Part 15 (1/2)
Not without reason, therefore, did they look upon the doctrine of government by unvarying law with disfavor. It seemed to depreciate their dignity, to lessen their importance. To them there was something shocking in a G.o.d who cannot be swayed by human entreaty, a cold, pa.s.sionless divinity--something frightful in fatalism, destiny.
But the orderly movement of the heavens could not fail in all ages to make a deep impression on thoughtful observers--the rising and setting of the sun; the increasing or diminis.h.i.+ng light of the day; the waxing and waning of the moon; the return of the seasons in their proper courses; the measured march of the wandering planets in the sky--what are all these, and a thousand such, but manifestations of an orderly and unchanging procession of events? The faith of early observers in this interpretation may perhaps have been shaken by the occurrence of such a phenomenon as an eclipse, a sudden and mysterious breach of the ordinary course of natural events; but it would be resumed in tenfold strength as soon as the discovery was made that eclipses themselves recur, and may be predicted.
Astronomical predictions of all kinds depend upon the admission of this fact--that there never has been and never will be any intervention in the operation of natural laws. The scientific philosopher affirms that the condition of the world at any given moment is the direct result of its condition in the preceding moment, and the direct cause of its condition in the subsequent moment. Law and chance are only different names for mechanical necessity.
About fifty years after the death of Copernicus, John Kepler, a native of Wurtemberg, who had adopted the heliocentric theory, and who was deeply impressed with the belief that relations.h.i.+ps exist in the revolutions of the planetary bodies round the sun, and that these if correctly examined would reveal the laws under which those movements take place, devoted himself to the study of the distances, times, and velocities of the planets, and the form of their orbits. His method was, to submit the observations to which he had access, such as those of Tycho Brahe, to computations based first on one and then on another hypothesis, rejecting the hypothesis if he found that the calculations did not accord with the observations. The incredible labor he had undergone (he says, ”I considered, and I computed, until I almost went mad”) was at length rewarded, and in 1609 he published his book, ”On the Motions of the Planet Mars.” In this he had attempted to reconcile the movements of that planet to the hypothesis of eccentrics and epicycles, but eventually discovered that the orbit of a planet is not a circle but an ellipse, the sun being in one of the foci, and that the areas swept over by a line drawn from the planet to the sun are proportional to the times. These const.i.tute what are now known as the first and second laws of Kepler. Eight years subsequently, he was rewarded by the discovery of a third law, defining the relation between the mean distances of the planets from the sun and the times of their revolutions; ”the squares of the periodic times are proportional to the cubes of the distances.” In ”An Epitome of the Copernican System,” published in 1618, he announced this law, and showed that it holds good for the satellites of Jupiter as regards their primary. Hence it was inferred that the laws which preside over the grand movements of the solar system preside also over the less movements of its const.i.tuent parts.
The conception of law which is unmistakably conveyed by Kepler's discoveries, and the evidence they gave in support of the heliocentric as against the geocentric theory, could not fail to incur the reprehension of the Roman authorities. The congregation of the Index, therefore, when they denounced the Copernican system as utterly contrary to the Holy Scriptures, prohibited Kepler's ”Epitome” of that system. It was on this occasion that Kepler submitted his celebrated remonstrance: ”Eighty years have elapsed during which the doctrines of Copernicus regarding the movement of the earth and the immobility of the sun have been promulgated without hinderance, because it was deemed allowable to dispute concerning natural things, and to elucidate the works of G.o.d, and now that new testimony is discovered in proof of the truth of those doctrines--testimony which was not known to the spiritual judges--ye would prohibit the promulgation of the true system of the structure of the universe.”
