Tycho and Kepler (49 page)

Kepler examined the planets’ distances
from the Sun at perihelion and at aphelion, and their mean distances from the Sun. He could find no helpful harmonious relationships there. He tried looking for relationships between a single planet’s slowest speed (at aphelion) and its fastest speed (at perihelion), and between and among those speeds using more than one planet. Within a few months he did indeed find an arrangement that was
true both to the principles of musical harmony and to the planets’ observed distances, speeds, and eccentricities.

Of more significance, on May 15, 1618, as he was finishing the book, he discovered a third law of planetary motion, his “harmonic law,” the true relationship between the orbital periods of the planets and their distances from the Sun. Kepler was ecstatic, wanting to give way to
a “sacred frenzy,”
²
as he put it. “I am . . . writing the book,” he rejoiced, “whether for my contemporaries or for posterity, it does not matter. It can await its reader for a hundred years, if God Himself waited six thousand years for His contemplator.” Near the end of the book he included a prayer that vividly reveals this remarkable man:

O you who by the light
³
of nature arouse in us a
longing for the light of grace, so that by means of that You can transport us into the light of glory: I give thanks to You, Lord Creator, because You have lured me into the enjoyment of Your work, and I have exulted in the works of Your hands: behold, now I have consummated the work to which I pledged myself, using all the abilities that You gave to me; I have shown the glory of Your works to men,
and those demonstrations to readers, so far as the meanness of my mind can capture the infinity of it, for my mind was made for the most perfect philosophizing; if anything unworthy of Your deliberations has been proposed by me, a worm, born and raised in a hog wallow of sin, which You want mankind to know about, inspire me as well to change it; if I have been drawn by the admirable beauty of Your
works into indiscretion, or if I have pursued my own glory among men while engaged in a work intended for Your glory, be merciful, be compassionate, and forgive.

Figure 22.1: Kepler’s third law of planetary motion, the “harmonic law.” Kepler discovered the true relationship between the orbital periods of the planets and their distances from the Sun in 1618, as he was finishing his book
Harmonice Mundi
. Kepler’s third law of planetary motion states that the ratio of the squares of the orbital periods of two planets is equal to the ratio of the cubes
of their average distances from the Sun.

Kepler dedicated the five-volume work
Harmonice Mundi
(Harmony of the World) to King James I of England, expressing the hope that these examples of the glorious harmony with which God had endowed his creation might strengthen James in attempts to bring harmony and peace among the tragically divided churches and other polities. However, only four days
before Kepler completed his book and penned that dedication, Protestant Bohemia, where he had spent the ten best years of his life, exploded in a revolution that began the Thirty Years War.
⁴

For Kepler there was soon to be trouble closer to home. In the summer of 1618, an ominous letter came from an old classmate (possibly acting as Kepler’s lawyer) on the law faculty at the University of
Tübingen, warning of a strategy that the Reinbolds and Einhorn might be planning. In autumn 1619 the warning proved correct. A counter civil suit was filed against Katharina Kepler for damages for poisoning Frau Reinbold with the “witch’s drink.” By that time Katharina’s enemies had collected a forty-nine-count indictment against her, including a plethora of local gossip and fancy that recalled unnatural,
eerie behavior. The charges included riding a calf to death, muttering fatal “blessings” over infant children, causing pain without touching people, the unnatural death of animals, and trying to entice a young girl to become a witch. One accusation was true. Katharina, having heard in a sermon about an archaic custom of fashioning goblets from the skulls of dead relatives, had asked the gravedigger
for her father’s skull so that she could have it set in silver for her son Johannes, the imperial mathematician.

With Einhorn still acting as bailiff, testimony began in November 1619. The following July the Reinbolds succeeded in getting the duke of Württemberg to turn their complaint into a criminal case. A few days later, on August 7, the seventy-four-year-old Katharina was awakened from
her sleep in the dead of night, bundled into a large chest, carried out of her daughter’s house, and put in prison in chains. At this point her son Christoph managed to have the trial,
with
all the spectacle and scandal attached to it, transferred to Güglingen, but he and Margarethe’s husband, Georg Binder, were inclined to abandon Katharina and scramble to salvage whatever they could of their
own dwindling reputations. The faithful Margarethe was of a different mind. Once again she wrote to her brother in Linz. Kepler applied to the duke of Württemberg for a delay in the trial until he could arrive, for he planned to defend Katharina himself.

Kepler chose to take his family with him when he left Linz that September of 1620. He and Susanna now had a young son, Sebald, who had been
born in January 1619, and Susanna was pregnant again. They crept away like thieves in the night, without even telling Kepler’s assistant Gringalletus where they were headed. The reason for the trip was too shocking to have it spread abroad in the town. Kepler left his family in Regensburg, where his daughter Susanna may still have been living with Regina’s family, and proceeded alone on his grim
journey to Württemberg. The mystified people of Linz thought their mathematician had fled for good.

Kepler found his mother in prison in chains with two guards and required to pay these guards herself, as well as for her food and upkeep. The Reinbolds complained that so much of her money was being used up in this manner that there would be little left for them when the trial was over.

