This discovery, as he considered it, harmonized in a very rude way with the measures of the planetary orbits given by Copernicus; but Kepler was so enamoured with it, that he ascribed the differences to errors of observation, and declared that he would not renounce the glory of having made it for the whole Electorate of Saxony.

In his attempt to discover the relation between the periodic times of the planets and their distances from the sun, he was not more successful; but as this relation had a real existence, he made some slight approach to its determination. These extraordinary researches, which indicate the wildness and irregularity of Kepler's genius, were published in 1596, in a work ent.i.tled, "Prodromus of Cosmographical Dissertations; containing the cosmographical mystery respecting the admirable proportion of the celestial orbits, and the genuine and real causes of the number, magnitude, and periods of the planets demonstrated by the five regular geometrical solids."

Notwithstanding the speculative character of this volume, it obtained for its author a high name among astronomers. Galileo and Tycho, whose opinions of it he requested, spoke of it with some commendation. The former praised the ingenuity and good faith which it displayed; and Tycho, though he requested him to try to adapt something of the same nature to the Tychonic system, saw the speculative character of his mind, and advised him "to lay a solid foundation for his views by actual observation, and then, by ascending from these, to strive to reach the causes of things."

In 1592, before Kepler had quitted Tubingen, he was on the eve of entering into the married state. Though the foolish scheme was fortunately broken off, yet he resumed it again in 1596, when he paid his addresses to Barbara Millar of Muleckh, who was a widow for the second time, though only twenty-three years of age. Her parents, however, would not consent to the match till Kepler proved his n.o.bility; and, owing to the delay which arose from this circ.u.mstance, the marriage did not take place till 1597. The income which Kepler derived from his professorship was very small, and as his wife's fortune turned out much less than he had been led to expect, he not only was annoyed with pecuniary difficulties, but was involved in disputes with his wife's relations. These evils were greatly increased by the religious troubles which took place in Styria. The Catholics at Gratz rose against the Protestants, and threatened to expell them from the city. Kepler, who openly professed the Protestant religion, saw the risks to which he was exposed, and retired with his wife into Hungary.

Here he continued nearly a year, during which he composed and transmitted to his friend Zehentmaier, at Tubingen, several small treatises, "On the Magnet," "On the cause of the Obliquity of the Ecliptic," and "On the Divine Wisdom, as shewn in the Creation"--all of which seem to have been lost. In 1599, Kepler was recalled to Gratz by the States of Styria, and resumed his professorship; but the city was still divided into two factions, and Kepler, who was a lover of peace, found his situation very uncomfortable. Having learned from Tycho that he had been able to determine more accurately than had been done the eccentricities of the orbits of the planets, Kepler was anxious to avail himself of these observations, and set out on a visit to Tycho at Prague, where he arrived in January 1600. Tycho received him with great kindness, notwithstanding the part which he had taken against him along with Raimar, and he spent three or four months with him at Benach. It was then arranged that Kepler should be appointed Tycho's a.s.sistant in the observatory, with a salary of 100 florins, provided the States of Styria should, on the Emperor's application, allow him to be absent for two years and retain his salary. Kepler had returned to Gratz before this arrangement was completed, and new troubles having broke out in that city, he resigned his professorship. Dreading lest this step would frustrate his scheme of joining Tycho, he resolved to ask the patronage of the Duke of Wirtemberg for the professorship of medicine at Tubingen; and with this view he corresponded with Moestlin and his other friends in that University. When Tycho heard of this plan, he pressed him to abandon it, and promised his best exertions to procure a permanent situation for him from the Emperor.

Encouraged by these promises, Kepler and his wife set off for Prague, but he was unfortunately attacked on the road with a quartan ague, which lasted seven months; and having exhausted the little money which he had along with him, he was obliged to apply to Tycho for a supply. After his arrival at Prague he was supported entirely by the bounty of his friend, and he endeavoured to make some return for this kindness by attacking in a controversial pamphlet two of the scientific opponents of Tycho.

