The Martyrs of Science, or, The lives of Galileo, Tycho Brahe, and Kepler Part 7

_Tycho resumes his Astronomical Observations--Is attacked with a Painful Disease--His Sufferings and Death in 1601--His Funeral--His Temper--His Turn for Satire and Raillery--His Piety--Account of his Astronomical Discoveries--His Love of Astrology and Alchymy--Observations on the Character of the Alchymists--Tycho's Elixir--His Fondness for the Marvellous--His Automata and Invisible Bells--Account of the Idiot, called Lep, whom he kept as a Prophet--History of Tycho's Instruments--His great Bra.s.s Globe preserved at Copenhagen--Present state of the Island of Huen._

Although Tycho continued in this new position to observe the planets with his usual a.s.siduity, yet the recollection of his sufferings, and the inconveniences and disappointments which he had experienced, began to prey upon his mind, and to affect his health. Notwithstanding the continued liberality of the Emperor, and the kindness of his friends and pupils, he was yet a stranger in a distant land. Misfortune was unable to subdue that love of country which was one of the most powerful of his affections; and, though its ingrat.i.tude might have broken the chain which bound him to the land of his nativity, it seems only to have rivetted it more firmly. His imagination, thus influenced, acquired an undue predominance over his judgment. He viewed the most trifling occurrences as supernatural indications; and in those azure moments when the clouds broke from his mind, and when he displayed his usual wit and pleasantry, he frequently turned the conversation to the subject of his latter end.

This state of mind was the forerunner, though probably the effect, of a painful disease, which had, doubtless, its origin in the severity and continuity of his studies. On the 13th October, when he was supping at the house of a n.o.bleman called Rosenberg, he was seized with a retention of urine, which forced him to leave the party.

This attack continued with little intermission for more than a week, and, during this period, he suffered great pain, attended with want of sleep and temporary delirium, during which, he frequently exclaimed, _Ne frustra vixisse videor_. On the 24th he recovered from this painful situation, and became perfectly tranquil. His strength, however, was gone, and he saw that he had not many hours to live. He expressed an anxious wish that his labours would redound to the glory of his Maker, to whom he offered up the most ardent prayers. He enjoined his sons and his son-in-law not to allow them to be lost. He encouraged his pupils not to abandon their pursuits, he requested Kepler to complete the Rudolphine Tables, and to his family he recommended piety and resignation to the Divine will. Among those who never quitted Tycho in his illness, was Erick Brahe, Count Wittehorn, a Swede, and a relation of his own, and Counsellor to the King of Poland. This amiable individual never left the bedside of his friend, and administered to him all those attentions which his situation required. Tycho, turning to him, thanked him for his affectionate kindness, and requested him to maintain the relations.h.i.+p with his family. He then expired without pain, amid the consolations, the prayers, and the tears of his friends. This event took place on the 24th of October 1601, when he was only fifty-four years and ten months old.

The Emperor Rudolph evinced the greatest sorrow when he was informed of the death of his friend, and he gave orders that he should be buried in the most honourable manner, in the princ.i.p.al church of the ancient city.[41] The funeral took place on the 4th November, and he was interred in the dress of a n.o.bleman, and with the ceremonies of his order. The funeral oration was p.r.o.nounced by Jessenius, before a distinguished a.s.semblage, and many elegies were written on his death.

[41] The church of Tiers, where a monument has been erected to his memory.

Tycho was a little above the middle size, and in the last years of his life he was slightly corpulent. He had reddish yellow hair and a ruddy complexion. He was of a sanguine temperament, and is said to have been sometimes irritable, and even obstinate. This failing, however, if he did possess it, was not exhibited towards his pupils or his scientific friends, who ever entertained for him the warmest affection and esteem.

