Kepler

THE acceptance of a doctrine is often out of all proportion to the authority that fortifies it. There are sweeps of generalization quite permeable to objection, which yet find metaphysical support; there are irrefragable dogmas which the mind drops as futile and fruitless. It is recorded of Harvey’s discovery of the circulation of the blood, that it found reception from no physician then over forty years old. We believe the splendid nebular construction of Laplace has its own difficulties; yet what noble or aspiring mind does not find interior warranties for the truth of that audacious synthesis ? Is it that the soul darts responsive impartments to the heavens ? that the whirl is elemental in the mind ? that baffling intervals stretch deeper within us, and shoals of stars with no parallax appear ?

Among the functions of Science, then, may well be included its power as a metre of the intellectual advance of mankind. In these splendid symbols man writes the record of his advancing humanity. How all is interwoven with the All! A petrified national mind will certainly appear in a petrified national Science. And that sublime upsurging from the depths of human nature which came with the last half of the eighteenth century appeared not alone in the new political and social aspirations, but in a fresh insight into Nature. This spirit manifested itself in the new sciences that sprang from the new modes of vision,—Magnetism, Electricity, Chemistry, — the old crystalline spell departing before a dynamical system of Physics, before the thought of the universe as a living organic whole. And what provokers does the discovery of the celestial circles bring to new circles of politics and social life !

The illustrations of Astronomy to this thought are very large. First of the sciences to assume a perfectly rational form, it presents the eternal type of the unfolding of the speculative spirit of man. This springs, no doubt, from the essentially subjective character of astronomy, — more than all the other sciences a construction of the creative reason. From the initiative of scientific astronomy, when the early Greek geometers referred the apparent diurnal movements to geometrical laws, to the creation of the nebular hypothesis, the logical filiation of the leading astronomical conceptions obeys corresponding tidal movements in humanity. Thus it is that

“ through the ages one increasing purpose runs,
And the thoughts of men are widened with the process of the suns.’

It was for reasons the Ptolemaic system so long held its sway. It was for reasons it went, too, when it did, hideous and oppressive nightmare ! The celestial revelations of the sixteenth century came as the necessary complement of the new mental firmaments then dawning on the thought of man. The intellectual revolution caused by the discovery of the double motion of our planet was undoubtedly the mightiest that man had ever experienced, and its effect was to change the entire aspect of his speculative and practical activity. What a proof that ideas rule the world! Two hundred and fifty years ago, certain new sidereal conceptions arose in the minds of half a dozen philosophers, (isolated and utterly destitute of political or social influence, powerful only in the possession of a sublime and seminal thought,)— conceptions which, during these two centuries, have succeeded in overthrowing a doctrine as old as the human mind, closely interknit with the entire texture of opinions, authority, polities, and religion, and establishing a theory flatly contradicted by the universal dictates of experience and common sense, and true only to the transcendental and interpretative Reason!

At the advent of Modern Astronomy, the apparition of the German, John Kepler, presents itself. Familiarly associated in general apprehension with that inductive triad known as “ Kepler’s Laws,” which form the foundation of Celestial Geometry, it is much less generally known that he was an august and oracular soul, one of those called Mystics and Transcendeutalists, perhaps the greatest genius for analogy that ever lived,—that he led a truly epic life, a hero and helper of men, a divine martyr of humanity.

The labors of Kepler were mathematical, optical, cosmographical, and astronomical,—but chiefly astronomical. Two or three of his principal works are the “Cosmograpluc Mystery,” (Mysterium Cosmographicum,) the “ New Astronomy,” (Astronomia Nova, seu Physica Cœlestis,) and the “Harmonies of the World” (Harmonices Mundi). His whole published works comprise some thirty or forty volumes, while twenty folio volumes of manuscript lie in the Library at St. Petersburg. These Euler, Lexell, and Kraft undertook some years ago to examine and publish, but the result of this examination has never appeared. An elegant complete edition of the works of Kepler is at present being issued at Frankfort, under the editorship of Frisch.1 It is to be in sixteen volumes, Svo, two of which are published. For his biography, the chief source is the folio volume of Correspondence, published in 1718, by Hansch,2 who has prefixed to these letters between Kepler and his contemporaries a Life, in which his German heartiness beats even through the marble encasement of his Latinity.