Kepler's total dependence on the generosity of his friend had made him suspicious of his sincerity. He imagined that Tycho had not freely communicated to him all his observations, and that he had not been sufficiently liberal in supplying his wife with money in his absence.

While absent a second time from Prague, and influenced by these feelings, he addressed a violent letter to Tycho, filled with reproaches. On the plea of being occupied with his daughter's marriage, Tycho requested Ericksen, one of his a.s.sistants, to reply to Kepler's letter; and he did this with so much effect, that Kepler saw his mistake, and in the n.o.blest and most generous manner supplicated the forgiveness of his friend. Tycho exhibited the same good feeling; and the kindness of Hoffman, President of the States of Styria, completed the reconciliation of the two astronomers.

On his return to Prague in 1601, he was presented by Tycho to the Emperor, who conferred upon him the t.i.tle of Imperial Mathematician, on the condition that he would a.s.sist Tycho in his calculations. This connexion was peculiarly valuable to Kepler, as the observations of his colleague were the only ones made in the world which could enable him to carry on his own theoretical inquiries. These two astronomers now undertook to compute, from Tycho's observations, a new set of astronomical tables, to be called the Rudolphine Tables, in honour of the Emperor. This scheme flattered the vanity of their master, and he pledged himself to pay all the expenses of the work. Longomonta.n.u.s, Tycho's princ.i.p.al a.s.sistant, took upon himself the labour of arranging and discussing the observations on the stars, while Kepler devoted himself to the more congenial task of examining those on the planet Mars, with which Tycho was at that time particularly occupied. The appointment of Longomonta.n.u.s to a professorship in Denmark, and the death of Tycho in October 1601, put a stop to these important schemes.

Kepler succeeded Tycho as princ.i.p.al mathematician to the Emperor, and was provided with a handsome salary, which was partly charged on the imperial treasury, and partly on the States of Silesia, and the first instalment of which was to be paid in March 1602. The generosity of the Emperor did not fail to excite the jealousy of ignorant individuals, who were not aware of the value of science to the state; but the increasing fame of Kepler, and the valuable works which he published, soon silenced their opposition.

In September 1604, astronomers were surprised with the appearance of a new star in the foot of Serpentarius. It was not seen before the 29th of September, and Moestlin informs us that, on account of clouds, he did not obtain a good view of it till the 6th of October. Like that of 1572,[45] it at first surpa.s.sed Jupiter in brightness, and rivalled even Venus, but it afterwards became as small as Regulus, and as dull as Saturn, and disappeared at the end of a few months. It constantly changed its colour, and was at first tawny, then yellow, then purple and red, and often white at great alt.i.tudes. It had no parallax, and therefore was a fixed star. Kepler wrote a short account of this remarkable body, and maintained its superiority to that of 1572, as this last came in an ordinary year, while the other appeared in the year of the _fiery trigon_, or that in which Saturn, Jupiter, and Mars, are in the three fiery signs, Aries, Leo, and Sagittarius, an event which occurs only every 800 years. After discussing a great variety of topics, but little connected with his subject, and in a style of absurd jocularity, he attacks the opinions of the Epicureans, that the star was a fortuitous concourse of atoms, in the following remarkable paragraph, which is a good specimen of the work:--"When I was a youth with plenty of idle time on my hands, I was much taken with the vanity, of which some grown men are not ashamed, of making anagrams by transposing the letters of my name, written in Latin. Out of _Joannes Keplerus_ came _Serpens in Akuleo_ (a serpent in his sting); but not being satisfied with the meaning of these words, and being unable to make another, I trusted the thing to chance, and taking out of a pack of playing cards as many as there were letters in the name, I wrote one upon each, and then began to shuffle them, and at each shuffle to read them in the order they came, to see if any meaning came of it. Now, may all the Epicurean G.o.ds and G.o.ddesses confound this same chance, which, although I have spent a good deal of time over it, never shewed me anything like sense even from a distance. So I gave up my cards to the Epicurean eternity, to be carried away into infinity; and, it is said, they are still flying about there in the utmost confusion among the atoms, and have never yet come to any meaning. I will tell those disputants, my opponents, not my own opinion, but my wife's. Yesterday, when weary with writing, and my mind quite dusty with considering these atoms, I was called to supper, and a salad I had asked for was set before me. 'It seems then,' said I, aloud, 'that if pewter dishes, leaves of lettuce, grains of salt, drops of water, vinegar, and oil, and slices of egg, had been flying about in the air from all eternity, it might at last happen by chance that there would come a salad.' 'Yes,' says my wife, 'but not so nice and well dressed as this of mine is.'"

