Tycho and Kepler (18 page)

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 shun
⁸
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

A
DELBERG
,
M
AULBRONN
,
U
RANIBORG

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 hostile
¹
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.