Volume II Part 13 (2/2)

[Sidenote: and of the third.] A thorough exposition of the third law of motion was left by Galileo to his successors, who had directed their attention especially to the determination of the laws of impact. Indeed, the whole subject was ill.u.s.trated and the truth of the three laws verified in many different cases by an examination of the phenomena of freely falling bodies, pendulums, projectiles, and the like. Among those who occupied themselves with such labours may be mentioned Torricelli, Castelli, Viviani, Borelli, Ga.s.sendi. Through the investigations of these, and other Italian, French, and English natural philosophers, the principles of Mechanics were solidly established, and a necessary preparation made for their application in astronomy. By this time every one had become ready to admit that the motion of the planetary bodies would find an explanation on these principles.

[Sidenote: Application of Mechanics to the celestial motions.] The steps thus far taken for an explanation of the movements of the planets in curvilinear paths therefore consisted in the removal of the old misconception that for a body to continue its motion forward in a straight line a continued application of force is necessary, the first law of motion disposing of that error. In the next place, it was necessary that clear and distinct ideas should be held of the combination or composition of forces, each continuing to exercise its influence without deterioration or diminution by the other. The time had now come for it to be shown that the perpetual movement of the planets is a consequence of the first law of motion; their elliptic paths, such as had been determined by Kepler, a consequence of the second. Several persons almost simultaneously had been brought nearly to this conclusion without being able to solve the problem completely. Thus Borelli, A.D.

1666, in treating of the motions of Jupiter's satellites, distinctly shows how a circular motion may arise under the influence of a central force; he even uses the ill.u.s.tration so frequently introduced of a stone whirled round in a sling. In the same year a paper was presented to the Royal Society by Mr. Hooke, ”explicating the inflection of a direct motion into a circular by a supervening attractive principle.” Huygens also, in his ”Horologium Oscillatorium,” had published some theorems on circular motions, but no one as yet had been able to show how elliptical orbits could, upon these principles, be accounted for, though very many had become satisfied that the solution of this problem would before long be given.

[Sidenote: Newton; publication of the ”Principia.”] In April, 1686, the ”Principia” of Newton was presented to the Royal Society. This immortal work not only laid the foundation of Physical Astronomy, it also carried the structure thereof very far toward its completion. It unfolded the mechanical theory of universal gravitation upon the principle that all bodies tend to approach each other with forces directly as their ma.s.ses, and inversely as the squares of their distances.

[Sidenote: Propounds the theory of universal gravitation.] To the force producing this tendency of bodies to approach each other the designation of attraction of gravitation, or gravity, is given. All heavy bodies fall to the earth in such a way that the direction of their movement is toward its centre. Newton proved that this is the direction in which they must necessarily move under the influence of an attraction of every one of the particles of which the earth is composed, the attraction of a sphere taking effect as if all its particles were concentrated in its centre.

[Sidenote: Preparation for Newton.] Galileo had already examined the manner in which gravity acts upon bodies as an accelerating force, and had determined the connexion between the s.p.a.ces of descent and the times. He ill.u.s.trated such facts experimentally by the use of inclined planes, by the aid of which the velocity may be conveniently diminished without otherwise changing the nature of the result. He had also demonstrated that the earth's attraction acts equally on all bodies.

This he proved by inclosing various substances in hollow spheres, and showing that, when they were suspended by strings of equal length and made to vibrate, the time of oscillation was the same for all. On the invention of the air-pump, a more popular demonstration of the same fact was given by the experiment proving that a gold coin and a feather fall equally swiftly in an exhausted receiver. Galileo had also proved, by experiments on the leaning tower of Pisa, that the velocity of falling bodies is independent of their weight. It was for these experiments that he was expelled from that city.

[Sidenote: Extension of attraction or gravity.] Up to the time of Newton there were only very vague ideas that the earth's attraction extended to any considerable distance. Newton was led to his discovery by reflecting that at all alt.i.tudes accessible to man, gravity appears to be undiminished, and that, therefore, it may possibly extend as far as the moon, and actually be the force which deflects her from a rectilinear path, and makes her revolve in an orbit round the earth. Admitting the truth of the law of the inverse squares, it is easy to compute whether the moon falls from the tangent she would describe if the earth ceased to act upon her by a quant.i.ty proportional to that observed in the case of bodies falling near the surface. In the first calculations made by Newton, he found that the moon is deflected from the tangent thirteen feet every minute; but, if the hypothesis of gravitation were true, her deflection should be fifteen feet. It is no trifling evidence of the scrupulous science of this great philosopher that hereupon he put aside the subject for several years, without, however, abandoning it. At length, in 1682, learning the result of the measures of a degree which Picard had executed in France, and which affected the estimate of the magnitude of the earth he had used, and therefore the distance of the moon, he repeated the calculations with these improved data. It is related that ”he went home, took out his old papers, and resumed his calculations. As they drew to a close, he became so much agitated that he was obliged to desire a friend to finish them.” The expected coincidence was verified. And thus it appeared that the moon is retained in her orbit and made to revolve round the earth by the force of terrestrial gravity.