[45] See the Life of Tycho, page 137.

CHAPTER II.

_Kepler's Pecuniary Embarra.s.sments--His Inquiries respecting the Law of Refraction--His Supplement to Vitellio--His Researches on Vision--His Treatise on Dioptrics--His Commentaries on Mars--He discovers that the orbit of Mars is an Ellipse, with the Sun in one focus--And extends this discovery to all the other Planets--He establishes the two first laws of Physical Astronomy--His Family Distresses--Death of his Wife--He is appointed Professor of Mathematics at Linz--His Method of Choosing a Second Wife--Her Character, as given by Himself--Origin of his Treatise on Gauging--He goes to Ratisbon to give his Opinion to the Diet on the change of Style--He refuses the Mathematical Chair at Bologna._

Although Kepler now filled one of the most honourable situations to which a philosopher could aspire, and possessed a large salary fitted to supply his most reasonable wants, yet, as the imperial treasury was drained by the demands of an expensive war, his salary was always in arrear. Owing to this cause he was constantly involved in pecuniary difficulties, and, as he himself described his situation, he was perpetually begging his bread from the Emperor at Prague. His increasing family rendered the want of money still more distressing, and he was driven to the painful alternative of drawing his income from casting nativities. From the same cause he was obliged to abandon his plan of publishing the Rudolphine Tables, and to devote himself to works of a less expensive kind, and which were more likely to yield some pecuniary advantages.

In spite of these embarra.s.sments, and the occupation of his time in the practice of astrology, Kepler found leisure for his favourite pursuits.

No adverse circ.u.mstances were capable of extinguishing his scientific ardour, and whenever he directed his vigorous mind to the investigation of phenomena, he never failed to obtain interesting and original results. Since the death of Tycho, his attention had been much occupied with the subject of refraction and vision; and, in 1606, he published the result of his researches in a work, ent.i.tled "A Supplement to Vitellio, in which the optical part of astronomy is treated, but chiefly on the artificial observation and estimation of diameters, and of the eclipses of the Sun and Moon." Astronomers had long been perplexed with the refraction of the atmosphere, and so little was known of the general subject, as well as of this branch of it, that Tycho believed the refraction of the atmosphere to cease at 45 of alt.i.tude.

Even at the beginning of the second century, Claudius Ptolemy of Alexandria had unravelled its princ.i.p.al mysteries, and had given in his Optics a theory of astronomical refraction more complete than that of any astronomer before the time of Ca.s.sini;[46] but the MSS. had unfortunately been mislaid, and Alhazen and Vitellio and Kepler were obliged to take up the subject from its commencement. Ptolemy had not only determined that the refraction of the atmosphere had gradually increased from the zenith to the horizon, but he had measured with singular accuracy the angles of refraction for water and gla.s.s, from a perpendicular incidence to a horizontal one.

[46] Ca.s.sini was born in 1625, and died in 1712.

