Of the discoveries of Kepler, we can here have to do with their universal and humanitary bearings alone. It is to be understood, however, that the three grand sweeps of Deduction which we call Kepler's Laws formed the foundation of the higher conception of astronomy, that is, the dynamical theory of astronomical phenomena, and prepared the way for the "Mécanique Céleste." Whewell, the learned historian of the Sciences, speaks of them as "by far the most magnificent and most certain train of truths which the whole expanse of human knowledge can show"; and Comte declares, that "history tells of no such succession of philosophical efforts as in the case of Kepler, who, after constituting Celestial Geometry, strove to pursue that science of Celestial Mechanics which was by its very nature reserved for a future generation." These laws are, first, the law of the velocities of the planets; second, the law of the elliptic orbit of the planets; and, third, the harmonic law, that the squares of the times of the planetary revolutions are proportional to the cubes of their mean distances from the sun. They compass the whole sweep of Celestial Geometry, and stamp their seer as unapproachably the greatest of astronomers, as well as one of the chief benefactors of mankind.
The announcement of Kepler's first two laws was made in his New Astronomy,—"Astronomia Nova, seu Physica Caelestis, tradita Commentariis de Motibus Stellae Martis: Ex Observationibus G.V. Tychonis Brahe." Folio. Prague: 1609. This he published in his thirty-eighth year. The title he gave to this work, "Celestial Physics," must ever be regarded as a stroke of philosophical genius; it is the prediction of Newton and Laplace, and prefigures the path on which astronomical discovery has advanced these two hundred and fifty years.
An auspicious circumstance conspired to forward the astronomical discoveries of Kepler. Invited to Prague in 1600 by Tycho Brahe, as Assistant Royal Astronomer, he had access to the superb series of observations which Tycho had been accumulating for twenty-five years. Endowed with a genius for observation unsurpassed in the annals of science, the noble Dane had obtained a grant from the king of Denmark of the island of Hven, at the mouth of the Baltic. Here he erected a magnificent observatory, which he named Uranienborg, City of the Heavens. This he fitted up with a collection of instruments of hitherto unapproached size and perfection, and here, for twenty years, he pursued his observations. Thus it was that Kepler, himself a poor observer, found his complement in one who, without any power of constructive generalization, was yet the possessor of the richest series of astronomical observations ever made. From this admirable conjunction admirable realizations were to be expected. And, indeed, the "Astronomia Nova" presents an unequalled illustration of observation vivified by theory, and theory tested and fructified by observation.
To appreciate the significance of the discovery of the elliptical orbit of the planets, it is necessary to understand the complicated confusion that prevailed in the conception of planetary motions. The primal thought was that the motions of the planets were uniform and circular. This intuition of circular orbits was a happy one, and was, perhaps, necessitated by the very structure of the human mind. The sweeping and centrifugal soul, darting manifold rays of equal reach, realizes the conception of the circle, that is, a figure all of whose radii are equidistant from a central point. But this conception of the circle afterwards came to acquire superstitious tenacity, being regarded as the perfect form, and the only one suitable for such divine natures as the stars, and was for two thousand years an impregnable barrier to the progress of Astronomy. To account for every new appearance, every deviation from circular perfection, a new cycloid was supposed, till all the simplicity of the original hypothesis was lost in a complication of epicycles:—
"The sphere,
With centric and eccentric scribbled o'er,
Cycle and epicycle, orb in orb."
By the end of the sixteenth century the number of circles supposed necessary for the seven stars then known amounted to seventy-four, while Tycho Brahe was discovering more and more planetary movements for which these circles would not account.
