History of the Intellectual Development of Europe, Volume II (of 2) / Revised Edition

by John William Draper

Resistless spread of the heliocentric theory.This point gained, it is obvious that the evidence was becoming unquestionable, that as the moon is made to revolve round the earth through the influence of an attractive force exercised by the earth, so likewise each of the planets is compelled to move in an elliptical orbit round the sun by his attractive force. The heliocentric theory, at this stage, was presenting physical evidence of its truth. It was also becoming plain that the force we call gravitation must be imputed to the sun, and to all the planetary bodies as well as to the earth. Accordingly, this was what Newton asserted in respect to all material substance.

Perturbations accounted for.But it is a necessary consequence of this theory that many apparent irregularities and perturbations of the bodies of the solar system must take place by reason of the attraction of each upon all the others. If there were but one planet revolving round the sun, its orbit might be a mathematically perfect ellipse; but the moment a second is introduced, perturbation takes place in a variable manner as the bodies change their positions or distances. An excessive complication must therefore be the consequence when the number of bodies is great. Indeed, so insurmountable would these difficulties be, that the mathematical solution of the general problem of the solar system would be hopeless were it not for the fact that [275] the planetary bodies are at very great distances from one another, and their masses, compared with the mass of the sun, very small.

Results of the theory of gravitation.Taking the theory of gravitation in its universal acceptation, Newton, in a manner that looks as if he were divinely inspired, succeeded in demonstrating the chief inequalities of the moon and planetary bodies; in determining the figure of the earth—that it is not a perfect sphere, but an oblate spheroid; in explaining the precession of the equinoxes and the tides of the ocean. To such perfection have succeeding mathematicians brought his theory, that the most complicated movements and irregularities of the solar system have been satisfactorily accounted for and reduced to computation. Trusting to these principles, not only has it been found possible, knowing the mass of a given planet, to determine the perturbations it may produce in adjacent ones, but even the inverse problem has been successfully attacked, and from the perturbations the place and mass of a hitherto unknown planet determined. It was thus that, from the deviations of Uranus from his theoretical place, the necessary existence of an exterior disturbing planet was foreseen, and our times have witnessed the intellectual triumph of mathematicians directing where the telescope should point in order to find a new planet. The discovery of Neptune was thus accomplished.

It adds to our admiration of the wonderful intellectual powers of Newton to know that the mathematical instrument he used was the ancient geometry. Not until subsequently was the analytical method resorted to and cultivated. This method possesses the inappreciable advantage of relieving us from the mental strain which would otherwise oppress us. It has been truly said that the symbols think for us. The "Principia;" its incomparable merit. Mr. Whewell observes: "No one for sixty years after the publication of the 'Principia,' and, with Newton's methods, no one up to the present day, has added any thing of value to his deductions. We know that he calculated all the principal lunar inequalities; in many of the cases he has given us his processes, in others only his results. But who has presented in his beautiful geometry or [276] deduced from his simple principles any of the inequalities which he left untouched? The ponderous instrument of synthesis, so effective in his hands, has never since been grasped by any one who could use it for such purposes; and we gaze at it with admiring curiosity, as on some gigantic implement of war which stands idle among the memorials of ancient days, and makes us wonder what manner of man he was who could wield as a weapon what we can hardly lift as a burden."

Philosophical import of Newton's discoveries.Such was the physical meaning of Newton's discoveries; their philosophical meaning was of even greater importance. The paramount truth was resistlessly coming into prominence—that the government of the solar system is under necessity, and that it is mathematically impossible for the laws presiding over it to be other than they are.