Kepler treated this branch of science in his own peculiar way, "hunting down," as he expressed it, every hypothesis which his fertile imagination had successively presented to him. In his various attempts to discover the law of refraction, or a measure of it, as varying with the density of the body and the angle of incidence of the light, he was nearer the goal, in his first speculation, than in any of the rest; and he seems to have failed in consequence of his not separating the question as it related to density from the question as it related to incidence. "I did not leave untried," says he, "whether, by a.s.suming a horizontal refraction according to the density of the medium, the rest would correspond to the sines of the distances from a vertical direction, but calculation proved that it was not so: and, indeed, there was no occasion to have tried it, for thus the _refraction would increase according to the same law in all mediums, which is contradicted by experiment_."

Although completely foiled in his search after the law of refraction, which was subsequently discovered by Willebrord Snell, and sometime afterwards by James Gregory, he was, singularly successful in his inquiries respecting vision. Regarding the eye as a.n.a.logous in its structure with the camera obscura of Baptista Porta, he discovered that the images of external objects were painted in an inverted position on the retina, by the union of the pencils of rays which issued from every point of the object. He ascribed an erect vision to an operation of the mind, by which it traces the rays back to the pupil, where they cross one another, and thus refers the lower parts of the image to the higher parts of the object. He also explained the cause of long-sighted and short-sighted vision, and shewed how convex and concave lenses enabled those who possessed these peculiarities of vision to see distinctly, by accurately converging the pencils of rays to a focus on the retina.

Kepler likewise observed the power of accommodating the eye to different distances, and he ascribed it to the contraction of the ciliary processes, which drew the sides of the eyeball towards the crystalline lens, and thus elongated the eye so as to produce an adjustment of it for near objects. Kepler wisely declined to inquire into the way in which the mind perceives the images painted on the retina, and he blames Vitellio for attempting to determine a question which he considered as not belonging to optics.

The work of Kepler, now under consideration, contains the method of calculating eclipses which is now in use at the present day.

The only other optical treatise written by Kepler, was his _Dioptrics_, with an appendix on the use of optics in philosophy. This admirable work, which laid the foundation of the science, was published at Augsburg in 1611, and reprinted at London in 1653. Although Maurolycus had made some slight progress in studying the pa.s.sage of light through different media, yet it is to Kepler that we owe the methods of tracing the progress of rays through transparent bodies with convex and concave surfaces, and of determining the foci of lenses, and of the relative positions of the images which they form, and the objects from which the rays proceed. He was thus led to explain the _rationale_ of the telescope, and to invent the astronomical telescope, which consists of two convex lenses, by which objects are seen inverted. Kepler also discovered the important fact, that spherical surfaces were not capable of converging rays to a single focus, and he conjectured, what Descartes afterwards proved, that this property might be possessed by lenses having the figure of some of the sections of the cone. The total reflection of light at the second surface of bodies was likewise studied by Kepler, and he determined that the total reflection commenced when the angle of incidence was equal to the angle of refraction, which corresponded to an incidence of 90.

Two years before the publication of his Dioptrics, viz. in 1609, Kepler had given to the world his great work, ent.i.tled "The New Astronomy, or Commentaries on the Motions of Mars." The discoveries which this volume records form the basis of physical astronomy. The inquiries by which he was led to them began in that memorable year 1601, when he became the colleague or a.s.sistant of Tycho. The powers of original genius were then for the first time a.s.sociated with inventive skill and patient observation; and though the astronomical data provided by Tycho were sure of finding their application in some future age, yet without them Kepler's speculations would have been vain, and the laws which they enabled him to determine would have adorned the history of another century. Having tried in vain to represent the motion of Mars by an uniform motion in a circular orbit, and by the cycles and epicycles with which Copernicus had endeavoured to explain the planetary inequalities, Kepler was led, after many fruitless speculations,[47] to suppose the orbit of the planet to be oval; and, from his knowledge of the conic sections, he afterwards determined it to be an ellipse, with the sun placed in one of its foci. He then ascertained the dimensions of the orbit; and, by a comparison of the times employed by the planet to complete a whole revolution or any part of one, he discovered that the time in which Mars describes any arches of his elliptic orbit, were always to one another as the areas contained by lines drawn from the focus or the centre of the sun to the extremities of the respective arches; or, in other words, that the radius vector, or the line joining the Sun and Mars described equal areas in equal times. By examining the inequalities of the other planets he found that they all moved in elliptic orbits, and that the radius vector of each described areas proportional to the times. These two great results are known by the name of the first and second laws of Kepler. The third law, or that which relates to the connexion between the periodic times and the distances of the planets, was not discovered till a later period of his life.