We have always admired, as a stroke of wit, the way Hansch takes to indicate Kepler’s birthplace. Disdaining to use any but mathematical symbols for so great a mathematician, he writes that he was born on the 21st of December, 1571, in longitude 29° latitude 48° 54/ ! It may be worth mentioning, that on this cryptic spot stood the little town of Weil in the Duchy of Würtemberg. His birth was cast at a time when his parents were reduced to great poverty, and he received very little early schooling. He was, however, sent to Tübingen, and here he pursued the scholastic studies of the age, designing: for the Church. But the old eternal creed-questionings arose in his mind. He stumbled at the omnipresence of Christ's body, wrote a Latin poem against it, and, when he had completed his studies, got for a testimonium that he had distinguished himself by his oratorical talents, but was considered unfit to be a fellow-laborer in the Church of Würtemberg. A larger priesthood awaited him.

The astronomical lectureship at the University of Gratz, in Styria, falling vacant, Kepler was in his twenty-third year appointed to fill it. He was, as he tells us, “ better furnished with talent than knowledge.” But, no doubt, things had conspired to forward him. While at Tübingen, under the mathematician Mastlin, he had eagerly seized all the hints his master threw out of the doctrines of Copernicus, integrating them with interior authorities of his own. “ The motion of the earth, which Copernicus had proved by mathematical reasons, I wanted to prove by physical, or, if you prefer it, metaphysical reasons.” So he wrote in his “Prodromus Dissertationum Cosmographicarum,” which he published two years after going to Grätz, that is, in his twentyfifth year. In this book his fiery and mystical spirit first found expression, flaming forth in meteoric coruscations. The problem which Kepler attempted to solve in the “Prodromus” was no less than the determination of the harmonic relations of the distances of the planets, which it was given him to solve more than twenty years afterwards. The hypothesis which he adopted proved utterly fallacious; but his primal intuition, that numerical and geometric relations connect the velocities, periods, and distances of the planets, was none the less fruitful and sublime.

Of the facts of Kepler’s external life, we may simply say, for the sake of readier apprehension, that, after remaining six years at Grätz, he, in 1600, on the invitation of Tycho Brahe, Astronomer Royal to Rodolph H. of Germany, removed to Prague and associated himself with Tycho, who shortly afterwards dying, Kepler was appointed in his place. The chief work was the construction of the new astronomical tables called the Rodolphine Tables, and on these he was engaged many years. In this situation he continued till 1613, when he left it to assume a professorship at Linz. Here he remained some years, and the latter part of his life was spent as astrologer to Wallenstein. Kepler is described as small and meagre of person, and he speaks of himself as “ troublesome and choleric in politics and domestic matters.” He was twice married, and left a wife and numerous children ill-provided for.

Indeed, a painful and perturbed life fell to the lot of Kepler. The most crushing poverty all his life oppressed him. For, though his nominal salary as Astronomer Royal was large enough, yet the treasury was so exhausted that it was impossible for him ever to obtain more than a pittance. What a sad tragedy do these words, in a letter to Mastlin, reveal:— “ I stand whole days in the antechamber, and am nought for study.” And then he adds the sublime compensation: “ I keep up my spirits, however, with the thought that I serve, not the Emperor alone, but the whole human race,— that I am laboring not merely for the present generation, but for posterity. If God stand by me and look to the victuals, I hope to perform something yet.” Eternal type of the consolation which the consciousness of truth brings with it, his ejaculation on the discovery of his third law remains one of the sublimest utterances of the human mind:—“The die is east; the book is written,—to be read 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! ” Cast in a stormy and chaotic age, he was persecuted by both Protestants and Catholics on account of the purity and elevation of his religious ideas; and from the disclosures of Baron von Breitschwert3 it seems, that, in the midst of his sublimest labors, he spent five years in the defence of his poor old mother against a charge of witchcraft. He died in 1630, in his sixtieth year, (with the prospect of starvation before him,) of a fever which he caught when on a journey to Ratisbon, whither he had gone in the attempt to get part of his pay !

In what bewildering and hampering environment he found himself with the “ Tübingen doctors ” and the “ Würtemberg divines,” his letters reveal. On the publication of the “ Prodromus,” Hafenreffer wrote to warn him : — “ God forbid you should endeavor to bring your hypothesis openly into argument with the Holy Scriptures! I require of you to treat the subject merely as a mathematician, and to leave the peace of the Church undisturbed.” To the Tübingen doctors he replied : — “ The Bible speaks to me of things belonging to human life as men are used to speak of them. It is no manual of Optics or of Astronomy; it has a higher object in view. It is a culpable misuse of it to seek in it for answers on worldly things. Joshua wished for the day to be lengthened. God hearkened to his wish. How ? This is not to be inquired after.” And surely the long-vexed argument has never since unfolded better statement than in the words of Kepler: — “The day will soon break when pious simplicity will be ashamed of its blind superstition,— when men will recognize truth in the book of Nature as well as in the Holy Scriptures, and rejoice in the two revelations.” 4

On this avowal he was branded as a hypocrite, heretic, and atheist.

