Library of the World's Best Literature, Ancient and Modern — Volume 02

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Having demonstrated the smallness of these periodic oscillations, Laplace next succeeded in determining the absolute dimensions of the orbits. What is the distance of the sun from the earth? No scientific question has occupied the attention of mankind in a greater degree. Mathematically speaking, nothing is more simple: it suffices, as in ordinary surveying, to draw visual lines from the two extremities of a known base line to an inaccessible object; the remainder of the process is an elementary calculation. Unfortunately, in the case of the sun, the distance is very great and the base lines which can be measured upon the earth are comparatively very small. In such a case, the slightest errors in the direction of visual lines exercise an enormous influence upon the results. In the beginning of the last century, Halley had remarked that certain interpositions of Venus between the earth and the sun--or to use the common term, the transits of the planet across the sun's disk--would furnish at each observing station an indirect means of fixing the position of the visual ray much superior in accuracy to the most perfect direct measures. Such was the object of the many scientific expeditions undertaken in 1761 and 1769, years in which the transits of Venus occurred. A comparison of observations made in the Southern Hemisphere with those of Europe gave for the distance of the sun the result which has since figured in all treatises on astronomy and navigation. No government hesitated to furnish scientific academies with the means, however expensive, of establishing their observers in the most distant regions. We have already remarked that this determination seemed imperiously to demand an extensive base, for small bases would have been totally inadequate. Well, Laplace has solved the problem without a base of any kind whatever; he has deduced the distance of the sun from observations of the moon made in one and the same place.

The sun is, with respect to our satellite the moon, the cause of perturbations which evidently depend on the distance of the immense luminous globe from the earth. Who does not see that these perturbations must diminish if the distance increases, and increase if the distance diminishes, so that the distance determines the amount of the perturbations? Observation assigns the numerical value of these perturbations; theory, on the other hand, unfolds the general mathematical relation which connects them with the solar distance and with other known elements. The determination of the mean radius of the terrestrial orbit--of the distance of the sun--then becomes one of the most simple operations of algebra. Such is the happy combination by the aid of which Laplace has solved the great, the celebrated problem of parallax. It is thus that the illustrious geometer found for the mean distance of the sun from the earth, expressed in radii of the terrestrial orbit, a value differing but slightly from that which was the fruit of so many troublesome and expensive voyages.

The movements of the moon proved a fertile mine of research to our great geometer. His penetrating intellect discovered in them unknown treasures. With an ability and a perseverance equally worthy of admiration, he separated these treasures from the coverings which had hitherto concealed them from vulgar eyes. For example, the earth governs the movements of the moon. The earth is flattened; in other words, its figure is spheroidal. A spheroidal body does not attract as does a sphere. There should then exist in the movement--I had almost said in the countenance--of the moon a sort of impress of the spheroidal figure of the earth. Such was the idea as it originally occurred to Laplace. By means of a minutely careful investigation, he discovered in its motion two well-defined perturbations, each depending on the spheroidal figure of the earth. When these were submitted to calculation, each led to the same value of the ellipticity. It must be recollected that the ellipticity thus derived from the motions of the moon is not the one corresponding to such or such a country, to the ellipticity observed in France, in England, in Italy, in Lapland, in North America, in India, or in the region of the Cape of Good Hope; for, the earth's crust having undergone considerable upheavals at different times and places, the primitive regularity of its curvature has been sensibly disturbed thereby. The moon (and it is this which renders the result of such inestimable value) ought to assign, and has in reality assigned, the general ellipticity of the earth; in other words, it has indicated a sort of average value of the various determinations obtained at enormous expense, and with infinite labor, as the result of long voyages undertaken by astronomers of all the countries of Europe.

Certain remarks of Laplace himself bring into strong relief the profound, the unexpected, the almost paradoxical character of the methods I have attempted to sketch. What are the elements it has been found necessary to confront with each other in order to arrive at results expressed with such extreme precision? On the one hand, mathematical formulae deduced from the principle of universal gravitation; on the other, certain irregularities observed in the returns of the moon to the meridian. An observing geometer, who from his infancy had never quitted his study, and who had never viewed the heavens except through a narrow aperture directed north and south,--to whom nothing had ever been revealed respecting the bodies revolving above his head, except that they attract each other according to the Newtonian law of gravitation,--would still perceive that his narrow abode was situated upon the surface of a spheroidal body, whose equatorial axis was greater than its polar by a three hundred and sixth part. In his isolated, fixed position he could still deduce his true distance from the sun!

Laplace's improvement of the lunar tables not only promoted maritime intercourse between distant countries, but preserved the lives of mariners. Thanks to an unparalleled sagacity, to a limitless perseverance, to an ever youthful and communicable ardor, Laplace solved the celebrated problem of the longitude with a precision even greater than the utmost needs of the art of navigation demanded. The ship, the sport of the winds and tempests, no longer fears to lose its way in the immensity of the ocean. In every place and at every time the pilot reads in the starry heavens his distance from the meridian of Paris. The extreme perfection of these tables of the moon places Laplace in the ranks of the world's benefactors.