[47] An interesting account of the steps by which Kepler proceeded will be found in Mr Drinkwater Bethune's admirable Life of Kepler, in the Library of Useful Knowledge.

When Kepler presented to Rudolph the volume which contained these fine discoveries, he reminded him jocularly of his requiring the sinews of war to make similar attacks upon the other planets. The Emperor, however, had more formidable enemies than Jupiter and Saturn, and from the treasury, which war had exhausted, he found it difficult to supply the wants of science. While Kepler was thus involved in the miseries of poverty, misfortunes of every kind filled up the cup of his adversity.

His wife, who had long been the victim of low spirits, was seized, towards the end of 1610, with fever, epilepsy, and phrenitis, and before she had completely recovered, all his three children were simultaneously attacked with the smallpox. His favourite son fell a victim to this malady, and at the same time Prague was partially occupied by the troops of Leopold. The part of the city where Kepler resided was hara.s.sed by the Bohemian levies, and, to crown this list of evils, the Austrian troops introduced the plague into the city.

Sometime afterwards Kepler set out for Austria with the view of obtaining the professorship of mathematics at Linz, which was now vacant; but, upon his return in June, he found his wife in a decline, brought on by grief for the loss of her son, and she was sometime afterwards seized with an infectious fever, of which she died.

The Emperor Rudolph was unwilling to allow Kepler to quit Prague. He encouraged him with hopes that the arrears of his salary would be paid from Saxony; but these hopes were fallacious, and it was not till the death of Rudolph, in 1612, that Kepler was freed from these distressing embarra.s.sments.

On the accession of Mathias, Rudolph's brother, Kepler was re-appointed imperial mathematician, and was allowed to accept the professorship at Linz. His family now consisted of two children--a daughter, Susannah, born in 1602, and a son, Louis, born in 1607. His own time was so completely occupied by his new professorial duties, as well as by his private studies, that he found it necessary to seek another parent for his children. For this purpose, he gave a commission to his friends to look out for him a suitable wife, and, in a long and jocular letter to Baron Strahlendorf, he has given an amusing account of the different negotiations which preceded his marriage. The substance of this letter is so well given by Mr Drinkwater Bethune, that we shall follow his account of it.

