Tycho Brahe: a picture of scientific life and work in the sixteenth century/Chapter 7

by John Louis Emil Dreyer

 

CHAPTER VII.

TYCHO'S BOOK ON THE COMET OF 1577, AND HIS SYSTEM OF THE WORLD.

The year 1588 is one of great importance in the life of Tycho Brahe, not only because his firm friend and benefactor died in that year, but also because he then published a volume containing some of the results of his work at Uraniborg, and embodying his views on the construction of the universe. The subject specially dealt with in this volume was the great comet of 1577, the most conspicuous of the seven comets observed in his time.

This comet was first noticed by Tycho on the 13th November 1577, but it had already been seen in Peru on the 1st, and in London on the 2nd November.^[1] On the evening of the 13th, a little before sunset, Tycho was engaged at one of his fishponds, trying to catch some fish for supper, when he remarked a very brilliant star in the west, which he would have taken for Venus if he had not known that this planet was at that time west of the sun. Soon after sunset a splendid tail, 22° in length, revealed itself, and showed that a new comet had appeared. It was situated just above the head of Sagittarius, with the slightly curved tail pointing towards the horns of Capricornus, and it moved towards Pegasus, in which constellation it was last seen on the 26th January 1578. During the time it was visible Tycho observed it diligently, measuring with a radius and a sextant the distance of the head from various fixed stars, and occasionally also with a quadrant furnished with an azimuth circle (four feet in diameter), the altitude and azimuth of the comet. The sextant, which afterwards was placed in the large northern observing room at Uraniborg,^[2] was constructed on the same principle as the one which Tycho had made at Augsburg in 1569, and was mounted on a convenient stand, which enabled the observer to place it in any plane he liked; the arms were about four feet long. The quadrant was about 32 inches in semi-diameter, and the arc was graduated both by the transversals nearly always employed by Tycho, and by the concentric circles on the plan proposed by Nunez; and on the back of the quadrant was a table, by means of which the readings of the latter could be converted into minutes without calculation.^[3] When observing this comet, Tycho had not yet at his disposal as many instruments and observers as in after years, nor had he as yet perceived the necessity of accurate daily time determinations by observing altitudes of stars, but merely corrected his clocks by sunset.^[4] The observations of this comet cannot therefore compare in accuracy with his later ones, but still they were immeasurably superior to those made by other observers, and they demonstrated most decisively that the comet had no perceptible parallax, and was consequently very far above the "elementary sphere" to which the Aristotelean philosophy had consigned all comets as mere atmospherical phenomena. By showing that the star of 1572 was situated among the stars, Tycho had already dealt the Aristoteleans a heavy blow, as it was now clear that new bodies could appear in the æthereal regions. But still that star was not a comet, and Tycho, who had formerly believed in the atmospherical origin of comets, now took the opportunity of testing this matter, and found that the comet had no appreciable daily parallax. Though he was not the only observer who placed the comet beyond the moon, his observations were known by his contemporaries to be of very superior accuracy, and his authority was so great that this question was decided once for all.^[5]

Before proceeding to pass in review the book which Tycho prepared on this comet, we shall shortly allude to the other comets observed at Hveen. On the 10th October 1580 Tycho found a comet in the constellation Pisces. It was observed at Hveen till the 25th November, and again after the perihelium passage on the morning of the 13th December. The observations are more numerous and better than those of the previous comet, and time determinations with a quadrant were made nearly every night, while there are very few quadrant observations of the comet. Moestlin had seen it already on the 2nd October, and both he and Hagecius observed it assiduously, but their observations are worthless compared with Tycho's.^[6] The next comet was visible in May 1582, and was observed by Tycho on three nights only, the 12th, 17th, and 18th, after which date the strong twilight prevented further observations; but in Germany it was still seen on the 23rd, and in China it was seen for twenty days after the 20th May.^[7] Of greater interest are the observations of the comet of 1585, which appeared at a time when Tycho's collection of instruments was complete, and when he was surrounded by a staff of assistants. The comet was first seen by Tycho on the 18th October after a week of cloudy weather, but at Cassel it had already been seen on the 8th (st. v.).^[8] Tycho compares its appearance when it was first seen with the cluster (or nebula, as it was then called) Præsepe Cancri, without any tail. The observations are very numerous, and were made partly with a sextant, partly with the large armillæ at Stjerneborg, with which newly-acquired instrument the declinations of the comet and the difference of right ascension with various bright stars were observed at short intervals on every clear night up to the 12th November. The excellence of the observations and the care with which the instruments were treated are fully demonstrated by the most valuable memoir on this comet by C. A. F. Peters.^[9] We have already mentioned that this comet gave rise to the correspondence between Tycho and the Landgrave and Rothmann. The next comet appeared in 1590, and was observed from the 23rd February to the 6th March inclusive, the declination with the armillæ, altitudes and azimuths with a quadrant, and distances with a sextant. The time determinations are numerous.^[10] In July and August 1593 a comet appeared near the northern horizon. It was not observed at Hveen, but only by a former pupil of Tycho's, Christen Hansen, from Ribe in Jutland, who at that time was staying at Zerbst in Anhalt. He had only a radius with him, and his observations were therefore not better than those made by the generality of observers in those days.^[11] The last comet observed at Hveen was that of 1596, which was first seen by Tycho at Copenhagen on the 14th July, south of the Great Bear. It was not properly observed till after his return home on the 17th, and then only on three nights. It was last seen on the 27th July.^[12]