Some of his pupils had remained in his house more than twenty years; and in the quarrel which arose between him and Kepler,[42] and which is allowed to have originated entirely in the temper of the latter, he conducted himself with the greatest patience and forbearance. There is reason to think that the irritability with which he has been charged was less an affection of his mind than the effect of that n.o.ble independence of character which belonged to him, and that it has been inferred chiefly from his conduct to some of those high personages with whom he was brought in contact. When Walchendorp, the President of the Council, kicked his favourite hound, it was no proof of irritability of character that Tycho expressed in strong terms his disapprobation of the deed.

[42] See the Life of Kepler.

It was, doubtless, a greater weakness in his character that he indulged his turn for satire, without being able to bear retaliation. His jocular habits, too, sometimes led him into disagreeable positions. When the Duke of Brunswick was dining with him at Uraniburg, the Duke said, towards the end of the dinner, that, as it was late, he must be going.

Tycho jocularly remarked that this could not be done without his permission; upon which the Duke rose and left the party, without taking leave of his host. Tycho became indignant in his turn, and continued to sit at table; but, as if repenting of what he had done, he followed the Duke, who was on his way to the s.h.i.+p, and, calling upon him, displayed the cup in his hand, as if he had washed out his offence by a draught of wine.

Tycho was a man of true piety, and cherished the deepest veneration for the Sacred Scriptures, and for the great truths which they reveal. Their principles regulated his conduct, and their promises animated his hopes.

His familiarity with the wonders of the heavens increased, instead of diminis.h.i.+ng, his admiration of Divine wisdom, and his daily conversation was elevated by a constant reference to a superintending Providence.

As a practical astronomer, Tycho has not been surpa.s.sed by any observer of ancient or of modern times. The splendour and number of his instruments, the ingenuity which he exhibited in inventing new ones and in improving and adding to those which were formerly known, and his skill and a.s.siduity as an observer, have given a character to his labours, and a value to his observations, which will be appreciated to the latest posterity. The appearance of the new star in 1572 led him to form a catalogue of 777 stars, vastly superior in accuracy to those of Hipparchus and Ulugh Beig. His improvements on the lunar theory were still more valuable. He discovered the important inequality called the _variation_, and also the annual inequality which depends on the position of the earth in its...o...b..t. He discovered, also, the inequality in the inclination of the moon's...o...b..t, and in the motion of her nodes.

He determined with new accuracy the astronomical refractions from an alt.i.tude of 45 down to the horizon, where he found it to be 34'; and he made a vast collection of observations on the planets, which formed the groundwork of Kepler's discoveries and the basis of the Rudolphine Tables. Tycho's powers of observation were not equalled by his capacity for general views. It was, perhaps, owing more to his veneration for the Scriptures than to the vanity of giving his name to a new system that he rejected the Copernican hypothesis. Hence he was led to propose a new system, called the Tychonic, in which the earth is stationary in the centre of the universe, while the sun, with all the other planets and comets revolving round him, performs his daily revolution about the earth. This arrangement of the planets afforded a sufficient explanation of the various phenomena of the heavens; and as it was consistent with the language of Scripture, and conformable to the indications of the senses, it found many supporters, notwithstanding the physical absurdity of making the whole system revolve round one of the smallest of the planets.

It is a painful transition to pa.s.s from the astronomical labours of Tycho to his astrological and chemical pursuits. That Tycho studied and practised astrology has been universally admitted. He calculated the nativity of the Emperor Rudolph, and foretold that his relations would make some attempts upon his life. The credulous Emperor confided in the prediction, and when the conduct of his brother seemed to justify his belief, he confined himself to his palace, and fell a prey to the fear which it inspired. Tycho, however, seems to have entirely renounced his astrological faith in his latter days; and Kepler states,[43] in the most pointed manner, that Tycho carried on his astronomical labours with his mind entirely free from the superst.i.tions of astrology; that he derided and detested the vanity and knavery of astrologers, and was convinced that the stars exercised no influence on the destinies of men.

[43] In his Preface to the Rudolphine Tables.