To Mästlin he wrote: — “What is to be done ? I think we should imitate the Pythagoreans, communicate our discoveries privatim, and be silent in public, that we may not die of hunger. The guardians of the Holy Scriptures make an elephant of a gnat. To avoid the hatred against novelty, I represented my discovery to the Rector of the University as a thing already observed by the ancients ; but he made its antiquity a greater charge against it than he could have made of its novelty.”

And, indeed, the devotion to truth in that age, as in others, required an heroic heart. Copernicus kept back the publication of his “ De Revolutionibus Orbium Cœlestium” for thirty-six years, and received a copy of it only on his death-bed. Galileo tasted the sweets of the Inquisition. Tycho Brahe was exiled. And Kepler himself was persecuted all his life, hounded from city to city. And yet the sixteenth century will ever be memorable in the history of the human mind. The breaking down of external authority, the uprise of the spirit of inquiry, of skepticism, and the splendid scientific conquests that came in consequence, inaugurated a mighty movement which separates the present promises of mankind from all past periods by an interval so vast as to make it not merely a great historical development, but the very birth of humanity. While Tycho Brahe, at the age of fifty-four, was making his memorable observations at Prague, Kepler, at the age of thirty, was applying his fiery mind to the determination of the orbit of Mars, and Galileo, at thirty-six, was bringing his telescope to the revelation of new celestial intervals and orbs. Within the succeeding century Huygens made the application of the pendulum to clocks; Napier invented Logarithms; Descartes and Galileo created the analysis of curves, and the science of Dynamics ; Leibnitz brought the Differential Calculus; Newton decomposed a ray of light, and synthesized Kepler’s Laws into the theory of Universal Gravitation.

Into this age, when the Old and New met face to face, came the questioning and quenchless spirit of Kepler. Born into an age of adventure, this new Prometheus, this heaven-scaler, matched it with an audacity to lift it to new reaches of realization.

A singular naïveté, too, marked this august soul. He has the frankness of Montaigne or Jean Jacques. He used to accuse himself of gabbling in mathematics,— “in re mathematica loquax,”— and claimed to speak with German freedom,— “ scripsi hœc, homo Germanicus, more el libertate Germanica.” He marries far and near, brings planetary eclipses into conjunction with pecuniary penumbræ, and his treatise on the perturbations of Mars reveals equal perturbations in his domestic economy. It may be to this candor, this gemüth, that we are to ascribe the powerful personal magnetism he exercises in common with Rousseau, Rabelais, and other rich and ingenuous natures. Who would be otherwise than frank, when frankness has this power to captivate ? The excess of this influence appears in the warmth betrayed by writers over their favorite. The coolheaded Delambre, in his “ Histoire de 1’Astronomie,” speaks of Kepler with the heat of a pamphleteer, and cannot repress a frequent sneer at his contemporary, Galileo. We know the splendor of the Newtonian synthesis; yet we do not find ourselves affected by Newton's character or discoveries. He touches us with the passionless love of a star.

Kepler puts the same naïveté into his speculative activity, with a subtile anatomy laying bare the metaphysique of his science. It was his habit to illumine his discoveries with an exhibition of the path that led to them, regarding the method as equally important with the result,— a principle that has acquired canonical authority in modern scientific research. “ In what follows,” writes he, introducing a long string of hypotheses, the fallacy of which he had already discovered, “ let the reader pardon my credulity, whilst working out all these matters by my own ingenuity. For it is my opinion that the occasions by which men have acquired a knowledge of celestial phenomena are not less admirable than the discoveries themselves.” His tentatives, failures, leadings, his glimpses and his glooms, those aberrations and guesses and gropings generally so scrupulously concealed, he exposes them all. From the first flashing of a discovery, through years of tireless toil, to when the glorious apparition emerges full-orbed and resplendent, we follow him, becoming party to the process, and sharing the ejaculations of exultation that leap to his lips. Seventeen years were required for the discovery of the harmonic law, that the squares of the times of the planetary revolutions are proportional to the cubes of their mean distances ; and no tragedy ever equalled in affecting intensity the account he has written of those Promethean years. What rays does he let into the subtile paths where the spirit travels in its interrogations of Nature ! We should say there was more of what there is of essential in metaphysics, more of the structural action of the human mind, in his books, than in the concerted introspection of all the psychologists. One sees very well that a new astronomy was predicted in the build of that sky-confronting mind; for harmonic ratios, laws, and rhymes played in his spheral soul, galaxies and gravitations stretched deeper within, and systems climbed their flaming ecliptic.