The star of 1572 and the comets observed at Hveen had cleared the way for the restoration of astronomy by helping to destroy old prejudices, and Tycho therefore resolved to write a great work on these recent phenomena which should embody all results of his observations in any way bearing on them. The first volume he devoted to the new star, but as the corrected star places which were necessary for the reduction of the observations of 1572–73 involved researches on the motion of the sun, on refraction, precession, &c., the volume gradually assumed greater proportions than was originally contemplated, and was never quite finished in Tycho's lifetime. On account of the wider scope of its contents he gave it the title Astronomiæ Instauratæ Progymnasmata, or Introduction to the New Astronomy, a title which marks the work as paving the way for the new planetary theory and tables which Tycho had hoped to prepare, but which it fell to Kepler's lot to work out in a very different manner from that contemplated by Tycho. The second volume was devoted to the comet of 1577, and as the subject did not lead to the introduction of extraneous matter, this volume was finished long before the first one. The third volume was in a similar manner to treat of the comets of 1580 and following years, but it was never published, nor even written, though a great deal of material about the comet of 1585 was put together and first published in 1845 with the observations of this comet.^[13]

The two volumes about the new star and the comet of 1577 were printed in Tycho's own printing-office at Uraniborg, and after some delay caused by want of paper, the second volume was completed in 1588.^[14] The title is "Tychonis Brahe Dani, De Mundi ætherei recentioribus phænomenis Liber secundus, qui est de illustri stella caudata ab elapso fere triente Nouembris anno mdlxxvii usque in finem Januarii sequentis conspecta. Vraniburgi cum Privilegio." The book is in demy 4to, 465 pp., and the colophon is the vignette "Svspiciendo Despicio," with the words underneath "Uranibvrgi In Insula Hellesponti Danici Hvenna imprimebat Authoris Typographus Christophorus Weida. Anno Domini mdlxxxviii."

The book is divided into ten chapters. The first contains most of the observations of the comet; the second deduces new positions for the twelve fixed stars from which the distance of the comet had been measured. Tycho mentions that while the comet was visible he had not yet any armillæ, and he therefore carefully placed a quadrant in the meridian, and thus determined the declination of the star, and by the time of transit (through the medium of the moon and the tabular place of the sun) also the right ascension. He does not give any particulars about the observations and method, but he goes through the computations of the latitude and longitude of each star from the right ascension, declination and the point of the ecliptic culminating with the star. In a note at the end of the chapter he gives improved star places from the later observations with better instruments and methods, and, as might be expected, these later results are really much better than those found in 1578.^[15] In the third chapter the longitude and latitude of the comet for each day of observation are deduced from the observed distances from stars; but though he gives diagrams of all the triangles, and gives all the numerical data, the trigonometrical process is not shown. In the fourth chapter the right ascensions and declinations of the comet are computed from the longitudes and latitudes.^[16] The fifth deals with the determination of the inclination and node of the apparent path of the comet with regard to the ecliptic, which Tycho found from two latitudes and the arc of the ecliptic between them; seven different combinations give results which only differ a few minutes inter se. The sixth chapter is a more lengthy one, and treats of the distance of the comet from the earth; and as this was of paramount importance as a test of the Aristotelean doctrine, he endeavours to determine the parallax in several different ways. First, he shows that the comet had moved in a great circle, and though not with a uniform velocity throughout, yet with a very gradually decreasing one; and if it had been a mere "meteor" in our atmosphere, it would have moved by fits and starts, and not in a great circle. The velocity never reached half that of the moon, the nearest celestial body. He next discusses two distance measures from ε Pegasi, made on the 23rd November, with an interval of three hours, and finds that if the comet had been at the same distance from the earth as the moon,^[17] the parallax would have had the effect of making the second angular distance from the star equal to the first, even after allowing for the motion of the comet in the interval, while the second observed distance was 12′ smaller than the first one. At least the comet must have been at a distance six times as great as that of the moon, and all that can be concluded from the distance measures is that the comet was far beyond the moon, and at such a distance that its parallax could not be determined accurately. The same appears from comparisons between distance measures from stars made at Hveen and those made at Prague by Hagecius, which should differ six or seven minutes if the comet was as near as the moon, whereas they only differed one or two minutes. The observations of Cornelius Gemma at Lou vain, when compared with those at Hveen, point in the same direction, but are much too inaccurate to build on. Again, Tycho takes two observations of altitude and azimuth; from the first he computes the declination, corrects this for the motion of the comet in the interval, and with this and the second azimuth computes the altitude for the time of the second observation. For a body as near as the moon there would be a considerable difference, while several examples show none. Finally, Tycho employs the method of Regiomontanus for finding the actual amount of parallax from two altitudes and azimuths, but several combinations gave the same result, that no parallax whatever could be detected in this way. Tycho was well aware that this was a bad method, and evidently only tried it as a duty.^[18] (The comet of 1585 was chiefly observed with the large armillæ, and the want of parallax was demonstrated by comparing the right ascension and declination observed with an interval of some hours with the daily motion of the comet.^[19])

In the seventh chapter the position of the comet's tail is examined. The increased attention which had been paid to comets during the sixteenth century had led to the discovery of the fact that their tails are turned away from the sun, and not only Peter Apianus, who is generally credited with the discovery, but also Fracastoro, and after them Gemma and Cardan, had pointed out this remarkable fact from observations of different comets. Tycho, who took nothing on trust, examined the matter, and computed from twelve observations of the direction of the tail of the comet of 1577 the position of the tail with regard to a great circle passing through the sun. He found that the direction of the tail never passed exactly through the sun, but seemed to pass much nearer to the planet Venus; he adds, that though the statement of Apianus was only approximately true, the opinion of Aristotle was far more erroneous, for according to him, the tails, as lighter than the head, should be turned straight away from the centre of the earth. The curvature he considers merely an illusion, caused by the head and the end of the tail being at different distances from the earth.

