Tycho Brahe: a picture of scientific life and work in the sixteenth century

Front matter

A PICTURE OF

SCIENTIFIC LIFE AND WORK IN THE

SIXTEENTH CENTURY

Chapter 1

TYCHO BRAHE.

CHAPTER I.

THE REVIVAL OF ASTRONOMY IN EUROPE.

The early part of the sixteenth century must always rank among the most remarkable periods in the history of civilisation. The invention of printing had made literature the property of many to whom it had hitherto been inaccessible, and the downfall of the Byzantine Empire had scattered over Europe a number of fugitive Greeks, who carried with them many treasures of classical literature hitherto unknown in the Western world, while Raphael, Michael Angelo, and other contemporaries of Leo X. revived the glory of the ancients in the realm of art. The narrow limits of the old world had vanished, and the Portuguese and Spanish navigators had led the way to boundless fields for human enterprise, while the Reformation revolutionised the spirit of mankind and put an end to the age of ignorance and superstition.

During this active period there were also signs of renewed vigour among the devotees of science, and the time was particularly favourable to a revival of astronomical studies. Students of astronomy were now enabled to study the Greek authors in the original language, instead of having to be content with Latin reproductions of Arabian translations from the Greek, which, through the Italian Univer , had been introduced into Europe during the Middle Ages. Another impulse was given by the voyages of discovery, as navigators were obliged to trust entirely to the stars and the compass, and therefore required as perfect a theory as possible of the motions of the heavenly bodies. We see accordingly at the end of the fifteenth century and the beginning of the sixteenth considerable stir in the camp of science, but as yet only in Germany—a circumstance not difficult to explain. Though divided into a great number of semi-independent states, Germany bore still the proud name of the Holy Roman Empire, and on account of the claims represented by this name the Germans had for a long time been in constant intercourse with Italy, the land with the great past, and still, notwithstanding its political misery, the leader of civilisation. It was an intercourse of a peaceful and commercial as well as of a warlike character; but in both ways was this of benefit to the Germans, producing among them much knowledge of foreign affairs, and giving them greater facilities for taking up the scientific work of the ancients than were found in other parts of Europe.

The first astronomer of note was Georg Purbach (1423–1461), who studied at the University of Vienna, and afterwards for some time in Italy. His principal work on astronomy (Theoricæ Novæ Planetarum) attempted to develop the old hypothesis of material celestial spheres, and was but a mixture of Aristotelean cosmology and Ptolemean geometry; but he was the first European to make use of trigonometry, the principal legacy which astronomers owe to the Arabs. Purbach endeavoured to get beyond the rudiments of spherical astronomy, which hitherto had formed the only subject for astronomical lectures, and had been taught through the medium of a treatise written in the thirteenth century by John Holy (Johannes de Sacrobosco) for use in the University of Paris. While lecturing at Vienna, Purbach's attention was drawn to a young disciple of great promise, Johann Müller, from Königsberg, a small village in Franconia, where he had been born in 1436. He is generally known by the name of Regiomontanus, though he does not seem to have used this name himself, but always that of Johannes de Monteregio. He entered heart and soul into his teacher's studies of the great work of Ptolemy, which embodied all the results of Greek astronomy, and the talented pupil soon became an invaluable co-operator to Purbach. They did not confine themselves to theoretical studies, but, with such crude instruments as they could construct, they convinced themselves of the fact that the places of the planets computed from the astronomical tables of King Alphonso X. of Castile differed very considerably from the actual positions of the planets in the sky. In the midst of these occupations the two astronomers had the good luck to become acquainted with a man who was well qualified to help them to carry out their greatest wishes. This man was Cardinal Bessarion, a Greek by birth, who, as Bishop of Nicæa, had accompanied the Byzantine Emperor on his journey to the Council of Ferrara in 1438, where he tried to bring about a reconciliation between the Greek and Roman Churches. Bessarion remained in Italy and joined the Roman Church, but he never forgot his old country, and contributed very much to make the classical Greek literature known in the West. The translation of the original Almagest (as Ptolemy's work was generally called, from a corruption of the Arabic Al megist, in its turn derived from μέγιστη σύνταξις) was a subject in which he was particularly interested, and during his stay at Vienna as Papal Nuncio he succeeded in communicating to Purbach his own anxiety to make Ptolemy better known in the scientific world. Purbach was on the point of starting for Italy for the purpose of collecting Greek manuscripts, when he died suddenly in 1461, but Regiomontanus succeeded to his place in the Cardinal's friendship, and set out for Italy with Bessarion in the following year.

