# A Short History of Astronomy (1898)/Chapter 5

CHAPTER V.
THE RECEPTION OF THE COPPERNICAN THEORY AND THE PROGRESS OF OBSERVATION.
"Preposterous wits that cannot row at ease
On the smooth channel of our common seas;
And such are those, in my conceit at least,
Those clerks that think—think how absurd a jest!—
That neither heavens nor stars do turn at all.
Nor dance about this great round Earthly Ball,
But the Earth itself, this massy globe of ours.
Turns round about once every twice twelve hours!" Du Bartas (Sylvester's translation).
93. The publication of the De Revolutionibus appears to have been received much more quietly than might have been expected from the startling nature of its contents. The book, in fact, was so written as to be unintelligible except to mathematicians of considerable knowledge and ability, and could not have been read at all generally. Moreover the preface, inserted by Osiander but generally supposed to be by the author himself, must have done a good deal to disarm the hostile criticism due to prejudice and custom, by representing the fundamental principles of Coppernicus as mere geometrical abstractions, convenient for calculating the celestial motions. Although, as we have seen (chapter iv., § 73), the contradiction between the opinions of Coppernicus and the common interpretation of various passages in the Bible was promptly noticed by Luther, Melanchthon, and others, no objection was raised either by the Pope to whom the book was dedicated, or by his immediate successors.
The enthusiastic advocacy of the Coppernican views by Rheticus has already been referred to. The only other ​astronomer of note who at once accepted the new views was his friend and colleague Erasmus Reinhold (born at Saalfeld in 1511), who occupied the chief chair of mathematics and astronomy at Wittenberg from 1536 to 1553, and it thus happened, curiously enough, that the doctrines so emphatically condemned by two of the great Protestant leaders were championed principally in what was generally regarded as the very centre of Protestant thought.
94. Rheticus, after the publication of the Narratio Prima and of an Ephemeris or Almanack based on Coppernican principles (1550), occupied himself principally with the calculation of a very extensive set of mathematical tables, which he only succeeded in finishing just before his death in 1576.
Reinhold rendered to astronomy the extremely important service of calculating, on the basis of the De Revolutionibus, tables of the motions of the celestial bodies, which were published in 1551 at the expense of Duke Albert of Prussia and hence called Tabulæ Prutenicæ, or Prussian Tables. Reinhold revised most of the calculations made by Coppernicus, whose arithmetical work was occasionally at fault; but the chief object of the tables was the development in great detail of the work in the De Revolutionibus, in such a form that the places of the chief celestial bodies at any required time could be ascertained with ease. The author claimed for his tables that from them the places of all the heavenly bodies could be computed for the past 3,000 years, and would agree with all observations recorded during that period. The tables were indeed found to be on the whole decidedly superior to their predecessors the Alfonsine Tables (chapter iii., § 66), and gradually came more and more into favour, until superseded three-quarters of a century later by the Rudolphine Tables of Kepler (chapter vii., § 148). This superiority of the new tables was only indirectly connected with the difference in the principles on which the two sets of tables were based, and was largely due to the facts that Reinhold was a much better computer than the assistants of Alfonso, and that Coppernicus, if not a better mathematician than Ptolemy, at any rate had better mathematical tools at command. Nevertheless the ​tables naturally had great weight in inducing the astronomical world gradually to recognise the merits of the Coppernican system, at any rate as a basis for calculating the places of the Celestial bodies.
Reinhold was unfortunately cut off by the plague in 1553, and with him disappeared a commentary on the De Revolutionibus which he had prepared but not published.
95. Very soon afterwards we find the first signs that the Coppernican system had spread into England. In 1556 John Field published an almanack for the following year avowedly based on Coppernicus and Reinhold, and a passage in the Whetstone of Witte (1557) by Robert Recorde (1510–1558), our first writer on algebra, shews that the author regarded the doctrines of Coppernicus with favour, even if he did not believe in them entirely. A few years later Thomas Digges (?–1595), in his Alae sive Scalae Mathematicae (1573), an astronomical treatise of no great importance, gave warm praise to Coppernicus and his ideas.
96. For nearly half a century after the death of Reinhold no important contributions were made to the Coppernican controversy. Reinhold's tables were doubtless slowly doing their work in familiarising men's minds with the new ideas, but certain definite additions to knowledge had to be made before the evidence, for them could be regarded as really conclusive.