The eighth chapter is the most important in the whole book, as the consideration of the comet's orbit in space leads Tycho to explain his ideas about the construction of the universe. The "æthereal world," he says, is of wonderfully large extent; the greatest distance of the farthest planet, Saturn, is two hundred and thirty-five times as great as the semi-diameter of the "elementary world" as bordered by the orbit of the moon. The moon's distance he assumes equal to fifty-two times the semi-diameter of the earth, which latter he takes to be 860 German miles.^[20] The distance of the sun he believes to be about twenty times that of the moon. In this vast space the comet has moved, and it therefore becomes necessary to explain shortly the system of the world, which he had worked out "four years ago," i.e., in 1583.^[21] The Ptolemean system was too complicated, and the new one which that great man Copernicus had proposed, following in the footsteps of Aristarchus of Samos, though there was nothing in it contrary to mathematical principles, was in opposition to those of physics, as the heavy and sluggish earth is unfit to move, and the system is even opposed to the authority of Scripture. The vast space which would have to be assumed between the orbit of Saturn and the fixed stars (to account for the want of annual parallax of these), was another difficulty in the Copernican system, and Tycho had therefore tried to find a hypothesis which was in accordance with mathematical and physical principles, and at the same time would not incur the censure of theologians. At last he had, "as if by inspiration," been led to the following idea on the planetary motions.

The Tychonic System of the World.

The earth is the centre of the universe, and the centre of the orbits of the sun and moon, as well as of the sphere of the fixed stars, which latter revolves round it in twenty-four hours, carrying all the planets with it. The sun is the centre of the orbits of the five planets, of which Mercury and Venus move in orbits whose radii are smaller than that of the solar orbit, while the orbits of Mars, Jupiter, and Saturn encircle the earth. This system accounts for the irregularities in the planetary motions which the ancients explained by epicycles and Copernicus by the annual motion of the earth, and it shows why the solar motion is mixed up in all the planetary theories.^[22] The remaining inequalities, which formerly were explained by the excentric circle and the deferent, and by Copernicus by epicycles moving on excentric circles, could also, in the new hypothesis, be explained in a similar way. As the planets are not attached to any solid spheres, there is no absurdity in letting the orbits of Mars and the sun intersect each other, as the orbits are nothing real, but only geometrical representations.

This is all which Tycho considered it necessary to set forth about his system in the book on the comet, but he stated his intention of giving a fuller account of it on a future occasion, which never came. We shall finish our account of his labours connected with the comet of 1577 before we consider his system a little more closely.

The comet was by Tycho supposed to move round the sun in an orbit outside that of Venus, and in the direction opposite to that of the planets, the greatest elongation from the sun being 60°. He was unable to represent the observed places of the comet by a uniform motion in this orbit, and was obliged to assume an irregular motion, slowest when in inferior conjunction, increasing when the comet was first discovered, and afterwards again decreasing. Tycho remarks that an epicycle might be introduced to account for this, but as the inequality was only 5′, he did not deem it necessary to go so far in refining the theory of a transient body like a comet; and besides, it is probable that comets, which only last a short time, do not move with the same regularity as the planets do. He finds the inclination of the orbit to the ecliptic equal to 29° 15′, and shows how to compute the place of the comet for any given time by means of the table of its orbital motion with which he concludes the first part of the book. The ninth chapter is a very short one, and treats of the actual size of the comet; as the apparent diameter of the head on the 13th November was 7′, the diameter was 368 miles, or 3/14 of the diameter of the earth. Similarly he calculates the length of the tail, and finds it equal to 96 semi-diameters of the earth. This is on the assumption that the tail is really turned away from Venus, and though he adds that he had also found this to be the case with the comet of 1582, he suspects that some optical illusion must be the cause of this, as it would be more natural that the tail should be turned from the sun than from Venus. In a letter to Rothmann in 1589, he expresses the opinion that the tail is not a mere prolongation of the head, for in 1577 head and tail were of a different colour, and stars could be seen through the tail. He apparently thought that the tail was merely an effect of the light from the sun or Venus shining through the head, and referred to the opinion of Benedict of Venice that the illumination of the dark side of the moon was due to Venus, about which he, however, does not express any decided opinion.^[23]

The only part of the tables of the comet's motion which requires notice is that relating to the horizontal parallax. This he makes out from his theory to have been nearly 20′ in the beginning of November, and then rapidly to have decreased; and, as an excuse for this considerable quantity not having been detected, he adds his belief that refraction would counteract the parallax near the horizon where the comet was observed.

The remainder of Tycho's book is devoted to a detailed examination of the writings and observations of other astronomers on the comet. This was the first comet which gave rise to a perfect deluge of pamphlets, in which the supposed significance of the terrible hairy star was set forth, and for more than a century afterwards every comet was followed by a flood of effusions from numberless scribblers. The astrological significance of the comet Tycho does not trouble himself about, though he takes the opportunity of stating that he does not consider astrology a delusive science, when it is kept within bounds and not abused by ignorant people. For the sun, moon, and fixed stars would have sufficed for dividing time and adorning the heavens, and the planets must have been created for some purpose, which is that of forecasting the future.^[24] But he goes through the observations or speculations of eighteen of his contemporaries, taking first those who had acknowledged the comet to be beyond the lunar orbit (Wilhelm IV., Moestlin, Cornelius Gemma, and Helisæus Roeslin), and afterwards the great herd of those who believed it to move in the "elementary world." Among these there are no generally known names except those of Hagecius and Scultetus. A theory very like that of Tycho was proposed by Moestlin, who also let the comet move in a circle round the sun outside the orbit of Venus, and accounted for the irregular motion by a small circle of libration perpendicular to the plane of the orbit, along the diameter of which the comet moved to and fro. This idea was borrowed from Copernicus, whose lead Moestlin also followed with regard to the motion of the earth.