Kepler had been advised that having the defense case written down would help the outcome, and he insisted that all the defense lawyer’s arguments be put in writing. Christoph lamented the greater cost for what he thought was already a lost cause. The proceedings dragged on, with more lawyers, more witnesses, and more written arguments. Kepler traveled to Stuttgart to consult his lawyer in person,
and they put together a 126-page legal brief, much of it in Kepler’s handwriting, that rebutted the charges one by one. The trial ended in August, and all the proceedings were sent, as was the custom, to the law faculty of the University of Tübingen. It was they who would
make
the decision. Kepler’s friend Christoph Besold was on that faculty. Nevertheless, even the force of Kepler’s presence
throughout the trial, his skill in devising the defense, and his powerful friend could not bring about an acquittal. The court declared itself uncertain and ordered that Frau Kepler be examined once more under the lightest form of torture, verbal terror while being shown the instruments of torture.

On September 28, 1621, Katharina was dragged to the torture chamber, accompanied by three representatives
of the court, a scribe, and a bailiff (not Einhorn this time). The torturer himself showed her his instruments, described their use, and with the greatest possible sternness and melodrama commanded her to tell the truth. Contrary to all expectation, Katharina Kepler gathered her aging wits about her, summoned the eloquence she had bequeathed to her son, and saved herself. As the report
reads:

She announced
⁵
one should do with her what one would. Should one pull one vein after another out of her body, she knew that she had nothing to say. She fell to her knees, uttered the Lord’s Prayer, and declared that God should make a sign if she were a witch or a demon or ever had anything to do with sorcery. Should she be killed, God would see that the truth came to light and reveal
after her death that injustice and violence had been done to her, for she knew that He would not take His Holy Spirit from her but would stand by her.

The charges were dismissed, and Katharina was set free. The Reinbolds were fined ten florins for having begun the proceedings, and Christoph Kepler was ordered to pay thirty florins for the expense of transferring the trial to Güglingen. Despite
the power of her self-defense, Kepler’s mother was a broken woman, and she died the following April.

As soon as he knew his mother was acquitted, Kepler set off on the
journey
back to Linz. There were two young children in his family now, for Susanna had given birth to a daughter, Cordula, the previous January, and Sebald was nearly three. But Linz, in the autumn of 1621, was a different city
from the one they had left in secret a year earlier. Not long after his departure, the Bohemian rebel army had been defeated at the Battle of White Mountain. The Protestant revolution in Bohemia was over, but the Bavarian army still occupied Linz. In Prague, Ferdinand II, the same man who had been responsible for the Counter-Reformation edicts that had forced Kepler out of Graz years before, was
now emperor of the Holy Roman Empire and was overseeing the brutal execution of Protestant leaders. Jesensky (who had aided Kepler in his early unhappy negotiations with Tycho, had delivered the eulogy at Tycho’s funeral, and had been Kepler’s powerful friend during the years in Prague) was one of them. Jesensky’s tongue was cut out before he was quartered. His gory head, along with others, was
stuck on a pike on the bridge tower, where they were left to decompose for ten years and finally fell off, one by one, onto the bridge or into the river.

A seventeenth-century drawing showing the heads of executed Protestant leaders impaled on the bridge in Prague.

There was fortunately less savage treatment of Protestants in Linz. Kepler remained unscathed, despite speculation in the city that he had fled because Ferdinand had put a price on his head, an odd suspicion since everyone knew the Lutherans had excluded Kepler from Communion.
Though Kepler entertained some doubts that it would happen, Ferdinand reconfirmed his appointment as imperial mathematician. The next year, 1622, when all Protestants in Linz were required to convert to Catholicism or leave the city, Kepler was allowed to stay, although his library was sealed
⁶
for a time and he agonized over the requirement that to have it unsealed he must choose which of his
beloved books to surrender to the censors. His children were forced to attend Catholic church services. But he was allowed to keep Protestant Planck, his printer, with him along with as many skilled assistants as Planck required. All the turmoil had not completely halted Kepler’s work on the Rudolfine Tables, nor had the death of yet another of his children, four-year-old Sebald, in the early summer
of 1623.

The production of the Tables had been a matter of the highest priority when Tycho died, and during his years in Prague Kepler had filled hundreds of sheets with calculations
⁷
in preparation for eventually completing them. Kepler’s discovery of his planetary laws were a huge step toward this end, but those discoveries also presented new challenges.

Kepler had derived his first
two laws from the Mars observations. In order to complete the Tables, he had to show that the same laws applied to the other planets. Much of this work had been accomplished in connection with the writing of
Epitome
and
Harmonice Mundi
, but it was not finished. Kepler explained in the preface to the Tables that the reason for the long delay in their appearance was “the novelty of
my
discoveries
⁸
and the unexpected transfer of the whole of astronomy from fictitious circles to natural causes.” No one, he pointed out, had ever attempted anything of the kind before.

In 1617, while at work on
Harmonice Mundi
, Kepler had come across a book by John Napier
⁹
on logarithms. A year later he realized how much this new invention would simplify the computations that took so much of his time. In
the winter of 1621–22 he wrote his own book on logarithms, and he proceeded to use them to solve some of the problems involved in composing the Tables.