Although Tycho informed Rothman that he devoted as much labour and expense to the study of terrestrial (chemistry) as he did to that of celestial astronomy, yet it is a singular fact that he never published any account of his experiments, nor has he left among his writings any trace of his chemical inquiries. He pretended, however, to have made discoveries in the science, and we should have been disposed to reprobate the apology which he makes for not publis.h.i.+ng them, did we not know that it had been frequently given by the other alchemists of the age--"On consideration," says he, "and by the advice of the most learned men, I thought it improper to unfold the secrets of the art (of alchemy) to the vulgar, as few persons were capable of using its mysteries to advantage and without detriment."

Admitting then, as we must do, that Tycho was not only a professed alchemist, but that he was practically occupied with its pursuits, and continually misled by its delusions, it may not be uninteresting to the reader to consider how far a belief in alchemy, and a practice of its arts, have a foundation in the weakness of human nature; and to what extent they are compatible with the piety and elevated moral feeling by which our author was distinguished.

In the history of human errors two cla.s.ses of impostors, of very different characters, present themselves to our notice--those who wilfully deluded their species, and those who permitted their species to delude themselves. The first of those cla.s.ses consisted of the selfish tyrants who upheld an unjust supremacy by systematic delusions, and of grovelling mountebanks who quenched their avaricious thirst at the fountains of credulity and ignorance. The second cla.s.s comprehended spirits of a n.o.bler mould: It embraced the speculative enthusiasts, whom the love of fame and of truth urged onward, in a fruitless research, and those great lights of knowledge and of virtue, who, while they stood forward as the landmarks of the age which they adorned, had neither the intellectual nor the moral courage to divest themselves of the supernatural radiance with which the ignorance of the vulgar had encircled them.

The thrones and shrines, which delusion once sustained even in the civilized quarter of the globe, are for ever fallen, and that civil and religious liberty, which in past ages was kept down by the marvellous exhibitions of science to the senses, is now maintained by its application to the reason of man. The charlatans, whether they deal in moral or in physical wonders, form a race which is never extinct. They migrate to the different zones of the social system, and though they change their place, and their purposes, and their victims, yet their character and motives remain the same. The philosophical mind, therefore, is not disposed to study either of these varieties of impostors; but the other two families which compose the second cla.s.s are objects of paramount interest. The eccentricities and even the obliquities of great minds merit the scrutiny of the metaphysician and the moralist, and they derive a peculiar interest from the state of society in which they are exhibited. Had Cardan and Cornelius Agrippa lived in modern times, their vanity and self-importance would have been checked by the forms of society, and even if their harmless pretensions had been displayed, they would have disappeared in the blaze of their genius and knowledge. But nursed in superst.i.tion, and educated in dark and turbulent times, when every thing intellectual was in a state of restless transition, the genius and character of great men necessarily reflected the peculiarities of the age in which they lived.

Had history transmitted to us correct details of the leading alchemists and scientific magicians of the dark ages, we should have been able to a.n.a.lyse their actions and their opinions, and trace them, probably, to the ordinary principles by which the human mind is in every age influenced and directed. But when a great man has once become an object either of interest or of wonder, and still more when he is considered as the possessor of knowledge and skill which transcend the capacity of the age, he is soon transformed into the hero of romance. His powers are overrated, his deeds exaggerated, and he becomes the subject of idle legends, which acquire a firmer hold on credulity from the slight sprinkling of truth with which they are seasoned. To disclaim the possession of lofty attributes thus ascribed to great men is a degree of humility which is not often exercised. But even when this species of modesty is displayed, it never fails to defeat its object. It but calls forth a deeper homage, and fixes the demiG.o.d more firmly in his shrine.