That the great Danish astronomer did not become convinced of the truth of the Copernican system, but, on the contrary, set up a system of his own founded on the immovability of the earth, may appear strange to many who are unacquainted with the state of astronomy in the sixteenth century, and it may to them appear to show that he cannot have been such a great reformer of astronomical science, as is generally supposed. But it is not necessary to concoct an apology for Tycho; we shall only endeavour to give an intelligible and correct picture of the state of science at that time with regard to the construction of the universe.

That Copernicus had precursors among the ancients who taught that the earth was in motion, is well known, and he was well aware of this fact himself. But none of those precursors had done more than throw out their ideas for the consideration of philosophers; they had not drawn the scientific conclusions from those ideas, and had not worked them into a complete system by which the complicated motions of the planets could be accounted for and made subject to calculation. Neither had this been done by the philosophers who made the earth the centre of the universe, and let it be surrounded by numerous solid crystal spheres to which the heavenly bodies were attached. All this was only philosophical speculation, and was not founded on accurate observations; but the only two great astronomers of antiquity, Hipparchus and Ptolemy, have handed down to posterity a complete astronomical system, by which the intricate celestial motions could be explained and the positions of the planets calculated. But this "Ptolemean system," in which a planet moved on an epicycle, whose centre moved on another circle (the deferent), with a velocity which was uniform with regard to the centre of a third circle, the equant,^[25] was only a most ingenious mathematical representation of the phenomena—a working hypothesis; it did not pretend to give a physically true description of the actual state of things in the universe.^[26] No doubt there were many smaller minds to which this did not become clear, but both by the great mathematician who completed it, and by astronomers of succeeding ages the Ptolemean system was merely considered a mathematical means of computing the positions of the planets.

When astronomy towards the end of the fifteenth century again began to be cultivated in Europe, the inconvenience of the extremely complicated system became felt, and soon the great astronomer of Frauenburg conceived how a different system might be devised on the basis of the earth's motion round the sun. But Copernicus did a great deal more than merely suggest that the earth went round the sun. He worked out the idea into a perfect system, and developed the geometrical theory for each planet so as to make it possible to construct new tables for their motion. And though he had but few and poor instruments, and did not observe systematically, he took from 1497 to 1529 occasional observations in order to get materials for finding the variations of the elements of the orbits since the time of Ptolemy. He was therefore able to produce a complete new system of astronomy, the first since the days of the Alexandrian school, and the first of all which gave the means of determining the relative distances of the planets. And it was in this way that he showed himself as the great master, and was valued as such by Tycho Brahe, who was better able than any one else to appreciate Copernicus, since his own activity left no part of astronomy untouched. But unfortunately the edifice which Copernicus had constructed was not very far from being as artificial and unnatural as that of Ptolemy. The expedient of letting the earth move in a circular orbit round the sun could explain those irregularities in the planetary motions (stations and retrogradations) of which the synodic revolution was the period (the second inequalities, as the ancients had called them), because they were caused by the observer being carried round by the moving earth. But this could not account for the variable distance and velocity (the first inequality) of which the orbital revolution was the period, and of which Kepler gave the explanation when he found that the planets move in ellipses, and detected the law which regulates the velocities in these. Until Kepler had discovered the laws which bear his name, there was no way of accounting for these variations, except by having recourse to the same epicycles and excentrics which Ptolemy had used so liberally; and the planetary theory of Copernicus was therefore nothing but an adaptation of the Ptolemean system to the heliocentric idea.^[27] And the motions were not referred to the real place of the sun, but to the middle sun, i.e., to the centre of the earth's orbit, while the orbit of Mercury required a combination of seven circles, Venus of five, the earth of three, the moon of four, and each of the three outer planets of five circles; and even with this complicated machinery the new system did not represent the actual motions in the heavens any better than the Ptolemean did. Copernicus himself said that he would be as delighted as Pythagoras was when he had discovered his theorem, if he could make his planetary theory agree with the observed positions of the planets within 10′.^[28] But the accuracy was very far indeed from reaching even that limit.^[29] Doubtless the Prutenic tables were better than the Alphonsine ones, but that was simply because Copernicus had been able to apply empiric corrections to the elements of the orbits, and because Reinhold did his work better than the numerous computers at Toledo had done theirs. The Copernican system as set forth by Copernicus, therefore, did not advance astronomy in the least; it merely showed that it was possible to calculate the motions of the planets without having the origin of co-ordinates in the centre of the earth. But of proofs of the physical truth of his system Copernicus had given none, and could give none; and though there can hardly be any doubt that he himself believed in the reality of the earth's motion, it is extremely difficult to say of most of his so-called followers whether they had any faith in that motion, or merely preferred it for geometrical reasons.^[30]

It is always difficult to avoid judging the ideas of former ages by our own, instead of viewing them in their connection with those which went before them and from which they were developed. The physical objections to the earth's motion, which to us seem so easy to refute, were in the sixteenth century most serious difficulties, and the merits of Galileo in conceiving the principles of elementary mechanics and fixing them by experiments must not be underrated. Neither should the advantage be forgotten which the seventeenth century had over the sixteenth from the invention of the telescope, which revealed the shape of the planets, the satellites of Jupiter, and the phases of Venus, and thus placed the planets on an equal footing with the earth, to which the unassisted vision could never have seen any similarity in them.