The serious mechanical difficulties connected with the assumption of a rapid motion of the earth which is quite imperceptible to its inhabitants could only be met by further progress in mechanics, and specially in knowledge of the laws according to which the motion of bodies is produced, kept up, changed, or destroyed; in this direction no considerable progress was made before the time of Galilei, whose work falls chiefly into the early 17th century (cf. chapter vi., §§ 116, 130, 133).
The objection to the Coppernican scheme that the stars shewed no such apparent annual motions as the motion of the earth should produce (chapter iv., § 92) would also be either answered or strengthened according as improved methods of observation did or did not reveal the required motion.
Moreover the Prussian Tables, although more accurate ​than the Alfonsine, hardly claimed, and certainly did not possess, minute accuracy. Coppernicus had once told Rheticus that he would be extravagantly pleased if he could make his theory agree with observation to within 10'; but as a matter of fact discrepancies of a much more serious character were noticed from time to time. The comparatively small number of observations available and their roughness made it extremely difficult, either to find the most satisfactory numerical data necessary for the detailed development of any theory, or to test the theory properly by comparison of calculated with observed places of the celestial bodies. Accordingly it became evident to more than one astronomer that one of the most pressing needs of the science was that observations should be taken on as large a scale as possible and with the utmost attainable accuracy. To meet this need two schools of observational astronomy, of very unequal excellence, developed during the latter half of the 16th century, and provided a mass of material for the use of the astronomers of the next generation. Fortunately too the same period was marked by rapid progress in algebra and allied branches of mathematics. Of the three great inventions which have so enormously diminished the labour of numerical calculations, one, the so-called Arabic notation (chapter iii., § 64), was already familiar, the other two (decimal fractions and logarithms) were suggested in the 16th century and were in working order early in the 17th century.
97. The first important set of observations taken after the death of Regiomontanus and Walther (chapter iii., § 68) were due to the energy of the Landgrave William IV. of Hesse (1532-1592). He was remarkable as a boy for his love of study, and is reported to have had his interest in astronomy created or stimulated when he was little more than 20 by a copy of Apian's beautiful Astronomicum Caesareum, the cardboard models in which he caused to be imitated and developed in metal-work. He went on with the subject seriously, and in 1561 had an observatory built at Cassel, which was remarkable as being the first which had a revolving roof, a device now almost universal. In this he made extensive observations (chiefly of fixed stars) during the next six years. The death of his father then compelled ​him to devote most of his energy to the duties of government, and his astronomical ardour abated. A few years later, however (1575), as the result of a short visit from the talented and enthusiastic young Danish astronomer Tycho Brahe (§ 99), he renewed his astronomical work, and secured shortly afterwards the services of two extremely able assistants. Christian Rothmann (in 1577) and joost Bürgi (in 1579). Rothmann, of whose life extremely little is known, appears to have been a mathematician and theoretical astronomer of considerable ability, and was the author of several improvements in methods of dealing with various astronomical problems. He was at first a Coppernican, but shewed his independence by calling attention to the needless complication introduced by Coppernicus in resolving the motion of the earth into three motions when two sufficed (chapter iv., § 79). His faith in the system was, however, subsequently shaken by the errors which observation revealed in the Prussian Tables. Bürgi (1552–1632) was originally engaged by the Landgrave as a clockmaker, but his remarkable mechanical talents were soon turned to astronomical account, and it then appeared that he also possessed unusual ability as a mathematician.
98. The chief work of the Cassel Observatory was the formation of a star catalogue. The positions of stars were compared with that of the sun, Venus or Jupiter being used as connecting links, and their positions relatively to the equator and the first point of Aries (♈︎) deduced; allowance was regularly made for the errors due to the refraction of light by the atmosphere, as well as for the parallax of the sun, but the most notable new departure was the use of a clock to record the time of observations and to measure the motion of the celestial sphere. The construction of clocks of sufficient accuracy for the purpose was rendered possible by the mechanical genius of Bürgi, and in particular by his discovery that a clock could be regulated by a pendulum, a discovery which he ​appears to have taken no steps to publish, and which had in consequence to be made again independently before it received general recognition. By 1586 121 stars had been carefully observed, but a more extensive catalogue which was to have contained more than a thousand stars was never finished, owing to the unexpected disappearance of Rothmann in 1590 and the death of the Landgrave two years later.