The first of the eleven ladies among whom his inclinations wavered, "was a widow, an intimate friend of his first wife; and who, on many accounts, appeared a most eligible match. At first," says Kepler, "she seemed favourably inclined to the proposal; it is certain that she took time to consider it, but at last she very quietly excused herself." It must have been from a recollection of this lady's good qualities, that Kepler was induced to make his offer; for we learn rather unexpectedly, after being informed of her decision, that when he soon afterwards paid his respects to her, it was the first time that he had seen her during the last six years; and he found, to his great relief, that "there was no single pleasing part about her." The truth seems to be, that he was nettled by her answer, and he is at greater pains than appears necessary, considering this last discovery, to determine why she would not accept his offered hand. Among other reasons, he suggested her children, among whom were two marriageable daughters; and it is diverting afterwards to find them also in the catalogue, which Kepler appeared to be making, of all his female acquaintance.... Of the other ladies, one was too old, another in bad health, another too proud of her birth and quarterings, a fourth had learned nothing but shewy accomplishments, "not at all suitable to the sort of life she would have to lead with me," another grew impatient, and married a more decided admirer, whilst he was hesitating. "The mischief," says he, "in all these attachments was, that whilst I was delaying, comparing and balancing conflicting reasons, every day saw me inflamed with a new pa.s.sion." By the time he reached the 8th, he found his match in this respect. "Fortune at length has avenged herself on my doubtful inclinations. At first she was quite complying, and her friends also; presently, whether she did or did not consent, not only I, but she herself did not know. After the lapse of a few days came a renewed promise, which, however, had to be confirmed a third time; and four days after that, she again repeated her confirmation, and begged to be excused from it. Upon this I gave her up, and this time all my counsellors were of one opinion." This was the longest courtship in the list, having lasted three whole months; and, quite disheartened by its bad success, Kepler's next attempt was of a more timid complexion. His advances to No. 9 were made by confiding to her the whole story of his recent disappointment, prudently determining to be guided in his behaviour, by observing whether the treatment he had experienced met with a proper degree of sympathy. Apparently the experiment did not succeed; and, almost reduced to despair, Kepler betook himself to the advice of a friend, who had for some time past complained that she was not consulted in this difficult negotiation. When she produced No. 10, and the first visit was paid, the report upon her was as follows:--"She has, undoubtedly, a good fortune, is of good family, and of economical habits: but her physiognomy is most horribly ugly; she would be stared at in the streets, not to mention the striking disproportion in our figures. I am lank, lean, and spare; she short and thick: in a family notorious for fulness, she is considered superfluously fat." The only objection to No. 11 seems to have been her excessive youth; and when this treaty was broken off on that account, Kepler turned his back upon all his advisers, and chose for himself one who had figured as No. 5 in the list, to whom he professes to have felt attached throughout, but from whom the representations of his friends had hitherto detained him, probably on account of her humble station.

The following is Kepler's summary of her character:--"Her name is Susannah, the daughter of John Reuthinger and Barbara, citizens of the town of Eferdingen. The father was by trade a cabinetmaker, but both her parents are dead. She has received an education well worth the largest dowry, by favour of the Lady of Stahrenberg, the strictness of whose household is famous throughout the province. Her person and manners are suitable to mine--no pride, no extravagance. She can bear to work; she has a tolerable knowledge how to manage a family; middle-aged, and of a disposition and capability to acquire what she still wants. Her I shall marry, by favour of the n.o.ble Baron of Stahrenberg, at 12 o'clock on the 30th of next October, with all Eferdingen a.s.sembled to meet us, and we shall eat the marriage dinner at Maurice's at the Golden Lion."[48]

[48] Life of Kepler, chap. vi.

Kepler's marriage seems to have taken place at the time here mentioned; for, in his book on gauging, published at Linz in 1615, he informs us that he took home his new wife in November, on which occasion he found it necessary to stock his cellar with a few casks of wine. When the wine-merchant came to measure the casks, Kepler objected to his method, as he made no allowance for the different sizes of the bulging parts of the cask. From this accident, Kepler was led to study the subject of gauging, and to write the book which we have mentioned, and which contains the earliest specimens of the modern a.n.a.lysis.

About this period, Kepler was summoned to the Diet at Ratisbon, to give his opinion on the reformation of the kalendar, and he published a short essay on the subject; but though the Government did not scruple to avail themselves of his services, yet his pension was allowed to fall in arrear, and, in order to support his family, he was obliged to publish an Almanac, suited to the taste of the age. "In order," says he, "to defray the expense of the Ephemeris for two years,[49] I have been obliged to compose _a vile prophesying Almanac, which is scarcely more respectable than begging_, unless from its saving the Emperor's credit, who abandons me entirely, and would suffer me to perish with hunger."

[49] These Ephemerides, from 1617 to 1620, were published at Linz in 1616. The one for 1620 was dedicated to Baron Napier of Merchiston.

Although Kepler's residence at Linz was rendered uncomfortable by the Roman Catholics, who had excommunicated him on account of his refusing to subscribe to some opinions respecting the ubiquity of our Saviour, or, as others maintain, on account of some opinions which he had expressed respecting transubstantiation, yet he refused, in 1617, to accept of an invitation to fill the mathematical chair at Bologna. The prospect of his fortune being bettered by such a change could not reconcile him to live in a country where his freedom of speech and manners might expose him to suspicion; and he accordingly declined, in the most respectful manner, the offer which was made him.