The highest problem of Science is the problem of Method. Hitherto man has worked on Nature only piecemeal. The understanding and the logic-faculty are allowed to usurp the rational and creative powers. One would say that scientists systematically shut themselves out of three-fourths of their minds, and the English have been insane on Induction these two hundred years. This unholy divorce has, as it always must do, brought poverty and impotence into the sciences, many of which stand apart, stand haggard and hostile, accumulations of incoherent facts, inhospitable, dead.

It is when contemplated in its historic bearings, as an education of the faculties of man, that the emphasis that has been placed on special scientific methods discloses its significance. The speculative synthesis of Greek and Alexandrine Science was a superb training in Deduction, — in the descent from consciousness to Nature. Abstracted from its relations with reality, the scholasticism of the Middle Ages pushed Deduction to mania and moonshine. Then it was, that, in the sixteenth and seventeenth centuries, the Occidental mind, astir under the oceanic movements of the modern, arose to break the spell of scholasticism that had fettered and frozen the intellect of man. An all-invading spirit of inquiry, analysis, skepticism, became rife. An unappeasable hunger for facts, facts, facts, took possession of the general intellect. It was felt that abstraction was disease, was death,— that speculation had to be vitalized and enriched from experience and experiment. This tendency was inevitable and sublime, no doubt. But it remains for modern times to emulate Nature and carry on analysis and synthesis at once. A great discovery is the birth of the whole soul in its creative activity. Induction becomes fruitful only when married to Deduction. It is those luminous intuitions that light along the path of discovery that give the eye and animus to generalization. Science must be open to influx and new beneficent affections and powers, and so add fleet wings to the mind in its exploration of Nature.

In Kepler was the perfect realization of the highest mission of Method. Powerfully deductive in the structure of his intellect, nourished on the divine bread of Plato and the Mystics, he yet united to these a Baconian breadth of practical power. Years before the publication of the “ Novum Organum,” he gave, in his “Commentaries on the Motions of Mars,” a specimen of the logic of Induction whose circular sweep has never been matched. Prolific in the generation of hypotheses, he was yet remorseless in bringing them to the test of experiment. “ Hypotheses which are not founded in Nature please me not,” wrote he,— as Newton inscribed “Hypotheses non fingo” on the “ Principia.” Surely never was such heroic self-denial. Centurial vigils of baffling calculations—(remember, there was then little Algebra, and neither Calculus nor Logarithms) — were sacrificed without a regret except for the time expended, his tireless intellect pressing on to new heights of effort. His first work, the “ Mysterium Cosmographicum,” is the record ot a splendid blunder that cost him five years’ toil, and he spent ten years of fruitless and baffled effort in the deduction of the laws of areas and orbital ellipticity.

But this audacious diviner knew well the use of Hypothesis, and he applied it as an instrument of investigation as it had never been applied before. The vast significance of Hypothesis in the theory of Scientific Method has never been recognized. It would be a good piece of psychology to explore the principles of this subtile mental power, and might go far to give us a philosophy of Anticipation. The men of facts, men of the understanding, observers,—as we might suppose,—universally show a disposition to shun theorizing, as opposed to the exactness of demonstrative science. And yet it is quite certain, that, in proportion as one rises to a more liberal apprehension, the immense provisional power of speculative ideas becomes apparent. Laplace asserted that no great discovery was ever made without a great guess; and long before, Plato had intimated of these “ sacred suspicions of truth,” that descend dawnlike on the mind, sublime premonitions of beautiful gates of laws. It is these launching tentatives which bring phenomena to interior and metaphysical tests and bear the mind swift-winged to Nature. Of course, there are various kinds of conjecture, and its value will depend on the brain from which it departs. But a powerful spirit will justify Hypothesis by the high functions to which he puts it. His guesses are not for nothing. Many and long processes go to them.—The inexhaustible fertility displayed by Kepler is a psychologic marvel. He had that subtile chemistry that turns even failures to account, consumes them in its flaming ascent to new reaches. After years of labor on his theory of Mars, he found it failed in application to latitudes and longitudes “ out of opposition.” Remorselessly he let his hypothesis go, and drew from his failure an important inference, the first step towards emancipation from the ancient prejudice of uniform, circular motion.