None of Kepler's contemporaries believed the law of the areas, nor was it accepted until the publication of the ”Principia” of Newton. In fact, no one in those times understood the philosophical meaning of Kepler's laws. He himself did not foresee what they must inevitably lead to. His mistakes showed how far he was from perceiving their result. Thus he thought that each planet is the seat of an intelligent principle, and that there is a relation between the magnitudes of the orbits of the five princ.i.p.al planets and the five regular solids of geometry. At first he inclined to believe that the orbit of Mars is oval, nor was it until after a wearisome study that he detected the grand truth, its elliptical form. An idea of the incorruptibility of the celestial objects had led to the adoption of the Aristotelian doctrine of the perfection of circular motions, and to the belief that there were none but circular motions in the heavens. He bitterly complains of this as having been a fatal ”thief of his time.” His philosophical daring is ill.u.s.trated in his breaking through this time-honored tradition.
In some most important particulars Kepler antic.i.p.ated Newton. He was the first to give clear ideas respecting gravity. He says every particle of matter will rest until it is disturbed by some other particle--that the earth attracts a stone more than the stone attracts the earth, and that bodies move to each other in proportion to their ma.s.ses; that the earth would ascend to the moon one-fifty-fourth of the distance, and the moon would move toward the earth the other fifty-three. He affirms that the moon's attraction causes the tides, and that the planets must impress irregularities on the moon's motions.
The progress of astronomy is obviously divisible into three periods:
1. The period of observation of the apparent motions of the heavenly bodies.
2. The period of discovery of their real motions, and particularly of the laws of the planetary revolutions; this was signally ill.u.s.trated by Copernicus and Kepler.
3. The period of the ascertainment of the causes of those laws. It was the epoch of Newton.
The pa.s.sage of the second into the third period depended on the development of the Dynamical branch of mechanics, which had been in a stagnant condition from the time of Archimedes or the Alexandrian School.
In Christian Europe there had not been a cultivator of mechanical philosophy until Leonardo da Vinci, who was born A.D. 1452. To him, and not to Lord Bacon, must be attributed the renaissance of science. Bacon was not only ignorant of mathematics, but depreciated its application to physical inquiries. He contemptuously rejected the Copernican system, alleging absurd objections to it. While Galileo was on the brink of his great telescopic discoveries, Bacon was publis.h.i.+ng doubts as to the utility of instruments in scientific investigations. To ascribe the inductive method to him is to ignore history. His fanciful philosophical suggestions have never been of the slightest practical use. No one has ever thought of employing them. Except among English readers, his name is almost unknown.
To Da Vinci I shall have occasion to allude more particularly on a subsequent page. Of his works still remaining in ma.n.u.script, two volumes are at Milan, and one in Paris, carried there by Napoleon. After an interval of about seventy years, Da Vinci was followed by the Dutch engineer, Stevinus, whose work on the principles of equilibrium was published in 1586. Six years afterward appeared Galileo's treatise on mechanics.
To this great Italian is due the establishment of the three fundamental laws of dynamics, known as the Laws of Motion.
The consequences of the establishment of these laws were very important.
It had been supposed that continuous movements, such, for instance, as those of the celestial bodies, could only be maintained by a perpetual consumption and perpetual application of force, but the first of Galileo's laws declared that every body will persevere in its state of rest, or of uniform motion in a right line, until it is compelled to change that state by disturbing forces. A clear perception of this fundamental principle is essential to a comprehension of the elementary facts of physical astronomy. Since all the motions that we witness taking place on the surface of the earth soon come to an end, we are led to infer that rest is the natural condition of things. We have made, then, a very great advance when we have become satisfied that a body is equally indifferent to rest as to motion, and that it equally perseveres in either state until disturbing forces are applied. Such disturbing forces in the case of common movements are friction and the resistance of the air. When no such resistances exist, movement must be perpetual, as is the case with the heavenly bodies, which are moving in a void.
Forces, no matter what their difference of magnitude may be, will exert their full influence conjointly, each as though the other did not exist.