CHAPTER III.

_Kepler's continued Embarra.s.sments--Death of Mathias--Liberality of Ferdinand--Kepler's "Harmonies of the World"--The Epitome of the Copernican Astronomy--It is prohibited by the Inquisition--Sir Henry Wotton, the British Amba.s.sador, invites Kepler to England--He declines the Invitation--Neglect of Genius by the English Government--Trial of Kepler's Mother--Her final Acquittal--And Death at the age of Seventy-five--The States of Styria burn publicly Kepler's Calendar--He receives his Arrears of Salary from Ferdinand--The Rudolphine Tables published in 1628--He receives a Gold Chain from the Grand Dulce of Tuscany--He is Patronised by the Duke of Friedland--He removes to Sagan, in Silesia--Is appointed Professor of Mathematics at Rostoch--Goes to Ratisbon to receive his Arrears--His Death, Funeral, and Epitaph--Monument Erected to his Memory in 1803--His Family--His Posthumous Volume, ent.i.tled "The Dream, or Lunar Astronomy."_

Kepler was kept in a state of constant anxiety from the delay in the Government to pay up the arrears of his pension, while their repeated promises prevented him from accepting of other employments. He had hoped that the affair of the Bolognese chair would rouse the imperial treasury to a sense of its duty, and enable him to publish the Rudolphine Tables,--that great work which he owed to the memory both of Tycho and of Rudolph. But though he was disappointed in this expectation, an event now occurred which at least held out the prospect of a favourable change in his circ.u.mstances. The Emperor Mathias died in 1619, and was succeeded by Ferdinand III., who not only continued him in the situation of his princ.i.p.al mathematician, with his former pension, but promised to pay up the arrears of it, and to furnish the means for publishing the Rudolphine Tables.

The year 1619, so favourable to Kepler's prospects in life, was distinguished also by the publication, at Linz, of one of his most remarkable productions, ent.i.tled "The Harmonies of the World." It is dedicated to James I. of England, and will be for ever memorable in the history of science, as containing the celebrated law that the squares of the periodic times of the planets are to one another as the cubes of their distances. This singular volume, which is marked with all the peculiarities which distinguish his Cosmographical Mystery, is divided into five books. The two first books are princ.i.p.ally geometrical, and relate to regular polygons inscribed in a circle; the third book is a treatise on music, in which musical proportions are derived from figures; the fourth book is astrological, and treats of the harmony of rays emanating on the earth from the heavenly bodies, and on their influence over the sublunary or human soul; the fifth book is astronomical and metaphysical, and treats of the exquisite harmonies of the celestial motions, and of the celebrated third law of the universe, which we have already referred to.

This law, as he himself informs us, first entered his mind on the 8th March 1618; but, having made an erroneous calculation, he was obliged to reject it. He resumed the subject on the 15th May; and having discovered his former error, he recognised with transport the absolute truth of a principle which for seventeen years had been the object of his incessant labours. The delight which this grand discovery gave him had no bounds.

"Nothing holds me," says he; "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 G.o.d, 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 G.o.d has waited six thousand years for an observer."

About the same time, in 1618, Kepler published, at Linz, the _three_ first books of his "Epitome of the Copernican Astronomy," of which the _fourth_ was published at the same place in 1622, and the _fifth_, _sixth_, and _seventh_ at Frankfort in the same year. This interesting work is a kind of summary of all his astronomical views, drawn up in the form of a dialogue for the perusal of general readers. Immediately after its publication, it was placed by the Inquisition in the list of prohibited books; and the moment Kepler learned this from his correspondent Remus, he was thrown into great alarm, and requested from him some information respecting the terms and consequences of the censure which was then p.r.o.nounced against him. He was afraid that it might compromise his personal safety if he went to Italy; that he would be compelled to retract his opinions; that the censure might extend to Austria; that the sale of his work would be ruined; and that he must either abandon his country or his opinions.