Tycho Brahe evidently was not content with a mere geometrical representation of the planetary system, but wanted to know how the universe was actually constructed. He felt the "physical absurdity" of letting the earth move, but, on the other hand, the clearness of mind which made him so determined an opponent of the scholastic philosophy enabled him to see how unfounded some of the objections to the earth's motion were. In a letter to Rothmann in 1587 Tycho remarks that the apparent absurdity is not so great as that of the Ptolemean idea of letting a point move on one circle with a velocity which is uniform with regard to the centre of another circle. He adds that the objections which Buchanan had made to the revolution of the earth in his poem on the sphere are futile, since the sea and the air would revolve with the earth without any violent commotion being caused in them.^[31] But all the same he thought that a stone falling from a high tower ought to fall very far from the foot of the tower if the earth really turned on its axis. This remark is made in another letter to Rothmann in 1589, in which he made several objections to the annual motion of the earth.^[32] The immense space between Saturn and the fixed stars would be wasted. And if the annual parallax of a star of the third magnitude was as great as one minute, such a star, which he believes to have an angular diameter of one minute, would be as large as the annual orbit of the earth. And how big would the brightest stars have to be, which he believes to have diameters of two or three minutes? And how enormously large would they be if the annual parallax was still smaller?^[33] It was also very difficult to conceive the so-called "third motion" of the earth, which Copernicus (so needlessly) had introduced to account for the immovable direction of the earth's axis.

Tycho alludes in several places to the difficulty of reconciling the motion of the earth with certain passages of Scripture.^[34] He was far from being the only one who believed this difficulty to be a very serious one against accepting the new doctrine. The Roman Church had not yet taken any official notice of the Copernican system, but in Protestant countries the tendency of the age was decidedly against the adoption of so stupendous a change in cosmological ideas. Nobody cared to study anything but theology, and theology meant a petrified dogmatism which would not allow the smallest iota in the Bible to be taken in anything but a strictly literal sense. Luther had in his usual pithy manner declared what he thought of Copernicus,^[35] and even Melanchthon, who was better able to take a dispassionate view of the matter, had declared that the authority of Scripture was against accepting the theory of the earth's motion.^[36] This may have had some weight with Tycho, at least it might at first have made him indisposed openly to advocate the Copernican system, as the most narrow-minded intolerance was rampant in Denmark (as in most other countries), notwithstanding the king's more liberal disposition. But the king did not wish to be considered unorthodox, and had yielded to the importunity of his brother-in-law, the Elector of Saxony, by dismissing the distinguished theologian Niels Hemmingsen from his professorship at the University, as suspected of leaning to Calvinism. It would certainly not have been prudent for the highly-salaried and highly-envied pensioner of the king, to declare himself an open adherent of a system of the world which was supposed not to be orthodox.

How far this consideration influenced Tycho it is not easy to decide, but the supposed physical difficulties of the Copernican system and a disinclination to adopt a mere geometrical representation, in the reality of which he could not believe, led him to attempt the planning of a system which possessed the advantages of the Copernican system without its supposed defects. In a letter to Rothmann in 1589^[37] Tycho states that he was induced to give up the Ptolemean system by finding from morning and evening observations of Mars at opposition (between November 1582 and April 1583) that this planet was nearer to the earth than the sun was, while according to the Ptolemean system the orbit of the sun intervened between that of Mars and the earth. To the modern reader who knows that the horizontal parallax of Mars can at most reach about 23″, a quantity which Tycho's instruments could not possibly measure, this looks a surprising statement, particularly when it is remembered that Tycho, like his predecessors, assumed the solar parallax equal to 3′. This mystery was believed to have been solved by Kepler, who states that he examined the observations of 1582–83, and found little or no parallax from them; but, to his surprise, he found among Tycho's manuscripts one written by one of his disciples, in which the observed places were compared with the orbit of Mars according to the planetary theory and numerical data of Copernicus, and a most laborious calculation of triangles ended in the result that the parallax of Mars was greater than that of the sun. Kepler suggests that Tycho meant his pupil to calculate the parallax from the observations, but that the pupil, by a misunderstanding, worked out the distance of Mars from the diameters of the excentrics and epicycles of Copernicus.^[38] The subject of the parallax of Mars is alluded to by Tycho in a letter to Brucæus, written in 1584. Here he does not hint at having already constructed a new system himself, but merely tries to disprove that of Copernicus, and among his arguments is, that, according to Copernicus, Mars should in 1582 have been at a distance equal to two-thirds of that of the sun, and consequently have had a greater parallax, whereas he found by very frequent and most exquisite observations that Mars had a far smaller parallax, and therefore was much farther from us than the sun.^[39] In other words, Tycho could not find any parallax of Mars from his observations, but somehow he afterwards imagined that he had found Mars to be nearer the earth at opposition than the sun was, and this decided him to reject the Ptolemean system. He adds in his letter to Rothmann, that the comets when in opposition did not move in a retrograde direction like the planets, for which reason he had to reject the Copernican system also. It did not strike him that comets might move in orbits greatly differing from those of the planets. Having rejected the two existing systems, there was nothing to do but to design a new one.

The Tychonic system could explain the apparent motions of the planets (including their various latitudes), and it might have been completed in detail by being furnished with excentrics and epicycles like its rival. Copernicus had referred the planetary motions, not to the sun, but to the centre of the earth's orbit, from which the excentricities were counted, and through which the lines of nodes passed, so that the earth still seemed to hold an exceptional position. The Copernican system, so long as it was not purged of the artificial appendage of epicycles by the laws of Kepler, was not very much simpler than the Tychonic, and, mathematically speaking, the only difference between them was, that the one placed the origin of co-ordinates in the sun (or rather in the centre of the earth's orbit), the other in the earth.^[40] Tycho's early death prevented the further development of the theory of the planets by his system, which he intended to do in a work to be called Theatrum astronomicum. He only gives a sketch of the theory of Saturn in the first volume of his book, in which the planet moves in a small epicycle in retrograde direction, making two revolutions while the centre of the small epicycle moves once round the circumference of a larger one in the same direction in which the centre of the latter moves along the orbit of Saturn.^[41]

The Tychonic system did not retard the adoption of the Copernican one, but acted as a stepping-stone to the latter from the Ptolemean. By his destruction of the solid spheres of the ancients and by the thorough discomfiture of the scholastics caused by this and other results of his observations of comets, he helped the Copernican principle onward far more effectually than he could have done by merely acquiescing in the imperfectly formed system, which the results of his own observations were to mould into the beautiful and simple system which is the foundation of modern astronomy.