To push aside forever this complicated chaos and evoke celestial order and harmony, came Kepler. Long had the sublime intuition possessed him, that numerical and geometrical relations connect the distances, times, and revolutions of the planets. He began his studies on the planet Mars,—a fortunate choice, as the marked eccentricity of that planet would afford ready suggestions and verifications of the true law of irregularity, and on which Tycho had accumulated copious data. It had long been remarked that the angular velocity of each planet increases constantly in proportion as the body approaches its centre of motion; but the relation between the distance and the velocity remained wholly unknown. Kepler discovered it by comparing the maximum and minimum of these quantities, by which their relation became more sensible. He found that the angular velocities of Mars at its nearest and farthest distances from the sun were in inverse proportion to the squares of the corresponding distances. This law, deduced, was the immediate path to the law of orbital ellipticity. For, on attempting to apply his newly-discovered law to Mars, on the old assumption that its orbit was a circle, he soon found that the results from the combination of the two principles were such as could not be reconciled with the places of Mars observed by Tycho. In this dilemma, finding he must give up one or the other of these principles, he first proposed to sacrifice his own theory to the authority of the old system,—a memorable example of resolute candor. But, after indefatigably subjecting it to crucial experiment, he found that it was the old hypothesis, and not the new one, that had to be sacrificed.[1] If the orbit was not a circle, what, then, was it? By a happy stroke of philosophical genius he lit on the ellipse. On bringing his hypothesis to the test of observation, he found it was indeed so; and rising from the case of Mars to universal statement, he generalized the law, that the planetary orbits are elliptical, having the sun for their common focus.
[Footnote 1: ROBERT SMALL: Astronomical Discoveries of Kepler.]
Kepler had now determined the course of each planet. But there was no known relation between the distances and times; and the evolution of some harmony between these factors was to him an object of the greatest interest and the most restless curiosity. Long he dwelt in the dream of the Pythagorean harmonies. Then he essayed to determine it from the regular geometrical solids, and afterwards from the divisions of musical chords. Over twenty years he spent in these baffled efforts. At length, on the 8th of March, 1618, it occurred to him, that, instead of comparing the simple times, he should compare the numbers expressing the similar powers, as squares, cubes, etc.; and lastly, he made the very comparison on which his discovery was founded, between the squares of the times and the cubes of the distances. But, through some error of calculation, no common relation was found between them. Finding it impossible, however, to banish the subject from his thoughts, he tells us, that on the 8th of the following May he renewed the last of these comparisons, and, by repeating his calculations with greater care, found, with the highest astonishment and delight, that the ratio of the squares of the periodical times of any two planets was constantly and invariably the same with the ratio of the cubes of their mean distances from the sun. Then it was that he burst forth in his memorable rhapsody:—"What I prophesied twenty-two years ago, as soon as I discovered the five solids among the heavenly orbits,—what I firmly believed long before I had seen Ptolemy's harmonics,—what I had promised my friends in the title of this book, which I named before I was sure of my discovery,—what sixteen years ago I urged as a thing to be sought,—that for which I joined Tycho Brahe, for which I settled in Prague, for which I have devoted the best part of my life to astronomical contemplation,—at length I have brought to light, and have recognized its truth beyond my most sanguine expectations. It is now eighteen months since I got the first glimpse of light, three months since the dawn, very few days since the unveiled sun, most admirable to gaze upon, burst out upon me. Nothing holds me; I will indulge in my sacred fury; I will triumph over mankind by the honest confession, that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God far away from the confines of Egypt. If you forgive me, I rejoice; if you are angry, I can bear it: the die is cast; the book is written, to be read either now or by posterity, I care not which: it may well wait a century for a reader, as God has waited six thousand years for an observer!"
These laws have, no doubt, a universal significance, and may be translated into problems of life. For, after the farthest sweep of Induction, a question yet remains to be asked: Whence comes the power to perceive a law? Whence that subtile correspondence and consanguinity, that the laws of man's mental structure tally with the phenomena of the universe? To this problem of problems our science as yet affords but meagre answers. It seems though, so far in the history of humanity, it had been but given man to recognize this truth as a splendid idealism, without the ability to make it potential in his theory of the world. Yet what a key to new and beautiful gates of laws!