Thus, when a ball is suffered to drop from the mouth of a cannon, it falls to the ground in a certain interval of time through the influence of gravity upon it. If, then, it be fired from the cannon, though now it may be projected some thousands of feet in a second, the effect of gravity upon it will be precisely the same as before. In the intermingling of forces there is no deterioration; each produces its own specific effect.
In the latter half of the seventeenth century, through the works of Borelli, Hooke, and Huyghens, it had become plain that circular motions could be accounted for by the laws of Galileo. Borelli, treating of the motions of Jupiter's satellites, shows how a circular movement may arise under the influence of a central force. Hooke exhibited the inflection of a direct motion into a circular by a supervening central attraction.
The year 1687 presents, not only an epoch in European science, but also in the intellectual development of man. It is marked by the publication of the ”Principia” of Newton, an incomparable, an immortal work.
On the principle that all bodies attract each other with forces directly as their ma.s.ses, and inversely as the squares of their distances, Newton showed that all the movements of the celestial bodies may be accounted for, and that Kepler's laws might all have been predicted--the elliptic motions--the described areas the relation of the times and distances. As we have seen, Newton's contemporaries had perceived how circular motions could be explained; that was a special case, but Newton furnished the solution of the general problem, containing all special cases of motion in circles, ellipses, parabolas, hyperbolas--that is, in all the conic sections.
The Alexandrian mathematicians had shown that the direction of movement of falling bodies is toward the centre of the earth. Newton proved that this must necessarily be the case, the general effect of the attraction of all the particles of a sphere being the same as if they were all concentrated in its centre. To this central force, thus determining the fall of bodies, the designation of gravity was given. Up to this time, no one, except Kepler, had considered how far its influence reached. It seemed to Newton possible that it might extend as far as the moon, and be the force that deflects her from a rectilinear path, and makes her revolve in her orbit round the earth. It was easy to compute, on the principle of the law of inverse squares, whether the earth's attraction was sufficient to produce the observed effect. Employing the measures of the size of the earth accessible at the time, Newton found that the moon's deflection was only thirteen feet in a minute; whereas, if his hypothesis of gravitation were true, it should be fifteen feet. But in 1669 Picard, as we have seen, executed the measurement of a degree more carefully than had previously been done; this changed the estimate of the magnitude of the earth, and, therefore, of the distance of the moon; and, Newton's attention having been directed to it by some discussions that took place at the Royal Society in 1679, he obtained Picard's results, 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 established. It was proved that the moon is retained in her orbit and made to revolve round the earth by the force of terrestrial gravity. The genii of Kepler had given place to the vortices of Descartes, and these in their turn to the central force of Newton.
In like manner the earth, and each of the planets, are made to move in an elliptic orbit round the sun by his attractive force, and perturbations arise by reason of the disturbing action of the planetary ma.s.ses on one another. Knowing the ma.s.ses and the distances, these disturbances may be computed. Later astronomers have even succeeded with the inverse problem, that is, knowing the perturbations or disturbances, to find the place and the ma.s.s of the disturbing body. Thus, from the deviations of Ura.n.u.s from his theoretical position, the discovery of Neptune was accomplished.
Newton's merit consisted in this, that he applied the laws of dynamics to the movements of the celestial bodies, and insisted that scientific theories must be substantiated by the agreement of observations with calculations.
When Kepler announced his three laws, they were received with condemnation by the spiritual authorities, not because of any error they were supposed to present or to contain, but partly because they gave support to the Copernican system, and partly because it was judged inexpedient to admit the prevalence of law of any kind as opposed to providential intervention. The world was regarded as the theatre in which the divine will was daily displayed; it was considered derogatory to the majesty of G.o.d that that will should be fettered in any way. The power of the clergy was chiefly manifested in the influence the were alleged to possess in changing his arbitrary determinations. It was thus that they could abate the baleful action of comets, secure fine weather or rain, prevent eclipses, and, arresting the course of Nature, work all manner of miracles; it was thus that the shadow had been made to go back on the dial, and the sun and the moon stopped in mid-career.