Tycho’s attitude toward his peasants and his treatment of them were not unusual. There were exceptions, of course, such as his uncle Steen, who reportedly acted toward his tenants at Herrevad “like a mild father”6 and “did not lay new burdens upon them,” which many of them “acknowledge to this day and bemoan with tears that they do miss their good master.” However, the charter of Hven served as a prototype for other similar documents all over the kingdom. It did not seem hypocritical for Tycho, in the context of the times, to talk of Uraniborg and Hven constituting a glorious link between humankind and a love whose force drove the universe, nor did he deny that his peasants were part of that humankind. They simply had to fulfill their obligations.
Though his tenants had come to regard Tycho as a monster, and some rival scholars such as Jørgen Dybvad must have had a scarcely better opinion of him, most of Tycho’s acquaintances during this period of his life probably found him to be an amiable, charming man. He had many of the unconscious attitudes and assumptions that went with his birth and breeding, but he was not a social snob. He had chosen a commoner for his life partner, and he preferred the company of those who belonged to a scholarly class whose social position was considered beneath his own. However, with the completion of Uraniborg, mounting wealth, close association with the king, and particularly with the remarkable lack of opposition he was meeting as he pursued his dreams, he was undeniably developing an increasingly elitist attitude and an inflated ego that were all the more problematical because they were in many respects well founded.
With success following on success, Tycho was beginning to equate “good” with “what contributes to the splendid work I am doing.” Students, assistants, and peasants should feel privileged to contribute to this magnificent venture that seemed to be favored by God and providence. There were those who did indeed see working with Tycho as likely to be their own closest brush with greatness. Tycho did not stop being an amiable, charming, even considerate man to those who saw things in this light, whose plans supported his own lofty ambitions, or whose intellects were in sync with his. He was also subjugating himself to this great cause of reforming astronomy. He could not think it unreasonable to expect others to burn willingly on the same altar, be grateful for the opportunity, and be respectful of the unique responsibility that was his.
The cause to which Tycho was dedicating himself and his great building project, and everyone around him, in the late 1570s was the achievement of a standard of observational precision undreamed of by his predecessors or contemporaries. Even the finest instrument makers had never been asked to produce instruments like those he wanted. At Herrevad he had recognized that it was essential for him to have his own shop where craftsmen who were already skilled could become specialists and devote all their time to his needs, under his close supervision. That had not materialized there. At Uraniborg, he was making sure it did.
Tycho’s “workshop for the artisans,”7 as he called his instrument shop, was admirably well equipped, beyond any other such shop in existence, with “mills driven partly by horses and partly by water power.” Instrument building was costly in material and labor, with some instruments taking six trained people three years to manufacture while peasant labor kept the mills running.
Tycho kept meticulous records of the manufacture and use of his instruments. He had learned a lesson from the controversy about the nova: Not only did he need to achieve instrumental accuracy to his own satisfaction, but he also had to be able to prove to others that he had achieved such precision. To that end, records had to show which instrument he used for each observation and be cross-referenced to identify all observations made with each instrument. For cross-checking, related observations had to be made with different instruments.
All this recording and documenting, as well as the everyday conversation at Uraniborg in the observatories and at the dinner table, used a vocabulary of astronomy that was elementary to Tycho and his associates and students, and much of which is, in fact, utilized by modern astronomers. Ancient and medieval astronomers, and most in Tycho’s time, thought of the stars as fixed onto an invisible “celestial sphere” centered on Earth. (That term is no longer taken literally, but the concept is still used.) The dome of sky visible at night by an observer on Earth is half the complete celestial sphere; the other half is hidden below the horizon. The stars, fixed points on the celestial sphere, serve as reference points for tracking the motion of the Sun, Moon, and planets as they move across this background.
Observing the sky long enough reveals that the stars are not really “fixed.” Earth is turning on its axis, so the celestial sphere appears to rotate. Stars rise in the east and set in the west. Their positions in relation to one another do not change while an observer stands and watches them at night, but their positions in relation to that observer and the horizon do change.