99. The work of the Cassel Observatory was, however, overshadowed by that carried out nearly at the same time by Tycho (Tyge) Brahe. He was born in 1546 at Knudstrup in the Danish province of Scania (now the southern extremity of Sweden), being the eldest child of a nobleman who was afterwards governor of Helsingborg Castle. He was adopted as an infant by an uncle, and brought up at his country estate. When only 13 he went to the University of Copenhagen, where he began to study rhetoric and philosophy, with a view to a political career. He was, however, very much interested by a small eclipse of the sun which he saw in 1560, and this stimulus, added to some taste for the astrological art of casting horoscopes, led him to devote the greater part of the remaining two years spent at Copenhagen to mathematics and astronomy. In 1562 he went on to the University of Leipzig, accompanied, according to the custom of the time, by a tutor, who appears to have made persevering but unsuccessful attempts to induce his pupil to devote himself to law. Tycho, however, was now as always a difficult person to divert from his purpose, and went on steadily with his astronomy. In 1563 he made his first recorded observation,, of a close approach of Jupiter and Saturn, the time of which he noticed to be predicted a whole month wrong by the Alfonsine Tables (chapter iii., § 66), while the Prussian Tables (§ 94) were several days in error. While at Leipzig he bought also a few rough instruments, and anticipated one of the great improvements afterwards carried out systematically, ​by trying to estimate and to allow for the errors of his instruments.
In 1565 Tycho returned to Copenhagen, probably on account of the war with Sweden which had just broken out, and stayed about a year, during the course of which he lost his uncle. He then set out again (1566) on his travels, and visited Wittenberg, Rostock, Basle, Ingolstadt, Augsburg, and other centres of learning, thus making acquaintance with several of the most notable astronomers of Germany. At Augsburg he met the brothers Hainzel, rich citizens with a taste for science, for one of whom he designed and had constructed an enormous quadrant (quarter-circle) with a radius of about 19 feet, the rim of which was graduated to single minutes and he began also here the construction of his great celestial globe, five feet in diameter, on which he marked one by one the positions of the stars as he afterwards observed them.
In 1570 Tycho returned to his father at Helsingborg, and soon after the death of the latter (1571) went for a long visit to Steen Bille, an uncle with scientific tastes. During this visit he seems to have devoted most of his time to chemistry (or perhaps rather to alchemy), and his astronomical studies fell into abeyance for a time.
100. His interest in astronomy was fortunately revived by the sudden appearance, in November 1572, of a brilliant new star in the constellation Cassiopeia. Of this Tycho took a number of extremely careful observations; he noted the gradual changes in its brilliancy from its first appearance, when it rivalled Venus at her brightest, down to its final disappearance 16 months later. He repeatedly measured its angular distance from the chief stars in Cassiopeia, and applied a variety of methods to ascertain whether it had any perceptible parallax (chapter ii., §§ 43, 49). No parallax could be definitely detected, and he deduced accordingly that the star must certainly be farther off than the moon; as moreover it had no share in the planetary motions, he inferred that it must belong to the region of the fixed stars. To us of to-day this result may appear fairly commonplace, but most astronomers of the time held so firmly to Aristotle's doctrine that the heavens generally, and the region of the fixed stars in particular, were incorruptible and ​unchangeable, that new stars were, like comets, almost universally ascribed to the higher regions of our own atmosphere. Tycho wrote an account of the new star, which he was ultimately induced by his friends to publish (1573), together with some portions of a calendar for that year which he had prepared. His reluctance to publish appears to have been due in great part to a belief that it was unworthy of the dignity of a Danish nobleman to write books! The book in question (De Nova . . . Stella) compares very favourably with the numerous other writings which the star called forth, though it shews that Tycho held the common beliefs that comets were in our atmosphere, and that the planets were carried round by solid crystalline spheres, two delusions which his subsequent work did much to destroy. He also dealt at some length with the astrological importance of the star, and the great events which it foreshadowed, utterances on which Kepler subsequently made the very sensible criticism that "if that star did nothing else, at least it announced and produced a great astronomer."
In 1574 Tycho was requested to give some astronomical lectures at the University of Copenhagen, the first of which, dealing largely with astrology, was printed in 1610, after his death. When these were finished, he set off again on his travels (1575). After a short visit to Cassel (§ 97), during which he laid the foundation of a lifelong friendship with the Landgrave, he went on to Frankfort to buy books, thence to Basle (where he had serious thoughts of settling) and on to Venice, then back to Augsburg and to Regensburg, where he obtained a copy of the Commentariolus of Coppernicus (chapter iv., § 73), and finally came home by way of Saalfeld and Wittenberg.