The book on the comet of 1577 was ready from the press in 1588, and though not regularly published as yet, copies were sent to friends and correspondents whenever an opportunity offered.^[42] Thus Tycho's pupil, Gellius Sascerides, who in the summer of 1588 started on a journey to Germany, Switzerland, and Italy, brought copies to Rothmann and Maestlin, to whom he was also the bearer of letters.^[43] The Landgrave did not receive a copy, but studied Rothmann's copy with great interest, and thought that it must have been meant for himself, until Rothmann suggested that it was only part of an unfinished work, and that he would get one later on, which of course he did as soon as Tycho heard of this incident. In the following year, while he was at the fair of Frankfurt, Gellius received another copy of the book, which he was to bring to Bologna to Magini, and this he forwarded from Padua in 1590, together with a letter in which he gave an account of the unfinished first volume of Tycho's work.^[44] A copy was sent to Tycho's old friend Scultetus, who let Monavius of Breslau partake of his joy over it. To Thomas Savelle of Oxford, a younger brother of the celebrated founder of the two Savillian professorships, who was then travelling on the Continent, Tycho sent two copies of the book, together with a letter in which he, among other things, asked him to remind Daniel Rogers about the copyright which he had promised to procure Tycho for his books in England.^[45] To Caspar Peucer, who had already heard of the book from Rantzov, Tycho sent a copy, and added a very long letter in which he entered fully into his reasons for rejecting the Copernican system, and discussed some passages of Scripture which had been made use of to prove the solidity of the celestial spheres. In this letter he also gives an interesting sketch of the plan of the great work to which the three volumes on the new star and comets were to be introductory. It was to consist of seven books; the first was to describe his instruments, the second the trigonometrical formulæ required in astronomy, the third the new positions of fixed stars from his observations, the fourth was to deal with the theories of the sun and moon, the fifth and sixth with the theories of the planets, the seventh with the latitudes of the planets.^[46] With the exception of the first chapter (which he made into a separate book), the contents of this projected work (or at least the outlines of them) were afterwards incorporated in Tycho's first volume of Progymnasmata.

When Rothmann had received the book he wrote to Tycho to thank him for it, and remarked that the new system of the world seemed to be the same as one which the Landgrave a few years previously had got his instrument-maker to represent by a planetarium.^[47] Tycho, who had kept his system a deep secret until the book was ready, was at first unable to understand from whom the Landgrave could have got a description of it,^[48] but he soon after received from a correspondent in Germany a recently published book which solved the riddle. The title of the book was Nicolai Raymari Ursi Dithmarsi Fundamentum astronomicum, printed at Strassburg in 1588. The author, Nicolai Reymers Bär, was a native of Ditmarschen, in the west of Holstein, and a son of very poor parents. He is even said to have earned his bread as a swineherd, but possessing great natural abilities, he rapidly acquired considerable knowledge both in science and in classics. In 1580 he published a Latin Grammar, and in 1583, at Leipzig, a Geodaesia Ranzoviana, dedicated to his patron, Heinrich Rantzov, Governor of Holstein.^[49] Having for some time worked as a surveyor, he seems to have entered the service of a Danish nobleman, Erik Lange of Engelholm, in Jutland, who was a devoted student of alchemy. Lange went on a visit to Tycho in September 1584, and brought Reymers with him, but this probably somewhat uncouth self-taught man seems to have been treated with but scant civility at Uraniborg. After having spent a winter as tutor in Pomerania, Reymers went to Cassel in the spring of 1586, where he informed the Landgrave that he had the previous winter, while living on the outskirts of Pomerania, designed a system of the world. This was exactly like Tycho's, except that it admitted the rotation of the earth. The Landgrave was so pleased with the idea, that he got Bürgi to make a model of the new system; but though he had been well received at Cassel, Reymers was not long in favour there, as he fell out with Rothmann, to whom he abused Tycho. Rothmann mentioned this in a letter to Tycho in September 1586,^[50] but did not mention Reymers' system, which first became known in 1588 by the above-mentioned book.^[51] This contains some chapters on trigonometry and some on astronomy, and in the last chapter the new system is explained and illustrated by a large diagram on about twice as large a scale as that in Tycho's book. The only important difference is, that the orbit of Mars does not intersect that of the sun, but lies quite outside it.

Tycho was apparently very proud of his system, and (as in the case of Wittich) he immediately jumped to the conclusion that Reymers Bär had robbed him of his glory.^[52] He wrote at once to Rothmann (in February 1589) that Reymers must have seen a drawing of the new system during his stay at Uraniborg in 1584, and as a proof of this he refers to the orbit of Mars, which in a drawing made before that time, by a mistake, had been made to surround the solar orbit instead of intersecting it. This cancelled drawing had got in among a number of maps in a portfolio, where Reymers must have seen it, as he copied the erroneous orbit of Mars in the diagram of his book. He therefore expressed his concurrence in the not very flattering expression which Rothmann had applied to Reymers Bär in a former letter.^[53]

It must, however, be said that this accusation of plagiarism is founded on very slight evidence, and the verdict of posterity can only be "not proved." In his writings Reymers has shown himself an able mathematician, and there is no reason whatever why he should not independently have arrived at a conclusion similar to the idea which Tycho conceived on the planetary motions. We shall afterwards see what a curious end this affair got, and how Tycho and Rothmann may have regretted that they had not let the bear alone.