The celestial sphere, like Earth, has an equator—the celestial equator, which is on a plane with Earth’s equator. Also like Earth it has an axis of rotation that can be thought of as an extension of Earth’s axis of rotation. Just as Earth’s axis of rotation runs from its North Pole to its South Pole, the celestial sphere’s axis of rotation runs from the north celestial pole to the south celestial pole.
Figure 7.2: On Earth, the equator is midway between the North and South Poles. On the celestial sphere, the celestial equator is midway between the north and south celestial poles, on a plane with Earth’s equator.
The horizon is another great circle (see figure 7.3) that, like the celestial equator, divides the celestial sphere in half. However, while the celestial equator (like Earth’s equator) is the same for observers in different places, the horizon is not. For Tycho, on Hven, the horizon was different from what it would have been had he set up his observatory in Basel. Stars whose paths dipped below the horizon at Hven would not have done so in Basel. Thus for any observer on Earth who is not standing on Earth’s North or South Pole, the horizon is tipped in relation to the celestial equator. How much tipped depends on where the observer is located. The celestial equator and the horizon meet at two points, one east and one west of the observer. They are like two hoops hinged together (see figure 7.4).
Figure 7.3: Anywhere an observer stands on Earth’s face, except on its North or South Pole, that observer’s horizon is tipped in relation to the equator and the celestial equator. In more technical language: The observer’s horizon is inclined at an angle to the celestial equator.
Figure 7.4: Two “hoops,” the horizon and the celestial equator, are hinged together and tipped in relation to one another.
The zenith is the point directly above an observer’s head, regardless of what happens to be up there at the moment or where the observer happens to be standing on the face of Earth. Hence, as is the case with the horizon, an observer can think of the zenith as belonging to him or her personally, while the celestial poles and the celestial equator do not—they are public property, worldwide.
There is one more hoop hinged into this arrangement (see figure 7.5): Tycho and most of his contemporaries believed that the Sun orbited Earth, completing one orbit in one year, moving in a great circle around Earth. (In fact, when the discussion involves only Earth and the Sun, there is no way of deciding which is orbiting which. The two arrangements are geometrically equivalent.) Astronomy’s name for that circle was and still is the ecliptic. The ecliptic is not the same as the celestial equator, because Earth’s axis of rotation (the line drawn between the North and South Poles) does not run at a ninety-degree angle to Earth’s orbit. Like a fishing bob tilting in relation to the surface of the water, Earth is tilted in relation to the plane of its orbit. During the summer in the northern hemisphere, the north pole tilts toward the Sun. When it is winter in the northern hemisphere, the North Pole tilts away from the Sun, while the South Pole tilts toward the Sun.
Figure 7.5: For a Ptolemaic astronomer, the ecliptic was the great circular path along which the Sun appears to travel as it orbits Earth. It is an
other “hoop,” with its plane tilted at an angle to the celestial equator.
The planets and the Moon also take part in the apparent daily rotation of the sky due to the rotation of Earth, but they also have additional movement of their own. To an observer, most of the time, each of them appears to move in a great circle around Earth. These orbits are not the same as the horizon, the celestial equator, or the ecliptic. They are inclined at angles to these and to one another. However, the angle between the orbit of a planet and the ecliptic is never large. Pluto’s orbit is much more inclined than the others, but Tycho and his contemporaries knew nothing of Pluto. They did know that the Moon and planets never strayed outside the zodiac, a belt of sky about ten degrees wide, centered on the ecliptic (figure 7.6). The position of a planet could be pinpointed by saying where it was in relation to the background stars in that zodiac belt: in other worlds, where a straight line of sight drawn from Earth through the planet would end in the zodiac.
Figure 7.6: The angle between the orbit of a planet and the plane of the ecliptic (the straight line from A to B in this drawing) is never large, so the planets are always found near the ecliptic, within the band known as the zodiac, the width of which is marked with lines at A and B.