[Sidenote: The cause of Kepler's laws.] These calculations were founded upon the hypothesis that the moon moves in a circular orbit with a uniform velocity. But in the ”Principia” it was demonstrated that when a body moves under the influence of an attractive force, varying as the inverse square of the distances, it must describe a conic section, with a focus at the centre of force, and under the circ.u.mstances designated by Kepler's laws. Newton, therefore, did far more than furnish the expected solution of the problem of elliptical motion, and it was now apparent that the existence of those laws might have been foreseen, since they arise in the very necessities of the case.

[Sidenote: 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 a.s.serted in respect to all material substance.

[Sidenote: 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...o...b..t 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 the planetary bodies are at very great distances from one another, and their ma.s.ses, compared with the ma.s.s of the sun, very small.

[Sidenote: 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 ma.s.s 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 ma.s.s of a hitherto unknown planet determined. It was thus that, from the deviations of Ura.n.u.s 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 a.n.a.lytical 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. [Sidenote: 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 princ.i.p.al 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 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.”

[Sidenote: 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. [Sidenote: Unity of idea in the construction of the universe.] Hence, before it can be a.s.serted 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.

[Sidenote: 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 determined was given by M. Savary in the case of chi Ursae Majoris, indicating an elliptic orbit of 58-1/4 years. But the period of others, since determined, is very much longer; thus, in sigma Coronae, 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 a.s.sert the prevalence of the law of gravitation throughout the universe.

[Sidenote: Coloured light of double stars.] If, in a.s.sociation with these double suns--sometimes, indeed, they are triple, and occasionally, as in the case of epsilon Lyrae, 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 s.h.i.+ning 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.

[Sidenote: 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 quant.i.ties 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 lat.i.tudes, and a mult.i.tude of other phenomena. The theory a.s.serted for itself that authority which belongs to intrinsic truth. It 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 Ga.s.sendi and Descartes do not agree so well with revealed truth as Aristotle does.”

[Sidenote: 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...o...b..t.

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 r.e.t.a.r.dation. In like manner, the same mathematician explained the observed acceleration in the mean motion of Jupiter, and r.e.t.a.r.dation of that of Saturn, as arising from the mutual attraction of the two planets, and showed that this secular inequality has a period of 929-1/2 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 ill.u.s.trations of the scale upon which the world is constructed as to time, as well as that upon which it is constructed as to s.p.a.ce.

[Sidenote: Dominion of law in the universe.] From what has been said, the conclusion forces itself upon us that the general laws obtaining as respects the earth, hold good likewise for all other parts of the universe; a conclusion sustained not only by the mechanism of such motions as we have been considering, but also by all evidence of a physical kind accessible to us. The circ.u.mstances under which our sun emits light and heat, and thereby vivifies his attendant planets, are indisputably the same as those obtaining in the case of every fixed star, each of which is a self-luminous sun. There is thus an aspect of h.o.m.ogeneousness in the structure of all systems in the universe, which, though some have spoken of it as if it were the indication of a uniformity of plan, and therefore the evidence of a primordial idea, is rather to be looked upon as the proof of unchangeable and resistless law.

[Sidenote: Ruin of anthropocentric ideas.] What, therefore, now becomes of the doctrine authoritatively put forth, and made to hold its sway for so many centuries, that the earth is not only the central-body of the universe, but in reality, the most n.o.ble body in it; that the sun and other stars are mere ministers or attendants for human use? In the place of these utterly erroneous and unworthy views, far different conceptions must be subst.i.tuted. Man, when he looks upon the countless mult.i.tude of stars--when he reflects that all he sees is only a little portion of those which exist, yet that each is a light and life-giving sun to mult.i.tudes of opaque, and therefore, invisible worlds--when he considers the enormous size of these various bodies and their immeasurable distance from one another, may form an estimate of the scale on which the world is constructed, and learn therefrom his own unspeakable insignificance.

[Sidenote: Aids for measurements in the universe.] In one beat of a pendulum a ray of light would pa.s.s eight times round the circ.u.mference of the earth. Thus we may take the sunbeam as a carpenter does his measuring-rule; it serves as a gauge in our measurements of the universe. A sunbeam would require more than three years to reach us from alpha Centauri; nine and a quarter years from 61 Cygni; from alpha Lyrae twelve years. These are stars whose parallax has been determined, and which are therefore nearest to us.

[Sidenote: Cl.u.s.ters of stars.] Of suns visible to the naked eye there are about 8000, but the telescope can discern in the Milky Way more than eighteen millions, the number visible increasing as more powerful instruments are used. Our cl.u.s.ter of stars is a disc divided into two branches at about one-third of its length. In the midst of innumerable compeers and superiors, the sun is not far from the place of bifurcation, and at about the middle of the thickness. Outside the plane of the Milky Way the appearance would be like a ring, and, still farther off, a nebulous disc.

[Sidenote: Distribution of matter and force in s.p.a.ce.] From the contemplation of isolated suns and congregated cl.u.s.ters we are led to the stupendous problem of the distribution of matter and force in s.p.a.ce, and to the interpretation of those apparent phantoms of self-luminous vapour, circular and elliptic discs, spiral wreaths, rings and fans, whose edges fade doubtfully away, twins and triplets of phosph.o.r.escent haze connected together by threads of light and grotesque forms of indescribable complexity. Perhaps in some of these gleaming apparitions we see the genesis, in some the melting away of universes. There is nothing motionless in the sky. In every direction vast transformations are occurring, yet all things proclaim the eternity of matter and the undiminished perpetuity of force.

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