The buildings were as remarkable for their magnificence as for their scientific utility. Tycho never forgot that he was a Danish nobleman as well as an astronomer, and built in a manner suitable to his rank. His chief building (fig. 51), called Uraniborg (the Castle of the Heavens), was in the middle of a large square enclosure, laid out as a garden, the corners of which pointed North, East, South, and West, and contained several observatories, a library and laboratory, in addition to living rooms. Subsequently, when the number of pupils and assistants who came to him had increased, he erected (1584) a second building, Stjerneborg (Star Castle), which was remarkable for having underground observatories. The convenience of being able to carry out all necessary work on his own premises induced him moreover to establish workshops, where nearly all his instruments were made, and afterwards also a printing press and paper mill. Both at Uraniborg and Stjerneborg not only the rooms, but even the instruments which were gradually constructed, were elaborately painted or otherwise ornamented.
102. The expenses of the establishment must have been enormous, particularly as Tycho lived in magnificent style and probably paid little attention to economy. His income was derived from various sources, and fluctuated from time to time, as the King did not merely make him a fixed annual payment, but added also temporary grants of lands or money. Amongst other benefactions he received in 1579 one of the canonries of the cathedral of Roskilde, the endowments of which had been practically secularised at the Reformation. Unfortunately most of his property was held on tenures which involved corresponding obligations, and as he combined the irritability of a genius with the haughtiness of a mediaeval nobleman, continual quarrels were the result. Very soon after his arrival at ​Hveen his tenants complained of work which he illegally forced from them; chapel services which his canonry required him to keep up were neglected, and he entirely refused to make certain recognised payments to the widow of the previous canon. Further difficulties arose out of a lighthouse, the maintenance of which was a duty attached to one of his estates, but was regularly neglected. Nothing shews the King's good feeling towards Tycho more than the trouble which he took to settle these quarrels, often ending by paying the sum of money under dispute. Tycho was moreover extremely jealous of his scientific reputation, and on more than one occasion broke out into violent abuse of some assistant or visitor whom he accused of stealing his ideas and publishing them elsewhere.
In addition to the time thus spent in quarrelling, a good deal must have been occupied in entertaining the numerous visitors whom his fame attracted, and who included, in addition to astronomers, persons of rank such as several of the Danish royal family and James VI. of Scotland (afterwards James I. of England).
Notwithstanding these distractions, astronomical work made steady progress, and during the 21 years that Tycho spent at Hveen he accumulated, with the help of pupils and assistants, a magnificent series of observations, far transcending in accuracy and extent anything that had been accomplished by his predecessors. A good deal of attention was also given to alchemy, and some to medicine. He seems to have been much impressed with the idea of the unity of Nature, and to have been continually looking out for analogies or actual connection between the different subjects which he studied.
103. In 1577 appeared a brilliant comet, which Tycho observed with his customary care; and, although he had not at the time his full complement of instruments, his observations were exact enough to satisfy him that the comet was at least three times as far off as the moon, and thus to refute the popular belief, which he had himself held a few years before (§ 100), that comets were generated in our atmosphere. His observations led him also to the belief that the comet was revolving round the sun, at a distance from it greater than that of Venus, a conclusion ​which interfered seriously with the common doctrine of the solid crystalline spheres. He had further opportunities of observing comets in 1580, 1582, 1585, 1590, and 1596, and one of his pupils also took observations of a comet seen in 1593. None of these comets attracted as much general attention as that of 1577, but Tycho's observations, as was natural, gradually improved in accuracy.