Regiomontanus stayed about seven years in Italy, visiting the principal cities, and losing no chance of studying the Greek language and collecting Greek manuscripts. At Venice he wrote a treatise on trigonometry, which branch of mathematics he also, during the remainder of his life, continued to develop, so that he constructed a table of tangents (tabula fecunda), and probably only was prevented by his early death from completing his treatise by introducing the use of tangents therein. After his return to Germany, he settled, in 1471, at Nürnberg. This city was one of the chief centres of German industry and literary life, and no other German city had such regular commercial communication with Italy, from whence the produce of the East was brought into the market, and nowhere did the higher classes of citizens use their wealth so willingly in support of art and science. The new art of printing had recently been introduced at Nürnberg, where a regular printing-press was now working—a circumstance of particular importance to the collector of Greek writings. A wealthy citizen, Bernhard Walther (born 1430, died 1504), became at once the friend and disciple of Regiomontanus, and arranged an observatory for their joint use. Instruments, as fine as the skilful artisans of Nürnberg could make them, adorned the earliest of European observatories, and the two friends made good use of them (they observed already the comet of 1472), and originated several new methods of observing. But Regiomontanus did not forget the printing operations, and published not only Purbach's Theoricæ Novæ and trigonometrical tables, but also his own celebrated Ephemerides, the first of their kind, which, some years afterwards, were made known to the navigators through the German geographer Martin Behaim, and guided Diaz, Columbus, Vasco de Gama, and many others safely across the ocean. Nothing spread the fame of the astronomer like these Ephemerides, and the Pope was thus induced to invite Regiomontanus to Rome to reform the confused calendar. The invitation was obeyed in 1475, but Regiomontanus died in July 1476 very suddenly at Rome. He only reached the age of forty, and no doubt much might have been expected from him if death had not so early stopped his career; but he had rendered great service to science, not only by his endeavours to save the Greek authors from oblivion, but by his Ephemerides, his development of trigonometry, and his observations. Walther survived him twenty-eight years, and continued his observations, which were published in 1544.

By Purbach and Regiomontanus the astronomy of the Alexandrian school had been introduced at the German Universities, and the increased demands which navigators made on astronomers continued to help forward the study of astronomy in Germany, which country, by having a sovereign in common with Spain, for a while had much intercourse with the latter country. Of the astronomers who worked during the first half of the sixteenth century we shall here mention Peter Apianus or Bienewitz, who taught at the University of Ingolstadt. Besides other works, he published in 1540 a large book, Astronomicum Cæsareum, dedicated to Charles the Fifth. In this beautiful volume the author represented, by means of movable circles of cardboard of various colours, the epicyclical motions of the planets according to the Ptolemean system, and expected to be able in this way to find their positions without computation. The book was received with much applause, and is really in some ways to be admired, though one cannot help agreeing with Kepler in regretting the "miserable industry" of Apianus, which after all only produced a very rough approximation to the real motions of the stars, but which is eminently characteristic of the low state of science at that time. Apianus deserves more thanks for having paid much attention to comets, and for having discovered the important fact that the tails of these bodies are turned away from the sun. This was also pointed out about the same time by Fracastoro of Verona in a work published in 1538, containing an elaborate attempt to revive the theory of concentric spheres of Eudoxus, which had been pushed into the background by the Ptolemean system of the world.