(Other terms that are useful for understanding the descriptions of Tycho’s instruments are defined in appendix 2.)
It was possible for Tycho and his contemporary astronomers to calculate from one set of measurements to another. For example, knowing the position of a star with reference to the horizon, they could calculate its position with reference to the celestial equator, or to the ecliptic, and vice versa. To make such transformations, they often chose to use a shortcut, an instrument called an armillary—an arrangement of rings showing the relative positions of these circles on the celestial sphere. Tycho spoke of armillaries disparagingly as devices for “people who shun8 labor,” but he built and used several of them himself. One of the wonders of Tycho’s island that guests would later gaze at with awe was an armillary larger than any other that has ever existed.
The last instrument Tycho commissioned before he began producing them himself at Uraniborg was his quadrans mediocris orichalcicus azimuthalis, or “medium-size azimuth quadrant of brass.”9 It was one of his favorites in a lifetime of instrument production and a landmark in the evolution of his instruments. The procedure for using a quadrant (see figure 7.7) was straightforward enough, but the degree of accuracy Tycho wanted created problems. The study of the movements of the planets, as well as positions of such phenomena as comets and novas, required more than precise viewing of the object in question. It also required a background catalog of fundamental star positions to serve as reference points. Compiling such a catalog (for he did not find anyone else’s nearly dependable enough for his needs) was one of the most essential tasks of Tycho’s career, and it continued for many years. The improvements he made in the development of the quadrans mediocris orichalcicus azimuthalis represented significant breakthroughs that were essential to what he was trying to achieve.
The age-old method was to sight through pinholes. Few astronomers before Tycho had demanded enough precision to be annoyed by the deficiencies of this method, much less to do anything about them. However, Tycho found that if the holes were large enough to see through and find the star, the sighting was not precise. The star would not necessarily be centered exactly in the holes, and the position could be off by a fraction. Thus, “driven by necessity”10 to seek an improvement, he came up with a better alidade (the straight piece of an observing instrument that connected the nearer and farther sights). It was such a rousing success that he included a drawing of it (figure 7.8a) much later in his book Astronomiae Instauratae Mechanica.
With this new alidade set on its sides, it was possible for Tycho to raise or lower it until he could see the star through slits he marked A–D on his drawing, lined up precisely with the side H–E at the other end of the alidade, while at the same moment lining it up so that just as much of the star could be seen through the slit B–C, sighting on the line F–G. In that way he measured the altitude of a star (its distance above the horizon). At the same moment he could look through the slit C–D toward the side G–H, and simultaneously through the slit B–A toward the side F–E. That gave him the azimuth measurement (distance from the meridian; see appendix 2). To study the Sun, he could adjust the instrument so that the Sun’s rays shone through the round hole in the far sight and filled a circle drawn on the inner side of the clover sight (not visible on his drawing).
A further innovation that Tycho came up with to improve accuracy of sighting was the use of a cylinder as the more distant sight (see figure 7.8b). Later, for his great mural quadrant, he positioned the cylinder in a rectangular opening in a wall of his house.
Figure 7.7: Tycho’s “quadrans mediocris orichalcicus azimuthalis” or “medium-size azimuth quadrant of brass,” in a drawing from Astronomiae Instauratae Mechanica. To use this quadrant, Tycho positioned it so that its plumb lines—G in the picture—showed that one of its straight edges was precisely horizontal and the other precisely vertical, pointing straight up toward the zenith. He rotated the quadrant on its pivot so that the curved edge, or arc, passed through the star or planet whose position he wanted to measure. The azimuth of the star or planet (its distance from the meridian) could then be read off the 360-degree circle within which the quadrant rotated. The sighting arm, a straight piece called the alidade, was attached at the point of the quadrant that corresponds to the center of a pie. Like the hand of a clock, its other end was able to move freely along the arc. Tycho and his assistants raised or lowered that end (D) of the alidade until, sighting along it from the other end (E), they had it pointed at the star or planet. The arc was marked off like a ruler into the ninety degrees represented by this segment of a complete circle, allowing one to measure the altitude of the star (its distance in degrees above the horizon).