1. According to Tycho, it had been seen by mariners on the 9th. In a copy of Cometæ anno humanitatis 1577 a 10 viiiibris . . . adparentis descriptio, by Bart. Scultetus (Gorlicii, 1578), which I picked up at Copenhagen some years ago, and which now belongs to the Royal Observatory, Edinburgh, there is written in a neat hand the following on the last blank page:—"Ego Londini in Anglia cometam hoc libro descriptum, et 2 die Nouembris visum, tertio obseruare coepi ut potui radio nautico necdum sesquipedali, ita ut triangulum faceret cometa cum stellis subnotatis, caudæ arcu comprehendente gradus 6m. 30 et amplius." [Then follow distance measures on November 3, 9, 13, 15, 24, and 25, but without indication of time.] "Tanto lumine corruscabat hic cometes primo meo aspectu idque per nubes obuersantes, ut antequam integram ejus formam vidissem, Lunam esse suspicarer, quam tamen eo tum loci et temporis lucere non potuisse statim, idque in tanto maiore admiratione, colligebam."
2. Figured in De Mundi Æth. Rec. Phenom., p. 460, and Astr. Inst. Mech., ol. D. 6 verso.
3. The quadrant is figured in De Mundi Æth. Rec. Phen., p. 463, and Mech., fol. A. 2.
4. The orbit of the comet of 1577 was computed from Tycho's sextant observations by F. Woldstedt, "De Gradu Præcisionis Positionum Cometæ Anni 1577 a celeberrimo T. B. . . . determinatarum et de fide elementorum orbitæ," &c. Helsingsfors, 1844, 15 pp. 4to.
5. Except that Scipione Chiaramonte and an obscure Scotchman, Craig, vainly endeavoured to deduce the very opposite result from Tycho's observations, but they were easily reduced in absurdum.
6. The orbit was determined by Schjellerup from a complete discussion of Tycho's sextant observations (Det kgl. danske Videnskabernes Selskabs Skrifter, math. Afdeling, 5te Række, 4de Bind, 1854).
7. The orbit is very uncertain. D'Arrest, Astr. Nachr., xxxviii. p. 35.
8. Tycho returned home from Copenhagen on October 18th. Elias Olsen Morsing had seen it on the 10th, as he wrote in the meteorological diary, "Stellam ignotam vidi." See also Introduction to the Observations.
9. Astr. Nachr., vol. xxix. The observations had been published by Schumacher in 1845 (Observationes cometæ anni 1585 Uraniburgi habitæ a Tychone Brahe. Altona, 4to).
10. Orbit computed by Hind, Astr. Nachr., xxv. p. 111.
11. Orbit by Lacaille, in Pingré's Cométographie, i. p. 560.
12. Orbits by Hind and Valz, Astr. Nachr., xxiii. pp. 229 and 383; the observations are published ibid., p. 371 et seq. Pingré gives the results of most of the observations of the seven comets from a copy of them which is still preserved at the Paris Observatory. A complete edition of all the observations was published in 1867 at Copenhagen, under the supervision of D'Arrest, Tychonis Brahe Dani Observationes Septem Cometarum. Nunc primum edidit F. R. Friis. 4to.
13. The third volume is alluded to in several places in Tycho's writings, e.g. Proyym., i. pp. 513 and 714; Epist., pp. 12, 20, 104, &c.
14. In the above-mentioned letter to Below, Tycho wrote in December 1587 that he should soon be in want of paper for a book which was being printed in his office, and had applied to the managers of two paper-mills in Mecklenburg without getting an answer. He therefore asked Below to write to the managers of these mills, and to ask some friend at the Duke's court to intercede for him; that he would willingly pay for the paper, which might be sent through his friend Brucæus at Rostock. Below wrote at once (28th December 1587) to Duke Ulrich, and asked him to do Tycho this favour, "der löblichen Kunst der Astronomie zur Beförderung " (Lisch, l. c., p. 6). To avoid a repetition of this inconvenience the paper-mill at Hveen was built a few years later.
15. In the above-mentioned paper Woldstedt compares the two sets of positions with modern star places (Åbo or Pond with proper motions from Bessel's Bradley or Åbo). The means of the errors of Tycho's places, irrespective of sign, are in longitude and latitude, for the older positions, 4′.8 and 1′.1, for the later ones, 1′.4 and 1′.5. About the methods by which these positions were found, see Chapter XII.
16. By the method of Al Battani, which employs the point of the equator having the same longitude as the comet. Delambre, Astr. du Moyen Age, p. 21.
17. Which he, with Copernicus, assumes = 52 semi-diameters of the earth.
18. See his remarks about the method, De mundi æth. rec. phen., p. 156, and in a letter to Hagecius (who had found a parallax of five degrees by the method), T. B. et doct. vir. Epist., p. 60. Delambre sets forth the method with his usual prolixity in Hist. de l'Astr. du Moyen Age, p. 341; Astr. Moderne, i. p. 212 et seq.
19. Epist. Astron., pp. 16-17.
20. The value for the earth's semi-diameter was probably taken from Fernels well-known Cosmotheoria, Paris, 1528. We shall see in the next chapter what ideas Tycho had formed as to the distance of the outer planets and the fixed stars (Progym., i. p. 465 et seq.).
21. The book was written in 1587, as appears from several allusions to time in it.
22. This alludes to the circumstance, which had appeared so strange to the ancients, that the period of the motion of each upper planet in its epicycle was precisely equal to the synodical period of the planet, while in the case of the two inferior planets the period in the deferent in the Ptolemean system was equal to the sun's period of revolution.
23. Epist. astron., p. 142.
24. De mundi æth. rec. phen., p. 287. Compare above, Chapter IV. p. 75.
25. The earth, the centre of the deferent, and the centre of the equant were in a straight line and equidistant; only in the case of Mercury the centre of the equant was midway between the earth and the centre of the deferent.