Only three years after Apian's volume appeared the great work of Nicolaus Copernicus, De Revolutionibus (1543), which was destined to become the corner-stone of modern astronomy. We shall in the following so often have occasion to refer to the labours of this great man, that a few words will suffice in this place. Copernicus, who not only discovered the greatest truth in astronomy, but who even by his opponents was admitted to be an astronomer worthy of being classed with Hipparchus and Ptolemy, was born in 1473 at Thorn, on the Vistula, a town which belonged to the Hansa League, and a few years before had come under the suzerainty of Poland. He studied first at the University of Krakau, where astronomy was specially cultivated, and at the age of twenty-four he proceeded to Bologna, where he enjoyed the teaching of Domenico Maria Novara. Thus Copernicus not only became acquainted with Ptolemy's work, but also acquired some familiarity with the astrolabe or astronomical circle, one of the few crude instruments then in use. From about the end of 1505 till his death in 1543, Copernicus lived in the diocese of Ermland, in Prussia, most of the time in the town of Frauenburg, where he held a canonry at the cathedral. It is much to be regretted that we are utterly unacquainted with the manner in which Copernicus came to design the new system of astronomy which has made his name immortal. But he had probably early perceived that, however valuable the labours of Regiomontanus had been, they had not improved the theory of celestial motion, so that the most important problem, that of computing beforehand the positions of the planets and accounting for their apparently intricate movements, was practically untouched since the days of Ptolemy. That great mathematician had completed and extended the planetary system of Hipparchus, and had in a wonderfully ingenious manner represented the complicated phenomena. But more than 1400 years had elapsed since his time, and the system, however perfect from a mathematical point of view, had long been felt to be too complicated, and not agreeing closely enough with the observed movements of the planets. This circumstance led Copernicus to attempt the construction of a new system, founded on the idea that the sun, and not the earth, is the ruler of the planets. But though Copernicus on the basis of this idea developed a theory of the planetary movements as complete as that of Ptolemy, he was unable to do more than to demonstrate the possibility of explaining the phenomena by starting from the heliocentric idea. Having no materials from which to deduce the true laws of the motion of the planets in elliptic orbits, he was obliged to make use of the excentric circles and epicycles of the ancients, by which he greatly marred the beauty and simplicity of his system. He did not possess accurate instruments, and took but few observations with those he had. The idea does not seem to have struck him that it was indispensable to follow the planets through a number of years with carefully constructed instruments, and that only in that way could the true theory of planetary motion be found.

There was much to be done yet ere the reform of astronomy could be accomplished. The pressing want of new tables to take the place of the antiquated Alphonsine tables was supplied a few years after the death of Copernicus by Erasmus Reinhold, but though the positions of the planets could be computed from them with greater accuracy than from the old tables, the "Prutenic tables" (published in 1551) did not by this superiority offer any proof of the actual truth of the Copernican principle.

A century had now elapsed since the study of astronomy had commenced to revive in Italy and Germany, but as yet the work accomplished had chiefly been of a tentative and preparatory kind, Copernicus alone having attempted to make science advance along a new path. Still, much useful work had been done. The labours of the ancients had now become accessible in the originals; the Arabs and Regiomontanus had developed trigonometry, and thereby greatly facilitated astronomical computations; Copernicus had shaken the implicit conviction of the necessity of clinging to the complicated Ptolemean system, and had offered the world an alternative and simpler system, while new tables had been computed to take the place of the Alphonsine tables. But otherwise the astronomy of the ancients reigned undisturbed. No advance had been made in the knowledge of the positions of the fixed stars, those stations in the sky by means of which the motions of the planets had to be followed; the value of almost every astronomical quantity had to be borrowed from Ptolemy, if we except a few which had been redetermined by the Arabs. No advance had been made in the knowledge of the moon's motion, so important for navigation, nor in the knowledge of the nature of the planetary orbits, the uniform circular motion being still thought not only the most perfect, but also the only possible one for the planets to pursue. Whether people believed the planets to move round the earth or round the sun, the complicated machinery of the ancients had to be employed in computing their motions, and crude as the instruments in use were, they were more than sufficient to show that the best planetary tables could not foretell the positions of the planets with anything like the desirable accuracy.

No astronomer had yet made up his mind to take nothing for granted on the authority of the ancients, but to determine everything himself. Nobody had perceived that the answers to the many questions which were perplexing astronomers could only be given by the heavens, but that the answers would be forthcoming only if the heavens were properly interrogated by means of improved instruments, capable of determining every astronomical quantity anew by systematic observations. The necessity of doing this was at an early age perceived by Tycho Brahe, whose life and work we shall endeavour to sketch in the following pages. By his labours he supplied a sure foundation for modern astronomy, and gave his great successor, Kepler, the means of completing the work commenced by Copernicus.

Chapter 2

CHAPTER II.

TYCHO BRAHE'S YOUTH.