In the beginning of the year 1611, Galileo supposed that he found in the eclipses of Jupiter's satellites a simple and rigorous solution of the famous problem of the longitude, and attempts to introduce the new method on board the numerous vessels of Spain and Holland at once began. They failed because the necessary observations required powerful telescopes, which could not be employed on a tossing ship. Even the expectations of the serviceability of Galileo's methods for land calculations proved premature. The movements of the satellites of Jupiter are far less simple than the immortal Italian supposed them to be. The labors of three more generations of astronomers and mathematicians were needed to determine them, and the mathematical genius of Laplace was needed to complete their labors. At the present day the nautical ephemerides contain, several years in advance, the indications of the times of the eclipses and reappearances of Jupiter's satellites. Calculation is as precise as direct observation.

Influenced by an exaggerated deference, modesty, timidity, France in the eighteenth century surrendered to England the exclusive privilege of constructing her astronomical instruments. Thus, when Herschel was prosecuting his beautiful observations on the other side of the Channel, we had not even the means of verifying them. Fortunately for the scientific honor of our country, mathematical analysis also is a powerful instrument. The great Laplace, from the retirement of his study, foresaw, and accurately predicted in advance, what the excellent astronomer of Windsor would soon behold with the largest telescopes existing. When, in 1610, Galileo directed toward Saturn a lens of very low power which he had just constructed with his own hands, although he perceived that the planet was not a globe, he could not ascertain its real form. The expression "tri-corporate," by which the illustrious Florentine designated the appearance of the planet, even implied a totally erroneous idea of its structure. At the present day every one knows that Saturn consists of a globe about nine hundred times greater than the earth, and of a ring. This ring does not touch the ball of the planet, being everywhere removed from it to a distance of twenty thousand (English) miles. Observation indicates the breadth of the ring to be fifty-four thousand miles. The thickness certainly does not exceed two hundred and fifty miles. With the exception of a black streak which divides the ring throughout its whole contour into two parts of unequal breadth and of different brightness, this strange colossal bridge without foundations had never offered to the most experienced or skillful observers either spot or protuberance adapted for deciding whether it was immovable or endowed with a motion of rotation. Laplace considered it to be very improbable, if the ring was stationary, that its constituent parts should be capable of resisting by mere cohesion the continual attraction of the planet. A movement of rotation occurred to his mind as constituting the principle of stability, and he deduced the necessary velocity from this consideration. The velocity thus found was exactly equal to that which Herschel subsequently derived from a series of extremely delicate observations. The two parts of the ring, being at different distances from the planet, could not fail to be given different movements of precession by the action of the sun. Hence it would seem that the planes of both rings ought in general to be inclined toward each other, whereas they appear from observation always to coincide. It was necessary then that some physical cause capable of neutralizing the action of the sun should exist. In a memoir published in February, 1789, Laplace found that this cause depended on the ellipticity of Saturn produced by a rapid movement of rotation of the planet, a movement whose discovery Herschel announced in November of the same year.

If we descend from the heavens to the earth, the discoveries of Laplace will appear not less worthy of his genius. He reduced the phenomena of the tides, which an ancient philosopher termed in despair "the tomb of human curiosity," to an analytical theory in which the physical conditions of the question figure for the first time. Consequently, to the immense advantage of coast navigation, calculators now venture to predict in detail the time and height of the tides several years in advance. Between the phenomena of the ebb and flow, and the attractive forces of the sun and moon upon the fluid sheet which covers three fourths of the globe, an intimate and necessary connection exists; a connection from which Laplace deduced the value of the mass of our satellite the moon. Yet so late as the year 1631 the illustrious Galileo, as appears from his 'Dialogues,' was so far from perceiving the mathematical relations from which Laplace deduced results so beautiful, so unequivocal, and so useful, that he taxed with frivolousness the vague idea which Kepler entertained of attributing to the moon's attraction a certain share in the production of the diurnal and periodical movements of the waters of the ocean.

Laplace did not confine his genius to the extension and improvement of the mathematical theory of the tide. He considered the phenomenon from an entirely new point of view, and it was he who first treated of the stability of the ocean. He has established its equilibrium, but upon the express condition (which, however, has been amply proved to exist) that the mean density of the fluid mass is less than the mean density of the earth. Everything else remaining the same, if we substituted an ocean of quicksilver for the actual ocean, this stability would disappear. The fluid would frequently overflow its boundaries, to ravage continents even to the height of the snowy peaks which lose themselves in the clouds.

No one was more sagacious than Laplace in discovering intimate relations between phenomena apparently unrelated, or more skillful in deducing important conclusions from such unexpected affinities. For example, toward the close of his days, with the aid of certain lunar observations, with a stroke of his pen he overthrew the cosmogonic theories of Buffon and Bailly, which were so long in favor. According to these theories, the earth was hastening to a state of congelation which was close at hand. Laplace, never contented with vague statements, sought to determine in numbers the rate of the rapid cooling of our globe which Buffon had so eloquently but so gratuitously announced. Nothing could be more simple, better connected, or more conclusive 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 must inevitably 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 call 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, following Laplace, take from the standard tables the smallest values, if you choose, of the expansions or contractions which solid bodies experience from changes of temperature; let us search 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. Eloquence cannot resist such a process of reasoning, or withstand the force of such figures. Mathematics has ever been the implacable foe of scientific romances. The constant object of Laplace was the explanation of the great phenomena of nature according to inflexible principles of mathematical analysis. No philosopher, no mathematician, could have guarded himself more cautiously against a propensity to hasty speculation. No person dreaded more the scientific errors which cajole the imagination when it passes the boundary of fact, calculation, and analogy.