Such a genius for Analogy the world never before saw. The perception of similitude, of correspondence, shot perpetual and prophetic in this man’s glances. To him had been opened the subtile secret, key to Nature, that Man and the Universe are built after one pattern, and he had faith to believe that the laws of his mind would unlock the phenomena of the world.

The law of Analogy flows from the inherent harmonies of Nature. Of this wise men have ever been intuitive. The eldest Scriptures express it. It is in the Zend-Avesta, primal Japhetic utterance. It vivified that subtile Egyptian symbolism. The early Greeks and the Mystics of Alexandria knew it. Jamblicus reports of Pythagoras, that “ he did not procure for himself a thing of this kind through instruments or the voice, but, by employing a certain inevitable divinity, and which it is difficult to apprehend, he extended his ears and fixed his intellect in the sublime symphonies of the world, — he alone hearing and understanding, as it appears, the universal harmony and consonance of the spheres and the stars that are moved through them, and which produce a fuller and more intense melody than anything effected by mortal sounds.”

From the sublime intuitions of the harmonies of Nature and the unity of the Universe unfold the bright doctrines of Series and Degrees, of Correspondence, of Similitude. On these thoughts all wise spirits have fed. Indeed, you can hardly say they were ever absent. They are of those flammg thoughts the soul projects, splendid prophecies that become the light of all our science and all our day. Plato formulated these laws. Two thousand years after him, the cosmic brain of Swedenborg traced their working throughout the universal economies of matter and spirit, and Fourier endeavored to translate them into axioms of a new social organization.

These doctrines were ever present to the mind of Kepler; and to what fruitful account he turned Analogy as a means of inductive speculation his wonderful anatomy of his discoveries reveals. He fed on the harmonies of the universe. He has it, that “ harmony is the perfection of relations.” The work of his mature intellect was the “Harmonices Mundi,” (Harmonies of the World,) in which many of the sublime leadings of Modern Science, as the Correlation of Sounds and Colors, the Significance of Musical Chords, the Undulatory Theory, etc., are prefigured. We must account him one of the chief of those prophetic spirits who, by attempting to give phenomena a necessary root in ideas, have breathed into Science a living soul. The new Transcendental Anatomy,—the doctrine of Homologies,— the Embryologic scheme, revealing that all animate forms are developed after one archetype,—the splendid Nebular guess of Laplace,— the thought of the Metamorphosis of Plants,—the attempts at profounder explanations of Light and Colors,— the rising transcendentalism of Chemistry,— the magnificent intuition of Correspondence, showing a grand unity of design in the nodes of shells, the phyllotaxism of plants, and the serialization of planets,— are all signs of the presence of a spirit that is to usher in a new dispensation of Science, fraught with divinest messages to the head and heart of man.

Kepler regarded Analogy as the soul of Science, and he has made it an instrument of prophecy and power. Thus, he inferred from Analogy that the sun turned on its axis, long before Galileo was able to direct his telescope to the solar spots and so determine this rotation as an actual fact. He anticipated a planet between Mars and Jupiter too small to be seen; and his inference that the obliquity of the ecliptic was decreasing, but would, after a long-continued diminution, stop, and then increase again, afterwards acquired the sanction of demonstration. A like instance of anticipation is afforded in the beautiful experiment of the freely-suspended ball revolving in an ellipse under the combined influence of the central and tangential forces, which Jeremiah Horrocks devised, when pursuing Kepler’s theory of planetary motion,— his intuition being, that the motions of the spheres might be represented by terrestrial movements. We may mention the observation which the ill-starred Horrocks makes, in a letter,5 on the occasion of this experiment, as one of the sublimities of Science: — “It appears to me, however, that I have fallen upon the true theory, and that it admits of being illustrated by natural movements on the surface of the earth ; for Nature everywhere acts according to a uniform plan, and the harmony of creation is such that small things constitute a faithful type of greater things.” Another instance is afforded in the grand intuition of Oken, who, when rambling in the Hartz Mountains, lit upon the skull of a deer, and saw that the cranium was but an expansion of vertebrae, and that the vertebra is the theoretical archetype of the entire osseous frame work,—the foundation of modern Osteology. And still another is the well-known instance of the change in polarization predicted by Fresnel from the mere interpretation of an algebraic symbol. This prophetic insight is very sublime, and opens up new spaces in man.