Tycho Brahe belonged to an ancient noble family which had for centuries flourished not only in Denmark, but also in Sweden, to which country it had spread in the fourteenth century, when one of its members, Torkil Brahe, fled thither from Denmark to escape punishment for manslaughter. The family still exists in both countries. In the sixteenth century the Danish nobility was still of purely national origin, unmingled with the foreign blood which became merged in it in the course of the next two hundred years, when every new royal bride brought with her a train of needy adventurers, with empty purses and long titles, from the Holy Roman Empire. Like their foreign fellow-nobles, they were descended from men who had received grants of land on tenure of military service, and until about the end of the thirteenth century they can hardly be said to have formed a separate class, as their privileges and duties were not yet of necessity hereditary. They were untitled (till 1671), but all the same they were as proud and jealous of the privileges of their order as any Norman count or baron, and were called by the characteristic names of "free and wellborn" or "good men." In the first half of the sixteenth century they had successfully resisted the attempts of King Christiern II. to curb their power, and had driven him from his throne; and when the lower orders afterwards had attempted to replace him on the throne rendered vacant by the death of his brother and successor, the nobles had, after a hard struggle, crushed their opponents, though the latter were backed by the powerful Hansa city of Lübeck. The Reformation had broken the rival power of the Church, and the nobles had in consequence (though not to the same extent as in Germany and England) increased in wealth and possessions. And during the next fifty years they did not abuse their worldly advantages, but were, as a rule, faithful servants of their king and country, generous and kind to their tenants, fond of studies and learning. Most of them had in their youth travelled abroad, frequently for years at a time, and studied at foreign universities, where they acquired knowledge not only of books, but also of the world. At their country-seats many of them encouraged and protected men of learning, and kept up their acquaintance with classical literature, as well as with the more humble folk-lore which, in the shape of old epics and ballads (Kjæmpeviser), had been handed down from one generation to another among the humble as well as among the high-born. Almost every country-seat possessed what was at that time considered a fine library, so that it was quite natural that hardly a pamphlet or book was published without a dedication to some noble patron.

The father of the great astronomer was Otto Brahe, born in 1517, from 1562 or 1563 a Privy Councillor, and successively lieutenant of various counties, finally governor of Helsingborg Castle (opposite Elsinore), where he died in 1571. His wife was Beate Bille, whom he had married in 1544, and their second child and eldest son, Tyge, was born on the 14th December 1546 at the family seat of Knudstrup, in Scania or Skaane, the most southern province of the Scandinavian peninsula, which at that time still belonged to Denmark, as it had done from time immemorial. Tyge, or Tycho (as he afterwards Latinised his name), had a still-born twin-brother, a fact alluded to in a Latin poem which he wrote and had printed in 1572. Otto Brahe had in all five sons and five daughters (in addition to the still-born son), the youngest being Sophia, born in 1556, who will often be mentioned in the sequel. Though he was the eldest son and heir to the family estate of Knudstrup, Tycho did not remain under his father's care for more than about a year, as his father's brother, Jörgen (George) Brahe, who was childless, had been promised by Otto, that if the latter got a son, he would let Jörgen bring him up as his own. The fulfilment of the promise was claimed in vain; but Jörgen Brahe was not to be put off so easily, and as soon as a second boy had been born to Otto, the uncle coolly carried off his eldest nephew by stealth as soon as he got an opportunity. The parents of Tycho gave way when the thing was done, knowing that the child was in good hands, and doubtless expecting that the foster-parents would eventually leave their adopted son some of their wealth, which they also seem to have done.

We know nothing of Tycho's childhood except that he was brought up at his uncle's seat of Tostrup, and was from the age of seven taught Latin and other rudiments of learning by a tutor. He acquired the necessary familiarity with the only language which was then properly studied, so that he was afterwards able not only to converse in and write Latin, but also to write poetry in this language, which was then and for a long time afterwards considered a very desirable accomplishment for a learned man. We shall often have occasion to quote his poetry, some of which is not without merit. Thus prepared, he was sent to Copenhagen in April 1559 to study at the University there. This seat of learning had been founded in the year 1479 by permission of the Pope, but it had languished for a number of years for want of money and good teachers. The confiscation of the property of the monasteries enabled King Christian III. to commence improving it, and by the statutes of 1539 (which were still in force in Tycho Brahe's time) the number of professors was fixed at fourteen, three of Divinity, one of Law, two of Medicine, and eight in the Faculty of Arts, among whom were several whose names were honourably known outside their own country. Tycho now commenced his studies here, devoting himself specially to rhetorics and philosophy, as being the branches of learning most necessary to the career of a statesman, for which he was destined by his uncle, and probably also by his father, who had at first objected to his receiving a classical education. But astronomy very soon claimed his attention. On the 21st of August 1560 an eclipse of the sun took place, which was total in Portugal, and of which Clavius has left us a graphic description. Though it was only a small eclipse at Copenhagen, it attracted the special attention of the youthful student, who had already begun to take some interest in the astrological predictions or horoscopes which in those days formed daily topics of conversation. When he saw the eclipse take place at the predicted time, it struck him "as something divine that men could know the motions of the stars so accurately that they could long before foretell their places and relative positions." He therefore lost no time in procuring a copy of the Ephemerides of Stadius in order to satisfy his curiosity as to astronomical matters; and not content with the meagre information he could get from this book, he very soon made up his mind to go to the fountain-head, and at the end of November in the same year he invested two Joachims-thaler in a copy of the works of Ptolemy, published at Basle in 1551. This copy is still in existence, and may be seen in the University Library at Prague; there are many marginal notes in it, and at the bottom of the title-page is written in Tycho's own hand that he had bought the book at Copenhagen on the last day of November for two thaler. This book contained a Latin translation of all the writings of Ptolemy except the Geography, the Almegist being in the translation of Georgios from Trebizond. The study of this complete compendium of the astronomy of the day must have given the youthful student enough to do; indeed, it may well be doubtful whether he was at that time able to master it.