Thus it appears that the law of gravitation holds good throughout our solar system. But the heliocentric theory, in its most general acceptation, considers every fixed star as being, like the sun, a planetary centre. Unity of idea in the construction of the universe. Hence, before it can be asserted that the theory of gravitation is truly universal, it must be shown that it holds good in the case of all other such systems. The evidence offered in proof of this is altogether based upon the observations of the two Herschels on the motions of the double stars. Among the stars there are some in such close proximity to each other that Sir W. Herschel was led to suppose it would be possible, from observations upon them, to ascertain the stellar parallax. While engaged in these inquiries, which occupied him for many years, he discovered that many of these stars are not merely optically in proximity, as being accidentally in the same line of view, but are actually connected physically, revolving round each other in regular orbits. The motion of these double suns is, however, in many instances so slow as to require many years for a satisfactory determination. Gravitation of double stars. Sir J. Herschel therefore continued the observations of his father, and with other mathematicians, investigated the characteristics of these motions. The first instance in which the true elliptic elements of the orbit of a binary star were [277] determined was given by M. Savary in the case of chi Ursæ Majoris, indicating an elliptic orbit of 58 ¼ years. But the period of others, since determined, is very much longer; thus, in sigma Coronæ, it is, according to Mr. Hind, more than 736 years. From the fact that the orbits in which these stars move round each other are elliptical, it necessarily follows that the law of gravitation, according to the inverse square, holds good in them. Considering the prodigious distances of these bodies, and the departure, as regards structure of the systems to which they belong, from the conditions obtaining in our unisolar system, we may perhaps assert the prevalence of the law of gravitation throughout the universe.

Coloured light of double stars.If, in association with these double suns—sometimes, indeed, they are triple, and occasionally, as in the case of epsilon Lyræ, quadruple—there are opaque planetary globes, such solar systems differ from ours not only in having several suns instead of a single one, but, since the light emitted is often of different tints, one star shining with a crimson and another with a blue light, the colours not always complementary to one another, a wonderful variety of phenomena must be the result, especially in their organic creations; for organic forms, both vegetable and animal, primarily depend on the relations of coloured light. How varied the effects where there are double, triple, or even quadruple sunrises, and sunsets, and noons; and the hours marked off by red, or purple, or blue tints.

Grandeur of Newton's discoveries.It is impossible to look back on the history of the theory of gravitation without sentiments of admiration and, indeed, of pride. How felicitous has been the manner in which have been explained the inequalities of a satellite like the moon under the disturbing influence of the sun; the correspondence between the calculated and observed quantities of these inequalities; the extension of the doctrine to satellites of other planets, as those of Jupiter; the determination of the earth's figure; the causes of the tides; the different force of gravity in different latitudes, and a multitude of other phenomena. The theory asserted for itself that authority which belongs to intrinsic truth. It [278] enabled mathematicians to point out facts not yet observed, and to foretell future events.

And yet how hard it is for truth to force its way when bigotry resists. In 1771, the University of Salamanca, being urged to teach physical science, refused, and this was its answer; "Newton teaches nothing that would make a good logician or metaphysician; and Gassendi and Descartes do not agree so well with revealed truth as Aristotle does."

The earth in time.Among the interesting results of Newton's theory may be mentioned its application to secular inequalities, such as the acceleration of the moon's mean motion, that satellite moving somewhat quicker now than she did ages ago. Laplace detected the cause of this phenomenon in the influence of the sun upon the moon, combined with the secular variation of the eccentricity of the earth's orbit. Moreover, he showed that this secular inequality of the motion of the moon is periodical, that it requires millions of years to re-establish itself, and that, after an almost inconceivable time, the acceleration becomes a retardation. In like manner, the same mathematician explained the observed acceleration in the mean motion of Jupiter, and retardation of that of Saturn, as arising from the mutual attraction of the two planets, and showed that this secular inequality has a period of 929 ½ years. With such slow movements may be mentioned the diminution of the obliquity of the ecliptic, which has been proceeding for ages, but which will reach a limit and then commence to increase. These secular motions ought not to be without interest to those who suffer themselves to adopt the patristic chronology of the world, who suppose that the earth is only six thousand years old, and that it will come to an end in about one thousand years more. They must accept, along with that preposterous delusion, its necessary consequences, that the universe has been so badly constructed, and is such a rickety machine, that it can not hold together long enough for some of its wheels to begin to revolve. Astronomy offers us many illustrations of the scale upon which the world is constructed as to time, as well as that upon which it is constructed as to space.