104. The valuable results obtained by means of the new star of 1572, and by the comets, suggested the propriety of undertaking a complete treatise on astronomy embodying these and other discoveries. According to the original plan, there were to be three preliminary volumes devoted respectively to the new star, to the comet of 1577, and to the later comets, while the main treatise was to consist of several more volumes dealing with the theories of the sun, moon, and planets. Of this magnificent plan comparatively little was ever executed. The first volume, called the Astronomiae Instauratae Progymnasmata, or Introduction to the New Astronomy, was hardly begun till 1588, and, although mostly printed by 1592, was never quite finished during Tycho's lifetime, and was actually published by Kepler in 1602. One question, in fact, led to another in such a way that Tycho felt himself unable to give a satisfactory account of the star of 1572 without dealing with a number of preliminary topics, such as the positions of the fixed stars, precession, and the annual motion of the sun, each of which necessitated an elaborate investigation. The second volume, dealing with the comet of 1577, called De Mundi aetherei recentioribus Phaenomenis Liber secundus (Second book about recent appearances in the Celestial World), was finished long before the first, and copies were sent to friends and correspondents in 1588, though it was not regularly published and on sale till 1603. The third volume was never written, though some material was collected for it, and the main treatise does not appear to have been touched.
105. The book on the comet of 1577 is of special interest, as containing an account of Tycho's system of the world, which was a compromise between those of Ptolemy and of Coppernicus. Tycho was too good an astronomer not to realise many of the simplifications which the ​Coppernican system introduced, but was unable to answer two of the serious objections; he regarded any motion of
"the sluggish and heavy earth" as contrary to "physical principles," and he objected to the great distance of the ​stars which the Coppernican system required, because a vast empty space would be left between them and the planets, a space which he regarded as wasteful. Biblical difficulties also had some weight with him. He accordingly devised (1583) a new system according to which the five planets revolved round the sun (c, in fig. 52), while the sun revolved annually round the earth (a), and the whole celestial sphere performed also a daily revolution round the earth. The system was never worked out in detail, and, like many compromises, met with little support; Tycho nevertheless was extremely proud of it, and one of the most violent and prolonged quarrels of his life (lasting a dozen years) was with Reymers Bär or Ursus (?-1600), who had communicated to the Landgrave in 1586 and published two years later a system of the world very like Tycho's. Reymers had been at Hveen for a short time in 1584, and Tycho had no hesitation in accusing him of having stolen the idea from some manuscript seen there. Reymers naturally retaliated with a counter-charge of theft against Tycho. There is, how ever, no good reason why the idea should not have occurred independently to each astronomer; and Reymers made in some respects a great improvement on Tycho's scheme by accepting the daily rotation of the earth, and so doing away with the daily rotation of the celestial sphere, which was certainly one of the weakest parts of the Ptolemaic scheme.
TYCHO BRAHE.[To face p. 139.
​their effect. In 1594 he lost one of his chief supporters at court, the Chancellor Kaas, and his successor, as well as two or three other important officials at court, were not very friendly, although the stories commonly told of violent personal animosities appear to have little foundation. As early as 1591 Tycho had hinted to a correspondent that he might not remain permanently in Denmark, and in 1594 he began a correspondence with representatives of the Emperor Rudolph II., who was a patron of science. But his scientific activity during these years was as great as ever; and in 1596 he completed the printing of an extremely interesting volume of scientific correspondence between the Landgrave, Rothmann, and himself. The accession of the young King to power in 1596 was at once followed by the withdrawal of one of Tycho's estates, and in the following year the annual payment which had been made since 1576 was stopped. It is difficult to blame the King for these economies; he was evidently not as much interested in astronomy as his father, and consequently regarded the heavy expenditure at Hveen as an extravagance, and it is also probable that he was seriously annoyed at Tycho's maltreatment of his tenants, and at other pieces of unruly conduct on his part. Tycho, however, regarded the forfeiture of his annual pension as the last straw, and left Hveen early in 1597, taking his more portable property with him. After a few months spent in Copenhagen, he took the decisive step of leaving Denmark for Germany, in return for which action the King deprived him of his canonry. Tycho thereupon wrote a remonstrance in which he pointed out the impossibility of carrying on his work without proper endowments, and offered to return if his services were properly appreciated. The King, however, was by this time seriously annoyed, and his reply was an enumeration of the various causes of complaint against Tycho which had arisen of late years. Although Tycho made some more attempts through various friends to regain royal favour, the breach remained final.
107. Tycho spent the winter 1597-8 with a friend near Hamburg, and, while there, issued, under the title of Astronomiae Instauratae Mechanica, a description of his instruments, together with a short autobiography and an ​interesting account of his chief discoveries. About the same time he circulated manuscript copies of a catalogue of 1,000 fixed stars, of which only 777 had been properly observed, the rest having been added hurriedly to make up the traditional number. The catalogue and the Mechanica were both intended largely as evidence of his astronomical eminence, and were sent to various influential persons. Negotiations went on both with the Emperor and with the Prince of Orange, and after another year spent in various parts of Germany, Tycho definitely accepted an invitation of the Emperor and arrived at Prague in June 1599.