Tycho remained at Copenhagen for three years, chiefly occupying himself with mathematical and astronomical studies. We are not acquainted with any details as to this period of his life; all we know is that he formed an intimate friendship with one of the professors of medicine, Hans Frandsen, from Ribe, in Jutland (Johannes Francisci Ripensis), and especially with Johannes Pratensis, a young man of French extraction, who also afterwards became professor of medicine. Jörgen Brahe now thought that the time had come to send his nephew to a foreign uni , as was then customary. He probably hoped that, when removed from his friends at Copenhagen, the young worshipper of Urania might be induced to give up his scientific inclinations and devote himself more to studies which would in after years enable him to take the place in his native land to which his birth entitled him. The university he selected for his nephew was that of Leipzig. During the thirteenth and fourteenth centuries Danish students had followed the universal custom of the age and repaired to the University of Paris, where several of them had risen to great distinction, and even occupied the rectorial chair; but gradually as the German universities improved they became more frequented by Danes than Paris. To accompany Tycho as tutor, Jörgen Brahe chose a young man of great promise, who, although only four years older than his pupil, was known to be steady enough to be intrusted with this responsible office. Anders Sörensen Vedel, son of a respected citizen of Veile, in Jutland, had been less than a year at the University, where he attended lectures on divinity, and at the same time devoted himself to the study of history. He became afterwards Royal Historiographer, and is particularly known by his translation of the Latin Chronicle of Saxo Grammaticus, an important source of Danish history from the end of the twelfth century, and also by his edition of the ancient national ballads or Kjæmpeviser. Vedel was only too happy to accept the proposal of accompanying the young nobleman abroad, as there was at that time no Professor of History in the Copenhagen University, while it was not uncommon to find professors in German universities who combined the chair of History with some other one.

Vedel and his pupil left Copenhagen on the 14th February 1562, and arrived at Leipzig on the 24th March following. They were at once installed in the house of one of the professors, possibly on the recommendation of some of their learned friends in Copenhagen, several of whom were in constant communication with their colleagues at the Leipzig University. They had at once their names entered in the book of matriculation, where they may still be seen as "Andreas Severinus Cimber" and "Tyho Brade ex Scandria." There is, however, no sign whatever that Tycho devoted himself to the study of law, while we know that he at once sought the acquaintance of the professor of mathematics, Johannes Homilius; of his disciple, Bartholomæus Scultetus (Schultz), and probably also of the "electoral mathematician," Valentine Thau. Homilius died on the 5th July, a little over three months after Tycho's arrival, but we shall afterwards see that he had even in that short time imparted valuable and practical knowledge to the young student. Vedel did his best to carry out his instructions by trying to keep Tycho to the study of jurisprudence, but Tycho would not allow himself to be hindered in his favourite pursuits, and spent most of his money on astronomical books and instruments, though he had to receive the money from his tutor and account to him for the way it was spent. He made use of the Ephemerides of Stadius to find the places of the planets, having first learned the names of the constellations by means of a small celestial globe not larger than his fist, which he hid from Vedel, and could only use when the latter was asleep. Though this state of things at first produced some coolness between tutor and pupil, it appears that they soon renewed their friendly intercourse. Tycho could not but see that Vedel was only doing his duty, and Vedel gradually had to acknowledge that the love of astronomy had become so deeply rooted in his pupil that it was utterly impossible to force him against his will to devote himself to a study he disliked, or at least looked on with indifference. Another circumstance which was a bond of union between them was that the learned men whose society Vedel sought were to a great extent the same to whom Tycho looked for instruction. Thus the above-mentioned Valentine Thau had a great regard for Vedel, and even tried to get him to enter the service of the Elector, while Homilius was a son-in-law of Camerarius, the most renowned of the professors at Leipzig, and a man whom Vedel later in one of his writings mentions as his beloved teacher. Drawn together through their intercourse with these and other men of learning, Vedel and Tycho laid the foundation of a warm friendship which lasted through life.