The history of learning furnishes us with many examples of that species of delusion in which a great mind submits itself to vulgar adulation, and renounces unwillingly, if it renounces at all, the unenviable reputation of supernatural agency. In cases where self-interest and ambition are the basis of this peculiarity of temperament, and in an age when the conjuror and the alchemist were the companions and even the idols of princes, it is easy to trace the steps by which a gifted sage retains his ascendancy among the ignorant. The hecatomb which is sacrificed to the magician, he receives as an oblation to his science, and conscious of possessing real endowments, the idol devours the meats that are offered to him without a.n.a.lysing the motives and expectations under which he is fed. But even when the idolater and his G.o.d are not placed in this transverse relation, the love of power or of notoriety is sufficient to induce good men to lend a too willing ear to vulgar testimony in favour of themselves; and in our own times it is not common to repudiate the unmerited cheers of a popular a.s.sembly, or to offer a contradiction to fict.i.tious tales which record our talents or our courage, our charity or our piety.

The conduct of the scientific alchemists of the thirteenth, fourteenth, and fifteenth centuries presents a problem of very difficult solution.

When we consider that a gas, a fluid, and a solid may consist of the very same ingredients in different proportions; that a virulent poison may differ from the most wholesome food only in the difference of quant.i.ty of the very same elements; that gold and silver, and lead and mercury, and indeed all the metals, may be extracted from transparent crystals, which scarcely differ in their appearance from a piece of common salt or a bit of sugarcandy; and that diamond is nothing more than charcoal,--we need not greatly wonder at the extravagant expectation that the precious metals and the n.o.blest gems might be procured from the basest materials. These expectations, too, must have been often excited by the startling results of their daily experiments.

The most ignorant compounder of simples could not fail to witness the magical transformations of chemical action; and every new product must have added to the probability that the tempting doublets of gold and silver might be thrown from the dice-box with which he was gambling.

But when the precious metals were found in lead and copper by the action of powerful re-agents, it was natural to suppose that they had been actually formed during the process; and men of well-regulated minds even might have thus been led to embark in new adventures to procure a more copious supply, without any insult being offered to sober reason, or any injury inflicted on sound morality.

When an ardent and ambitious mind is once dazzled with the fascination of some lofty pursuit, where gold is the object, or fame the impulse, it is difficult to pause in a doubtful career, and to make a voluntary s.h.i.+pwreck of the reputation which has been staked. Hope still cheers the aspirant from failure to failure, till the loss of fortune and the decay of credit disturb the serenity of his mind, and hurry him on to the last resource of baffled ingenuity and disappointed ambition. The philosopher thus becomes an impostor; and by the pretended trans.m.u.tation of the baser metals into gold, or the discovery of the philosopher's stone, he attempts to sustain his sinking reputation, and recover the fortune he has lost. The communication of the great secret is now the staple commodity with which he is to barter, and the grand talisman with which he is to conjure. It can be imparted only to a chosen few--to those among the opulent who merit it by their virtues, and can acquire it by their diligence, and the divine vengeance is threatened against its disclosure. A process commencing in fraud and terminating in mysticism is conveyed to the wealthy aspirant, or instilled into the young enthusiast, and the grand mystery pa.s.ses current for a season, till some cautious professor of the art, like Tycho, denounces its publication as detrimental to society.

Among the extravagant pretensions of the alchemists, that of forming a universal medicine was perhaps not the most irrational. It was only when they pretended to cure every disease, and to confer longevity, that they did violence to reason. The success of the Arabian physicians in the use of mercurial preparations naturally led to the belief that other medicines, still more general in their application, and efficacious in their healing powers, might yet be brought to light; and we have no doubt that many substantial discoveries were the result of such overstrained expectations. Tycho was not merely a believer in the medical dogmas of the alchemists, he was actually the discoverer of a new _elixir_, which went by his name, and which was sold in every apothecary's shop as a specific against the epidemic diseases which were then ravaging Germany. The Emperor Rudolph having heard of this celebrated medicine, obtained a small portion of it from Tycho by the hands of the Governor of Brandisium; but, not satisfied with the gift, he seems to have applied to Tycho for an account of the method of preparing it. Tycho accordingly addressed to the Emperor a long letter, dated September 7, 1599, containing a minute account of the process.