108. It was soon agreed that he should inhabit the castle of Benatek, some twenty miles from Prague, where he accordingly settled with his family and smaller instruments towards the end of 1599. He at once started observing, sent one of his sons to Hveen for his larger instruments, and began looking about for assistants. He secured one of the most able of his old assistants, and by good fortune was also able to attract a far greater man, John Kepler, to whose skilful use of the materials collected by Tycho the latter owes no inconsiderable part of his great reputation. Kepler, whose life and work will be dealt with at length in chapter vii., had recently published his first important work, the Mysterium Cosmographicum (§ 136), which had attracted the attention of Tycho among others, and was beginning to find his position at Gratz in Styria uncomfortable on account of impending religious disputes. After some hesitation he joined Tycho at Benatek early in 1600. He was soon set to work at the study of Mars for the planetary tables which Tycho was then preparing, and thus acquired special familiarity with the observations of this planet which Tycho had accumulated. The relations of the two astronomers were not altogether happy, Kepler being then as always anxious about money matters, and the disturbed state of the country rendering it difficult for Tycho to get payment from the Emperor. Consequently Kepler very soon left Benatek and returned to Prague, where he definitely settled after a short visit to Gratz; Tycho also moved there towards the end of 1600, and they then worked together harmoniously for ​the short remainder of Tycho's life. Though he was by no means an old man, there were some indications that his health was failing, and towards the end of 1601 he was suddenly seized with an illness which terminated fatally after a few days (November 24th). It is characteristic of his devotion to the great work of his life that in the delirium which preceded his death he cried out again and again his hope that his life might not prove to have been fruitless (Ne frustra vixisse videar).
109. Partly owing to difficulties between Kepler and one of Tycho's family, partly owing to growing political disturbances, scarcely any use was made of Tycho's instruments after his death, and most of them perished during the Civil Wars in Bohemia. Kepler obtained possession of his observations; but they have never been published except in an imperfect form.
110. Anything like a satisfactory account of Tycho's services to astronomy would necessarily deal largely with technical details of methods of observing, which would be out of place here. It may, however, be worth while to attempt to give some general account of his characteristics as an observer before referring to special discoveries.
Tycho realised more fully than any of his predecessors the importance of obtaining observations which should not only be as accurate as possible, but should be taken so often as to preserve an almost continuous record of the positions and motions of the celestial bodies dealt with; whereas the prevailing custom (as illustrated for example by Coppernicus) was only to take observations now and then, either when an astronomical event of special interest such as an eclipse or a conjunction was occurring, or to supply some particular datum required for a point of theory. While Coppernicus, as has been already noticed (chapter iv., § 73), only used altogether a few dozen observations in his book, Tycho—to take one instance—observed the sun daily for many years, and must therefore have taken some thousands of observations of this one body, in addition to the many thousands which he took of other celestial bodies. It is true that the Arabs had some idea of observing continuously (cf. chapter iii., § 57), but they had too little ​speculative power or originality to be able to make much use of their observations, few of which passed into the hands of European astronomers. Regiomontanus (chapter iii., § 68), if he had lived, might probably have to a considerable extent anticipated Tycho, but his short life was too fully occupied with the study and interpretation of Greek astronomy for him to accomplish very much in other departments of the subject. The Landgrave and his staff, who were in constant communication with Tycho, were working in the same direction, though on the whole less effectively. Unlike the Arabs, Tycho was, however, fully impressed with the idea that observations were only a means to an end, and that mere observations without a hypothesis or theory to connect and interpret them were of little use.