Though Tycho was during the greater part of the time he spent at Leipzig obliged to study astronomy in secret, he did not long content himself with the use of the Ephemerides of Stadius, but procured the Alphonsine tables and the Prutenic tables. We have already mentioned that the former were founded on the Ptolemean planetary system and the observations of the Arabs, as well as those made under the direction of Alphonso X. of Castile in the thirteenth century; while the latter, which got their name from being dedicated to Duke Albrecht of Prussia, were the work of Erasmus Reinhold, a disciple and follower of Copernicus. Tycho soon mastered the use of these tables, and perceived that the computed places of the planets differed from their actual places in the sky (even though he only inferred the latter from the relative positions of the planets and adjacent stars), the errors of the old Alphonsine tables being much more considerable than those of their new rivals. He even found out that Stadius had not computed his places correctly from Reinhold's tables. And already at that time, while Tycho was a youth only sixteen years of age, his eyes were opened to the great fact, which seems to us so simple to grasp, but which had escaped the attention of all European astronomers before him, that only through a steadily pursued course of observations would it be possible to obtain a better insight into the motions of the planets, and decide which system of the world was the true one. An astronomical phenomenon which took place in August 1563, a conjunction of Saturn and Jupiter, which in those days was looked on as a very important one, owing to the astrological significance it was supposed to have, induced him to begin at once to record his observations, even though they were taken with the crudest implements only. A pair of ordinary compasses was all he had to begin with; by holding the centre close to the eye, and pointing the legs to two stars or a planet and a star, he was able to find their angular distance by afterwards applying the compasses to a circle drawn on paper and divided into degrees and half degrees. His first recorded observation was made on the 17th August 1563, and on the 24th of August in the morning he noted that Saturn and Jupiter were so close together that the interval between them was scarcely visible. The Alphonsine tables turned out to be a whole month in error, while the Prutenic ones were only a few days wrong as to the moment of nearest approach. Tycho continued his observations, partly with the above-mentioned tool, partly using eye-estimations as to which stars formed with a planet a rectangular triangle, or which stars were in a right line with it. But in the following year he provided himself with a "radius," or "cross-staff," as it used to be called in English, one of the few instruments employed by the intrepid navigators who discovered the new worlds beyond the ocean. It consisted of a light graduated rod about three feet long and another rod of about half that length, also graduated, which at the centre could slide along the longer one, so that they always formed a right angle. The instrument could be used in two ways. Two sights might be fixed at the ends of the shorter rod, and one at the end of the longer rod, and the observer, having placed the latter close before his eye, moved the cross-rod along until he saw through its two sights the two objects of which he wanted to measure the angular distance. Or one of the sights of the shorter arm might be movable, and the observer first arbitrarily placed the shorter arm at any of the graduations on the longer one, and then shifted the movable sight along until he saw the two objects through it, and a sight fixed at the centre of the transversal arm. In either case the graduations and a table of tangents furnished the required angle. Tycho's instrument was of the latter kind, and was made according to the directions of Gemma Frisius. He got his friend Bartholomæus Scultetus to subdivide it by means of transversals, which method of subdividing small intervals was then beginning to be used, and which Tycho ascribes to Homilius. The earliest observations stated to have been made with the radius are from the 1st of May 1564, and Tycho says that he had to use it while his tutor was asleep, from which we see that Vedel had even at that time not given up his resistance to his pupil's scientific labours. The observer soon found that the divisions did not give the angles correctly, and as he could not get money from Vedel for a new instrument, he constructed a table of corrections to be applied to the results of his observations. This is deserving of notice as the first indication of that eminently practical talent which was in the course of years to guide the art of observing into the paths in which modern observers have followed. Kepler, who more than any one else was able to appreciate his great predecessor, justly says that the "restoration of astronomy" was "by that Phœnix of astronomers, Tycho, first conceived and determined on in the year 1564."