Figure 7.8 a.) Tycho’s drawing of his new alidade, in Astronomiae Instauratae Mechanica. The clover-shaped end (letters A, B, C, D) was the end of the alidade nearest the observer. The square end (F, G, H, E) was at its far end, the end that could swing freely along the arc. The clover had slits on four sides, forming a square that exactly corresponded to the square at the other end of the alidade. The width of the slits was adjustable. “By turning one single screw,11 that is by one single manipulation,” Tycho wrote, “it is possible to widen or narrow all the slits simultaneously without any trouble or waste of time.”
b.) Using a cylinder as the more distant sight: The diameter of the cylinder was the same as the distance between two slits in the near sight. Tycho lined up the sights so that the star appeared equally bright on both sides of the cylinder when he moved his eye from one slit to the other.
c.) Transversal points: The zigzag lines of dots on the arc of an instrument made it possible to fine-tune adjustments so as to have the line of sight passing through one of these points, allowing much more precise measurements.
Tycho made one final modification to his quadrans mediocris orichalcicus azimuthalis, at last fully utilizing the transversal points (see figure 7.8c) he had learned about years before when working with his cross staff. In his drawing of the quadrant (figure 7.7), the zigzag pattern of the dots that enabled him to make much finer measurements was visible on the curved edge.
Having his own instrument shop at Uraniborg proved to be an enormous advantage. Not only was Tycho able to supervise manufacture closely; he could also evaluate each instrument after it came out of the shop by using it for observation, studying its quality, identifying its problems, and experimenting with innovative ways of solving them. He could easily return the instrument to the shop any number of times to make the necessary adjustments and corrections or rebuild it completely. Instruments he had only been able to dream of at Herrevad were about to become a reality at Uraniborg.
fn1 The description of the room and of a meal that would have been served in such a setting comes
from John Robert Christianson, in his book On Tycho’s Island. Christianson, in turn, based his description on Tycho’s own account and on accounts of similar rooms and dining practices in other Danish manor houses.
fn2 Tycho’s poem “Urania Titani” is widely considered the finest poem any Dane has written in Latin.
8
ADELBERG, MAULBRONN, URANIBORG
1580–1588
LIFE AT THE seminaries in Adelberg, where Johannes Kepler, just barely in his teens, matriculated in 1584, and Maulbronn, where he went two years later, was severely regimented. The school day began at four A.M. in summer, five in winter, when all the students, dressed in identical sleeveless knee-length coats, gathered for psalm singing. Every hour had its assigned work, with no free time. All conversation continued to be in Latin, but at this level there was instruction in Greek as well, and also in rhetoric and music. Johannes and his schoolmates now read the classics and the Bible in both Latin and Greek, thus mastering the classical languages while at the same time assimilating the ideas, faith, and values of Western civilization. The higher seminary introduced them to “spherics” and arithmetic.
Though school may have provided the happiest moments in Kepler’s childhood and youth, he was oppressed by a series of real and imagined physical ailments and had difficulties typical of his age group when it came to getting along with fellow students. His long, rambling list of “only those who were hostile1 over long periods” contains many statements such as “I willingly incurred the hatred of Seiffer because the rest hated him too, and I provoked him although he had not harmed me. . . . I have often incensed everyone against me through my own fault . . . at Adelberg it was my treachery [under strong moral pressure from his instructors, Kepler had acted as an informer]; at Maulbronn, it was my defence of Graeter.” Kepler was also the butt of insults because of his father’s reputation, but he was particularly hurt when there was envious talk about him: “Why were all of them all the time jealous of competence, industry of work, progress, and success?” Each of his schoolmates at this age probably could have come up with a litany similar to Kepler’s. Kepler was candid enough to write it all down.
Tycho and Kepler Page 12