CHAPTER II.

_Kepler's Pecuniary Embarrassments--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 embarrassments, and the occupation of his time in the practice of astrology, Kepler found leisure for his favourite pursuits. No adverse circumstances 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, entitled "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 deg. of altitude. Even at the beginning of the second century, Claudius Ptolemy of Alexandria had unravelled its principal mysteries, and had given in his Optics a theory of astronomical refraction more complete than that of any astronomer before the time of Cassini;[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 glass, from a perpendicular incidence to a horizontal one.

[46] Cassini 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 assuming 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 analogous 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 passage 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, entitled "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 assistant of Tycho. The powers of original genius were then for the first time associated 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 harassed 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 embarrassments.

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 passion." 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 noble Baron of Stahrenberg, at 12 o'clock on the 30th of next October, with all Eferdingen assembled 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 analysis.

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.