The actual accuracy obtained by Tycho in his observations naturally varied considerably according to the nature of the observation, the care taken, and the period of his career at which it was made. The places which he assigned to nine stars which were fundamental in his star catalogue differ from their positions as deduced from the best modern observations by angles which are in most cases less than 1', and in only one case as great as 2' (this error being chiefly due to refraction (chapter ii., § 46), Tycho's knowledge of which was necessarily imperfect). Other star places were presumably less accurate, but it will not be far from the truth if we assume that in most cases the errors in Tycho's observations did not exceed 1' or 2'. Kepler in a famous passage speaks of an error of 8' in a planetary observation by Tycho as impossible. This great increase in accuracy can only be assigned in part to the size and careful construction of the instruments used, the characteristics on which the Arabs and other observers had laid such stress. Tycho certainly used good instruments, but added very much to their efficiency, partly by minor mechanical devices, such as the use of specially constructed "sights" and of a particular method of graduation, and partly by using instruments capable only of restricted motions, and therefore of much greater steadiness than instruments which were able to point to any part of the sky. Another extremely important idea ​was that of systematically allowing as far as possible for the inevitable mechanical imperfections of even the best constructed instruments, as well as for other permanent causes of error. It had been long known, for example, that the refraction of light through the atmosphere had the effect of slightly raising the apparent places of stars in the sky. Tycho took a series of observations to ascertain the amount of this displacement for different parts of the sky, hence constructed a table of refractions (a very imperfect one, it is true), and in future observations regularly allowed for the effect of refraction. Again, it was known that observations of the sun and planets were liable to be disturbed by the effect of parallax (chapter ii., §§ 43, 49), though the amount of this correction was uncertain. In cases where special accuracy was required, Tycho accordingly observed the body in question at least twice, choosing positions in which parallax was known to produce nearly opposite effects, and thus by combining the observations obtained a result nearly free from this particular source of error. He was also one of the first to realise fully the importance of repeating the same observation many times under different conditions, in order that the various accidental sources of error in the separate observations should as far as possible neutralise one another.
111. Almost every astronomical quantity of importance was re-determined and generally corrected by him. The annual motion of the sun's apogee relative to ♈︎, for example, which Coppernicus had estimated at 24", Tycho fixed at 45", the modern value being 61"; the length of the year he determined with an error of less than a second; and he constructed tables of the motion of the sun which gave its place to within 1', previous tables being occasionally 15' or 20' wrong. By an unfortunate omission he made no inquiry into the distance of the sun, but accepted the extremely inaccurate value which had been handed down, without substantial alteration, from astronomer to astronomer since the time of Hipparchus (chapter ii., § 41).
In the theory of the moon Tycho made several important discoveries. He found that the irregularities in its movement were not fully represented by the equation of the centre and the evection (chapter ii., §§ 39, 48), but that ​there was a further irregularity which vanished at opposition and conjunction as well as at quadratures, but in intermediate positions of the moon might be as great as 40'. This irregularity, known as the variation, was, as has been already mentioned (chapter iii., § 60), very possibly discovered by Abul Wafa, though it had been entirely lost subsequently. At a later stage in his career, at latest during his visit to Wittenberg in 1598-9, Tycho found that it was necessary to introduce a further small inequality known as the annual equation, which depended on the position of the earth in its path round the sun; this, however, he never completely investigated. He also ascertained that the inclination of the moon's orbit to the ecliptic was not, as had been thought, fixed, but oscillated regularly, and that the motion of the moon's nodes (chapter ii., § 40) was also variable.
112. Reference has already been made to the star catalogue. Its construction led to a study of precession, the amount of which was determined with considerable accuracy; the same investigation led Tycho to reject the supposed irregularity in precession which, under the name of trepidation (chapter iii., § 58), had confused astronomy for several centuries, but from this time forward rapidly lost its popularity.
The planets were always a favourite subject of study with Tycho, but although he made a magnificent series of observations, of immense value to his successors, he died before he could construct any satisfactory theory of the planetary motions. He easily discovered, however, that their motions deviated considerably from those assigned by any of the planetary tables, and got as far as detecting some regularity in these deviations.
* ↑ There is little doubt that he invented what were substantially legarithms independently of Napier, but, with characteristic inability or unwillingness to proclaim his discoveries, allowed the invention to die with him.
* ↑ A similar discovery was in fact made twice again, by Galilei (chapter vi., § 114) and by Huygens (chapter viii., § 157).
* ↑ He obtained leave of absence to pay a visit to Tycho Brahe and never returned to Cassel. He must have died between 1599 and 1608.
* ↑ He even did not forget to provide one of the most necessary parts of a mediæval castle, a prison!
* ↑ It would be interesting to know what use he assigned to the (presumably) still vaster space beyond the stars.
* ↑ Tycho makes in this connection the delightful remark that Moses must have been a skilled astronomer, because he refers to the moon as "the lesser light," notwithstanding the fact that the apparent diameters of sun and moon are very nearly equal!
* ↑ By transversals.