The reply of his friend Remus calmed his agitated mind, by explaining to him the true nature of the prohibition; and he concluded his letter with a piece of seasonable exhortation, "There is no ground for your alarm either in Italy or in Austria, only keep yourself within bounds, and put a guard upon your own pa.s.sions."

In the year 1620, Sir Henry Wotton, the English amba.s.sador at Venice, paid a visit to Kepler on his way through Germany. It does not appear whether or not this visit was paid at the desire of James I., to whom Kepler had dedicated one of his works, but from the nature of the communication which was made to him by the amba.s.sador, there are strong reasons to think that this was the case. Sir Henry Wotton urged Kepler to take up his residence in England, where he could a.s.sure him of a welcome and an honourable reception; but, notwithstanding the pecuniary difficulties in which he was then involved, he did not accept of the invitation. In referring to this offer in one of his letters, written a year after it was made, he thus balances the difficulties of the question--"The fires of civil war," says he, "are raging in Germany.

Shall I then cross the sea whither Wotton invites me? I, a German, a lover of firm land, who dread the confinement of an island, who presage its dangers, and must drag along with me my little wife and flock of children?" As Kepler seems to have entertained no doubt of his being well provided for in England, it is the more probable that the British Sovereign had made him a distinct offer through his amba.s.sador. A welcome and an honourable reception, in the ordinary sense of these terms, could not have supplied the wants of a starving astronomer, who was called upon to renounce a large though an ill-paid salary in his native land; and Kepler had experienced too deeply the faithlessness of royal pledges to trust his fortune to so vague an a.s.surance as that which is implied in the language of the English amba.s.sador. During the two centuries which have elapsed since this invitation was given to Kepler, there has been no reign during which the most ill.u.s.trious foreigner could hope for pecuniary support, either from the Sovereign or the Government of England. What English science has never been able to command for her indigenous talent, was not likely to be proffered to foreign merit. The generous hearts of individual Englishmen, indeed, are always open to the claims of intellectual pre-eminence, and ever ready to welcome the stranger whom it adorns; but through the frozen life-blood of a British minister such sympathies have seldom vibrated; and, amid the struggles of faction and the anxieties of personal and family ambition, he has turned a deaf ear to the demands of genius, whether she appeared in the humble posture of a suppliant, or in the prouder att.i.tude of a national benefactor.

If the imperial mathematician, therefore, had no other a.s.surance of a comfortable home in England than that of Sir Henry Wotton, he acted a wise part in distrusting it; and we rejoice that the sacred name of Kepler was thus withheld from the long list of distinguished characters whom England has starved and dishonoured.

In the year 1620, Kepler was exposed to a severe calamity, which continued to hara.s.s him for some time. His mother, Catherine Kepler, to whose peculiarities of temper we have already referred, was arrested on the 5th April, upon a charge of a very serious nature. One of her friends having some years before suffered a miscarriage, was subsequently attacked with violent headaches, and Catherine was charged with having administered poison to her friend. This accusation was indignantly repelled, and a young doctor of the law, whom she consulted, advised her to raise an action against her calumniator. From professional reasons, or probably pecuniary ones, this zealous pract.i.tioner continued to delay the lawsuit for five years. The judge who tried it happened to be displaced, and was succeeded by another, who had a personal quarrel with the prosecutor. The defender, who was aware of this favourable change in her case, became the accuser, and, in July 1620, Catherine Kepler was sent to prison, and condemned to the torture.

The moment this event reached the ears of her son, he quitted Linz, and arrived in time to save her from punishment. He found that the evidence upon which she was condemned had no other foundation but her own intemperate conduct; and, though his interference was successful, yet she was not finally released from prison till the 4th November 1621.