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 Cœlestis, tradita Commentarüs de Motibus Stellæ Martis: Ex Observationibus G. V. Tychonis Brahe.” Folio. Prague: 1609. This he published in his thirtyeighth 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.6 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.

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 harmonies, — 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 he 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 as 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!

41 Who can be sure to find its true degree,
Magister magnus in igne shall he be.”

Antique and intuitive nations — Indians, Egyptians, Greeks—Sought a solution of this august mystery in the doctrines of Transmigration and Anamnesis or Reminiscence. Nothing is whereto man is not kin. He knows all worlds and histories by virtue of having himself travelled the mystic spiral descent. Awaking through memory, the processes of his mind repeat the processes of the visible Kosmos. His unfolding is a hymn of the origination of the world.

Nature and man having sprung from the same spiritual source, a perfect agreement subsists between the phenomena of the world and man’s mentality. This is necessary to the very conception of Science. If the laws of reason did not exist in Nature, we should vainly attempt to force them upon her : if the laws of Nature did not exist in our reason, we should not be able to comprehend them.7 There is a saying reported of Zoroaster, and, coming from the deeps of fifty centuries, still authentic and intelligible, that “ the congruities of material forms to the laws of the soul are divine allurements.” Ever welcome is the perception of this truth,—as the sublime audacity of Paracelsus, that “those who would understand the course of the heavens above must first of all recognize the heaven in man ”; and the affirmation, that “ the laws of Nature are the same as the thoughts within us : the laws of motion are such as are required by our understanding.” It remains to say that Kepler, too, had intuition of this lofty thought. At the conclusion of his early work, “ The Prodromus Dissertationum Cosmographiearum,” he wrote,— “ As men enjoy dainties at the dessert, so do wise souls gain a taste for heavenly things when they ascend from their college to the universe and there look around them. Great Artist of the World! I look with wonder on the works of Thy hands, constructed after five regular forms, and in the midst the sun, the dispenser of light and life. I see the moon and stars strewn over the infinite field of space. Father of the World ! what moved Thee thus to exalt a poor, weak little creature of earth so high that he stands in light a far-ruling king, almost a god?—for he thinks Thy thoughts after Thee.”

It is impossible not to feel freer at the accession of so much power as these laws bring us. They carry farther on the bounds of humanity. The stars are the eternal monitions of spirituality. Who can estimate how much man’s thoughts have been colored by these golden kindred ? It seems as though it were but required to show man space, — space, space, space, — there is that in him will fill and pass it. There is that in the celestial prodigies — in gulfs of Time and Space — that seems to mate the greed of the soul. There is that greed in the soul to pass through worlds and ages,— through growths, griefs, desires, processes, spheres, — to travel the endless highways,— to pass and resume again. O Heavens, you are but a splendid fable of the elder mind ! Centripetal and centrifugal are in man, too, and primarily; and an aspiring soul will ascend into the sweeps and circles, and pass swift and devouring through baffling intervals and steep-down strata of galaxies and stars.

The thought that overarches the centuries with firmamental sweep is the thought of the Ensemble. To this all has led along,—but the disclosures of Astronomy especially. The discovery of the earth’s revolution, at once transporting the stars to distances outside of all telluric connection, broke the old spell, and replaced the petty provincialism of the earth as the All-Centre by the vast, sublime conception of the Universe. Laplace has pointed this out, showing how to the fantastic and enervating notion of a universe arranged for man has succeeded the sound and vivifying thought of man discovering, by a positive exercise of his intelligence, the general laws of the world, so as to be able to modify them for his own good, within certain limits. Dawning prophetic on modern times, the thought of the Ensemble holds the seeds of new humanitary growths. This is the vast similitude that binds together the ages,—that balances creeds, colors, eras. Through Nature, man, forms, spirit, the eternal conspiracy works and weaves. This is the water of spirituality. All is bound up in the Divine Scheme. The Divine Scheme encloses all.

  1. Joannis Kepleri Astronomi Opera Omnia. Edidit CH. FRISCH.
  2. Epistolœ ad Joannem Keplerum scriptœ. MICHAEL GOTTLIEB HANSCHIUS. Lipsiæ, 1718.
  3. Johann Keppler's Leben und Wirken: nach neuerlich aufgefundenen Manuscripten bearbeitet. Stuttgart, 1813.
  4. Harmonices Mundi.
  5. Correspondence, 1637.
  6. ROBERT SMALL : Astronomical Discoveries of Kepler.
  7. OERSTED: Soul in Nature.