« AnteriorContinuar »
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 masses 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 center of gravity. He maintains, on the contrary, that three bodies, in a state of rest, two of which have a much greater mass than the third, would concentrate into a single mass only in certain exceptional cases. In gen. eral, the two most considerable bodies would unite together, while the third would revolve around their common center 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 tbat 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 mass. 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 nebula, 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 tltey would otherwise have exactly coincided.
With respect to the zodiacal light, that rock against which so many reveries bave 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, continue to revolve at their original distances, and with their original relocities. The circumstance of this extremely rare substance being included wholly within the earth's orbit, and even within that of Venns, 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.*
Perhaps it is to be regretted that they did not receive a more complete development, especially in so far as it concerns the division of the matter into distinct rings; perhaps it would have been desirable if the illnstrious 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 Méca. nique Céleste are still the only speculations of the kind which, by their magnitude, their coberence, 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 nebulæ of every form and magnitade which are scattered throughout the celestial vault.
In this analysis, we have deemed it right to concentrate all our attention upon the Mécanique Céleste. The Système du Monde and the Théorie Analytique des Probabilités would also require detailed notices.
The Exposition du système du Monde is the Mécanique Céleste divested of the great apparatus of analytical formula which ought to be attentively pernsed by every astronomer wbo, to use an expression of Plato, is desirous of knowing the numbers which govern the physical universe. It is in the Exposition du Système 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 noble simplicity of style,
* Laplace has explained this theory in his Exposition du Système du Monde, (lio. 4, note 7.)-TRANSLATOR.
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 Cæsar, 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 labors undertaken in all ages for the purpose of extracting new truths from the heavens are there justly, clearly, and profoundly analyzed; it is genius presiding as the impartial judge of geuius. 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 sball coutique 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 assurances; the reserve funds for the disbursement of pensions, annuities, discounts, &c. It is under its influence that lotteries and other shameful spares 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 Théorie Analytique des Probabilités is worthy of the author of the Mécanique Céleste.
A philosopher, whose name is associated with immortal discoveries, said to his audience, who had allowed themselves to be influenced by ancient and consecrated anthorities, “ Bear in mind, gentlemen, that in questions of science the authority of a thousand is not worth the humble reasoning of a single individual.” Two centuries have passed over their words of Galileo, without depreciating their value or obliterating these truthful character. Thus, instead of displaying a long list of illustrious admirers of the three beautiful works of Laplace, we have preferred glancing briefly at some of the sublime truths which geometry has there deposited. Let us not, however, apply this principle in its utmost rigor, and since chance bas put into our hands some unpublished letters of one of those men of genius, whom nature has endowed with the rare faculty of seizing at a glance the salient points of an object, we may be permitted to extract from them two or three brief and characteristic appreciations of the Mécanique Céleste and the Traité des Probabilités.
On the 27th Vendémiaire, in the year X, General Bonaparte, after having received a volume of the Mécanique Céleste, wrote to Laplace in the following terms: "The first six months which I shall have at my disposal will be employed in reading your beautiful work.” It would appear that the words, “ the first six months," deprive the phrase of the character of a common place expression of thanks, and convey a just appreciation of the importance and difficulty of the subject matter.
On the 5th Frimaire, in the year XI, the reading of some chapters of the volume which Laplace had dedicated to him was to the general “ a new occasion for regretting that the force of circumstances had directed him into a career which removed him from the pursuit of science.”
" At all events," added he, “ I have a strong desire that future generations, upon reading the Mécanique Céleste, shall not forget the esteem and friendship which I have entertained toward its author.”
On the 17th Prairial, in the year XIII, the general, now become Emperor, wrote from Milan : “ The Mécanique Céleste appears to me destined to shed new luster on the age in which we live.”
Finally, on the 12th of August, 1812, Napoleon, who had just received the Traité du Calcul des Probabilités wrote from Witepask the letter which we transcribe textually:
"There was a time when I would have read with interest your Traité du Calcul des Probabilités. For the present, I must confine myself to expressing to you the satisfaction which I experience every time that I see you give to the world new works which serve to improve and extend the most important of the sciences and contribute to the glory of the nation. The advancement and the improvement of mathematiical science are connected with the prosperity of the state."
I bave now arrived at the conclusion of the task which I had imposed upon myself. I shall be pardoned for baving given so detailed an exposition of the principal discoveries for which philosopby, astronomy, and navigation are indebted to our geometers.
It has appeared to me that in thus tracing the glorious past, I have shown our contemporaries the full extent of their duty towards the country. In fact, it is for nations especially to bear in remembrance the ancient adage, noblesse oblige.
The following is a brief notice of some other interesting results of the researches of Laplace which have not been mentioned in the text:
Method for determining the orbits of comets.—Since comets are generally visible only during a few days or weeks at the utmost, the determination of their orbits is attended with peculiar difficulties. The method devised by Newton for effecting this object was in every respect worthy of his genius. Its practical value was illustrated by the brilliant researches of Halley on cometary orbits. It necessitated, however, a long train of tedious calculations, and, in consequence, was not much used, astronomers generally preferring to attain the same end by a tentative process. In the year 1780, Laplace communicatod to the Academy of Sciences an analytical method for determining the elements of a comet's orbit. This method has been extensively employed in France. Indeed, previously to the appearance of Olbers's method, about the close of the last century, it furnished the easiest and most expeditious process hitherto devised for calculating the parabolic elements of a comet's orbit.
Invariable plane of the solar system.-In consequence of the mutual perturbations of the different bodies of the planetary system, the planes of the orbits in which they revolve are perpetually varying in position. It becomes, therefore, desirable to ascertain some fixed plane to which the movements of the planets in all ages may be referred, so that the observations of one epoch might be rendered readily comparable with those of another. This object was accomplished by Laplace, who discovered that notwithstanding the perpetual fluctuations of the planetary orbits, there exists a fixed plane, to which the positions of the various bodies may at any instant be easily referred. This plane passes through the center of gravity of the solar system, and its position is such that if the movements of the planets be projected upon it, and if the mass of each planet be multiplied by the area which it describes in a given time, the sum of such products will be a maximum. The position of the plane for the year 1750 bas been calculated by referring it to the ecliptic of that year. In this way it has been found that the inclination of the plane is 1° 35' 31", and that the longitude of the ascending node is 1020 57' 30". The position of the plane when calculated for the year 1950, with respect to the ecliptic of 1750, gives 1° 35' 31" for the inclination, and 102° 57' 15" for the longitude of the ascending node. It will be seen that a very satisfactory accordance exists between the elements of the position of the invariable plane for the two epochs.
Diminution of the obliquity of the ecliptic.-The astronomers of the eighteenth century had found, by a comparison of ancient with modern observations, that the obliquity of the ecliptic is slowly diminishing from century to century. The researches of geometers on the tbeory of gravitation bad shown that an effect of this kind must be produced by the disturbing action of the planets on the earth. Laplace determined the secular displacement of the plane of the earth's orbit due to each of the planets, and in this way ascertained the whole effect of perturbation upon the obliquity of the ecliptic. A comparison which he instituted between the results of his formula and an ancient observation recorded in the Chinese Anuals exhibited a most satisfactory accordance. The observation in question indicated the obliquity of the ecliptic for the year 1100 before the Christian era to be 23° 54' 2".5. According to the principles of the theory of gravitation, the obliquity for the same epoch would be 230 51' 30".
Limits of the obliquity of the ecliptic modified by the action of the sun and moon upon the terrestrial spheroid.—The ecliptic will not continue indefinitely to approach the equator. After attaining a certain limit, it