The base of this remarkable medicine is Venetian treacle, which undergoes an infinity of chemical operations and admixtures before it is ready for the patient. When properly prepared he a.s.sures the Emperor that it is better than gold, and that it may be made still more valuable by mixing with it a single scruple either of the tincture of corals, or sapphire, or hyacinth, or a solution of pearls, or of potable gold, if it can be obtained free of all corrosive matter! In order to render the medicine _universal_ for all diseases which can be cured by perspiration, and which, he says, form a third of those which attack the human frame, he combines it with antimony, a well known sudorific in the present practice of physic. Tycho concludes his letter by humbly beseeching the Emperor to keep the process secret, and reserve the medicine for himself alone!

The same disposition of mind which made Tycho an astrologer and an alchemist, inspired him with a singular love of the marvellous.

He had various automata with which he delighted to astonish the peasants; and by means of invisible bells, which communicated with every part of his establishment, and which rung with the gentlest touch, he had great pleasure in bringing any of his pupils suddenly before strangers, muttering at a particular time the words "Come hither, Peter," as if he had commanded their presence by some supernatural agency. If, on leaving home, he met with an old woman or a hare, he returned immediately to his house: But the most extraordinary of all his peculiarities remains to be noticed. When he lived at Uraniburg he maintained an idiot of the name of Lep, who lay at his feet whenever he sat down to dinner, and whom he fed with his own hand. Persuaded that his mind, when moved, was capable of foretelling future events, Tycho carefully marked every thing he said. Lest it should be supposed that this was done to no purpose, Longomonta.n.u.s relates that when any person in the island was sick, Lep never, when interrogated, failed to predict whether the patient would live or die. It is stated also in the letters of Wormius, both to Ga.s.sendi and Peyter, that when Tycho was absent, and his pupils became very noisy and merry in consequence of not expecting him soon home, the idiot, who was present, exclaimed, _Juncher xaa laudit_, "Your master has arrived." On another occasion, when Tycho had sent two of his pupils to Copenhagen on business, and had fixed the day of their return, Lep surprised him on that day while he was at dinner, by exclaiming, "Behold your pupils are bathing in the sea." Tycho, suspecting that they were s.h.i.+pwrecked, sent some person to the observatory to look for their boat. The messenger brought back word that he saw some persons wet on the sh.o.r.e, and in distress, with a boat upset at a great distance. These stories have been given by Ga.s.sendi, and may be viewed as specimens of the superst.i.tion of the age.

Tycho left behind him a wife and six children, but even in the time of Ga.s.sendi nothing was known of their history, excepting that Tengnagel, who married one of the daughters, gave up his scientific pursuits, and, having been admitted among the Emperor's counsellors, was employed in several of his emba.s.sies.

The instruments of Tycho were purchased from his heirs, by the Emperor, for 22,000 crowns. They were shut up in the house of Curtius, and were treated with such veneration, that no astronomer, not even Kepler himself, was permitted to see or to use them.

Here they remained till the death of the Emperor Matthias, in 1619, when the troubles in Bohemia took place. When Prague was taken by the forces of the Elector Palatine, the instruments were carried off, and some were destroyed, and others converted to different purposes. The great bra.s.s globe, however, was saved. It was first carried to Niessa, the episcopal city of Silesia; and having been presented to the College of Jesuits, it was preserved in their museum, till Udalric, the son of Christian, King of Denmark, took Niessa in 1632. The globe was recognized as having belonged to Tycho, and it was carried in triumph to Denmark. An inscription was written upon it by Longomonta.n.u.s, and it was deposited with some pomp in the Library of the Academy of Sciences.

