labours undertaken in all ages for the purpose of extracting new truths from the heavens, are there justly, clearly, and profoundly a.n.a.lyzed; it is genius presiding as the impartial judge of genius. Laplace has always remained at the height of his great mission; his work will be read with respect so long as the torch of science shall continue to throw any light.
The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman. From the time when Pascal and Fermat established its first principles, it has rendered and continues daily to render services of the most eminent kind. It is the calculus of probabilities, which, after having suggested the best arrangements of the tables of population and mortality, teaches us to deduce from those numbers, in general so erroneously interpreted, conclusions of a precise and useful character: it is the calculus of probabilities which alone can regulate justly the premiums to be paid for a.s.surances; the reserve funds for the disburs.e.m.e.nt of pensions, annuities, discounts, &c.: it is under its influence that lotteries, and other shameful snares cunningly laid for avarice and ignorance, have definitively disappeared. Laplace has treated these questions, and others of a much more complicated nature, with his accustomed superiority. In short, the _Theorie a.n.a.lytique des Probabilites_ is worthy of the author of the _Mecanique Celeste_.