26. Perhaps we may illustrate this by an example from modern science. When the deflection of a magnetic needle in the neighbourhood of an electric current was first discovered, some difficulty was felt in giving a rule for the direction in which either pole of a needle is deflected by a current, whatever their relative positions may be, until Ampere suggested that if we imagine a human figure lying in the current facing the needle, so that the current comes in at his feet and out at his head, then the deflection of the north-seeking pole will be to his left. Nobody ever suspected Ampere of believing that there really was a little man lying in the current, but to many people in the Middle Ages the epicycles were doubtless really existing.
27. The chief claim of the system of Copernicus to be considered simpler than the Ptolemean was that it dispensed with the equant (which really violated the principle of uniform motion, so much thought of), and let the motion on the deferent be uniform with regard to its centre.
28. Rhetici Ephemerides novæ, 1550, p. 6.
29. Möbius has shown that the use of the mean place of the sun (i.e., the centre of the earth's orbit) instead of the true place might, in the Copernican theory of Mars, lead to errors of 2°. See a note in Apelt's Die Reformation der Sternkunde, Jena, 1852, p. 261.
30. The contemporaries of Copernicus were not aware that the introduction to his book, in which the system is spoken of as a mere hypothesis, was written without the knowledge of the author by Osiander of Nürnberg.
31. Epist. astron., p. 74.
32. Ibid., p. 167.
33. Tycho had in vain tried to find an annual parallax of the pole star and other stars. Letter to Kepler, December 1599, Kepleri Opera Omnia, viii. p. 717.
34. Epist., p. 148. He says here that Moses must have known astronomy, since he calls the moon the lesser light, though sun and moon are apparently of equal size. Therefore the prophets must also be assumed to have known more about astronomy than other people of their time did.
35. "Der Narr will die ganze Kunst Astronomiä umkehren! Aber wie die heilige Schrift anzeigt, so hiess Josua die Sonne still stehen und nicht das Erdreich."—Luther's Tischreden, p. 2260.
36. Melanchthon's Initia doctrinæ physicæ, in the chapter "Quis est motus mundi."
37. Epist. astr., p. 148; see also ibid., p. 42, and letter to Peucer of 1588, Weistritz, i. p. 243.
38. Kepler, De motibus stellæ Martis, ch. xi., Opera omnia, iii. p. 219; see also p. 474. In his Progymnasmata, i. p. 414, Tycho says that the outer planets have scarcely perceptible parallaxes, but that he had found by an exquisite instrument that Mars at opposition was nearer than the sun. On p. 661 he alludes to it again.
39. T. Brahei et doct. vir. Epistolæ, p. 76.
40. Might Tycho have got the idea of his system by reading the remark of Copernicus (De revol., iii. 15) when talking about the earth's orbit: "Estque prorsus eadem demonstratio, si terra quiesceret atque Sol in circumcurrente moveretur, ut apud Ptolemæum et alios"? According to Prowe (Nic. Coppernicus, Bd. i. Part 2, p. 509), this is one of the sentences struck out in the original MS., but reinserted by the editor of the first edition.
41. Progymn., i. p. 477, where he also alludes to the "Commentariolus" of Copernicus, see above, p. 83).
42. The book was not for sale till 1603. There are three copies in the Royal Library at Copenhagen with the original title-page of 1588.
43. About Maestlin see Kepleri Opera, i. p. 190.
44. Carteggio inedito di Ticone Brahe, G. Keplero, &c., con G. A. Magini. Ed. Ant. Favaro, Bologna, 1886, p. 193.
45. A Collection of letters illustrative of the progress of science in England. Edited by J. O. Halliwell. London, 1841, p. 32. Tycho also sent Savelle four copies of his portrait engraved at Amsterdam (by Geyn, 1586), and inquired whether there were any good poets in England who would write an epigram on this portrait or in praise of his works. He added that Rogers might also show his friendship by helping him in this matter.
46. Weistritz, i. pp. 239–264, reprinted from Resen's Inscriptiones Hafnienses.
47. Epist. astron., pp. 128, 129.
48. So Tycho says in his reply to Rothmann (Epist., p. 149), but before Rothmann's letter was written Tycho had in his letter to Peucer (dated 13th September 1588) mentioned that a German mathematician had two years previously heard of the system "per quendam meum fugitivum ministrum" (Weistritz, i. p. 255), and this he also mentions in the letter to Rothmann.
49. Kästner, Geschichte der Mathematik, i. p. 669; Kepleri Opera ed. Frisch, i. p. 218.
50. Epist. astron., p. 33, where Rothmann (who thought that Reymers had been employed in Tycho's printing-office) calls him a dirty blackguard ("plura scriberem, præsertim de impuro illo nebulone"), which expression Tycho now found very suitable (ibid., p. 149).
51. For accounts of this book see Kästner, i. p. 631; Delambre, Astron. moderne, i. p. 287; and Rudolf Wolf's Astronomische Mittheilungen, No. lxviii.
52. Already in 1589 or 1590 Duncan Liddel lectured at Rostock on the Tychonic system, calling it by this name. A report afterwards reached Tycho to the effect that Liddel privately took the credit of the new system to himself, and that he later on did so openly at Helmstadt (see letter from Cramer, a clergyman of Rostock, to Holger Rosenkrands, in Epistolæ ad J. Kepplerum, ed. Hanschius, p. 114 et seq.). It appears, however, that Liddel indignantly denied the charge, though he claimed to have deduced the system himself, and to owe Tycho nothing except the incitation to speculate on the matter, for which reason he had mentioned the system as the "Tychonic" (Kepleri Opera omnia, i. pp. 227, 228).
53. Epist. astr., pp. 149, 150.