After Tycho left Huen, the island was transferred to some of the Danish n.o.bility, and the following brief but melancholy description of it was given by Wormius. "There is, in the island, a field where Uraniburg was." The scientific antiquities of Huen, have been more recently described by Mr c.o.x, in his travels through Denmark.

"We landed," says he, "on the south west part in a small bay, just below the place where a stream, supplied by numerous pools and fish ponds, falls into the sea. We ascended the sh.o.r.e, which is clothed with short herbage, crossed the stream, and pa.s.sed over a gently waving surface, gradually sloping towards the sea, and walked a mile to a farm house, standing in the middle of the island, inhabited by Mr Schaw, a Swedish gentleman, to whom the greater part of the island belongs. He lives here in summer, but in winter resides at Landscrona. This dwelling is the same as existed in Tycho Brahe's time, and was the farm house belonging to his estate. A guide, whom we obtained from Mr Schaw, conducted us to the remains of Tycho's mansion, which are near the house, and consist of little more than a mound of earth which enclosed the garden, and two pits, the sites of his mansion and observatory."[44]

[44] c.o.x's Travels in Poland, &c., vol. v., p. 189, 190.

LIFE OF JOHN KEPLER.

CHAPTER I.

_Kepler's Birth in 1571--His Family--And early Education--The Distresses and Poverty of his Family--He enters the Monastic School of Maulbronn--And is admitted into the University of Tubingen, where he distinguishes himself, and takes his Degrees--He is appointed Professor of Astronomy and Greek in 1594--His first speculations on the Orbits of the Planets--Account of their Progress and Failure--His "Cosmographical Mystery" published--He Marries a Widow in 1597--Religious troubles at Gratz--He retires from thence to Hungary--Visits Tycho at Prague in 1600--Returns to Gratz, which he again quits for Prague--He is taken Ill on the road--Is appointed Tycho's a.s.sistant in 1601--Succeeds Tycho as Imperial Mathematician--His Work on the New Star of 1604--Singular specimen of it._

It is a remarkable circ.u.mstance in the history of science, that astronomy should have been cultivated at the same time by three such distinguished men as Tycho, Kepler, and Galileo. While Tycho, in the 54th year of his age, was observing the heavens at Prague, Kepler, only 30 years old, was applying his wild genius to the determination of the orbit of Mars, and Galileo, at the age of 36, was about to direct the telescope to the unexplored regions of s.p.a.ce. The diversity of gifts which Providence a.s.signed to these three philosophers was no less remarkable. Tycho was destined to lay the foundation of modern astronomy, by a vast series of accurate observations made with the largest and the finest instruments; it was the proud lot of Kepler to deduce the laws of the planetary orbits from the observations of his predecessors; while Galileo enjoyed the more dazzling honour of discovering by the telescope new celestial bodies, and new systems of worlds.

John Kepler, the youngest of this ill.u.s.trious band, was born at the imperial city of Weil, in the duchy of Wirtemberg, on the 21st December 1571. His parents, Henry Kepler and Catherine Guldenmann, were both of n.o.ble family, but had been reduced to indigence by their own bad conduct. Henry Kepler had been long in the service of the Duke of Wirtemberg as a petty officer, and in that capacity had wasted his fortune. Upon setting out for the army, he left his wife in a state of pregnancy; and, at the end of seven months, she gave premature birth to John Kepler, who was, from this cause, a sickly child during the first years of his life. Being obliged to join the army in the Netherlands, his wife followed him into the field, and left her son, then five years old, under the charge of his grandfather at Limberg. Sometime afterwards he was attacked with the smallpox, and having with difficulty recovered from this severe malady, he was sent to school in 1577.

Having become security for one of his friends, who absconded from his creditors, Henry Kepler was obliged to sell his house and all his property, and was driven to the necessity of keeping a tavern at Elmendingen. Owing to these misfortunes, young Kepler was taken from school about two years afterwards, and was obliged to perform the functions of a servant in his father's house. In 1585, he was again placed in the school of Elmendingen; but his father and mother having been both attacked with the smallpox, and he himself having been seized with a violent illness in 1585, his education had been much neglected, and he was prohibited from all mental application.

In the year 1586, on the 26th of November, Kepler was admitted into the school at the Monastery of Maulbronn, which had been established at the Reformation, and which was maintained at the expense of the Duke of Wirtemberg, as a preparatory seminary for the University of Tubingen.

After remaining a year at the upper cla.s.ses, the scholars presented themselves for examination at the College for the degree of Bachelor; and having received this, they returned to the school with the t.i.tle of Veterans. Here they completed the usual course of study; and being admitted as resident students at Tubingen, they took their degree of Master. In prosecuting this course of study, Kepler was sadly interrupted, not only by periodical returns of his former complaints, but by family quarrels of the most serious import. These dissensions, arising greatly from the perverseness of his mother, drove his father to a foreign land, where he soon died; and his mother having quarrelled with all her relations, the affairs of the family were involved in inextricable disorder. Notwithstanding these calamities, Kepler took his degree of Bachelor on the 15th September 1588, and his degree of Master in August 1591, on which occasion he held the second place at the annual examination.

In his early studies, Kepler devoted himself with intense pleasure to philosophy in general, but he entertained no peculiar affection for astronomy. Being well grounded in arithmetic and geometry, he had no difficulty in making himself master of the geometrical and astronomical theorems which occurred in the course of his studies. While attending the lectures of Moestlin, professor of mathematics, who had distinguished himself by an oration in favour of the Copernican system, Kepler not only became a convert to the opinions of his master, but defended them in the physical disputations of the students, and even wrote an essay on the primary motion, in order to prove that it was produced by the daily rotation of the earth.

In 1594, the astronomical chair at Gratz, in Styria, fell vacant by the death of George Stadt, and, according to Kepler's own statement, he was forced to accept this situation by the authority of his professional tutors, who recommended him to the n.o.bles of Styria. Though Kepler had little knowledge of the science, and no pa.s.sion for it whatever, yet the nature of his office forced him to attend to astronomy; and, in the year 1595, when he enjoyed some leisure from his lectures, he directed the whole energy of his mind to the three important topics of the number, the size, and the motion of the orbits of the planets. He first tried if the size of the planets' orbits, or the difference of their sizes, had any regular proportion to each other. Finding no proof of this, he inserted a new planet between Mars and Jupiter, and another between Venus and Mercury, which he supposed might be invisible from their smallness; but even with these a.s.sumptions the distances of the planets exhibited no regular progression. Kepler next tried if these distances varied as the cosines of the quadrant, and if their motion varied as the sun's, the sine of 90 representing the motion at the sun, and the sine of 0 that at the fixed stars; but in this trial he was also disappointed.

Having spent the whole summer in these fruitless speculations, and praying constantly to his Maker for success, he was accidentally drawing a diagram in his lecture-room, in July 1595, when he observed the relation between the circle inscribed in a triangle, and that described round it; and the ratio of these circles, which was that of 1 to 2, appeared to his eye to be identical with that of Jupiter's and Saturn's...o...b..ts. Hence he was led to compare the orbits of the other planets'

circles described in pentagons and hexagons. As this hypothesis was as inapplicable to the heavens as its predecessors, Kepler asked himself in despair, "What have _plane_ figures to do with _solid_ orbits? Solid bodies ought to be used for solid orbits." On the strength of this conceit, he supposed that the distances of the planets were regulated by the sizes of the five regular solids described within one another. "The Earth is the circle, the measurer of all. Round it describe a dodecahedron; the circle including this will be Mars. Round Mars describe a tetrahedron; the circle including this will be Jupiter.

Describe a cube round Jupiter; the circle including this will be Saturn.

Then inscribe in the Earth an icosahedron; the circle described in it will be Venus. Inscribe an octohedron in Venus; the circle inscribed in it will be Mercury."