He was not finished yet, not by a long way. In the Mysterium he had asked what is the connection between the time a planet takes to complete its orbit, and its distance from the sun, and had not found a satisfactory answer. Now the question came back more urgent than ever. Since the sun governs planetary motion, as he held to be the case, then that motion must be connected with the solar distances, or else the universe is a senseless and arbitrary structure. This was the darkest hour of his long night. For months he laboured over the problem, wielding the Tychonic observations like the enormous letter-wheels of a cabalist. When the solution came, it came, as always, through a back door of the mind, hesitating shyly, an announcing angel dazed by the immensity of its journey. One morning in the middle of May, while Europe was buckling on its sword, he felt the wing-tip touch him, and heard the mild voice say I am here.

It seemed a nothing, the merest trifle. It sat on the page with no more remarkable an air than if it had been, why, anything, a footnote in Euclid, one of Galileo's anagrams, a scrap of nonsense out of a schoolboy's bad dream, and yet it was the third of his eternal laws, and the supporting bridge between the harmonic ratios and the regular solids. It said that the squares of the periods of evolution of any two planets are to each other as the cubes of their mean distances from the sun. It was his triumph. It showed him that the discrepancies in distance which were left over after the insertion of the regular polygons between the orbits of the planets were not a defect of his calculations, but the necessary consequences of the dominant principle of harmony. The world, he understood at last, is an infinitely more complex and subtle construct than he or anyone else had imagined. He had listened for a tune, but here were symphonies. How mistaken he had been to seek a geometrically perfected, closed cosmos! A mere clockwork could be nothing beside the reality, which is the most harmonic possible. The regular solids are material, but harmony is form. The solids describe the raw masses, harmony prescribes the fine structure, by which the whole becomes that which it is, a perfected work of art.

Two weeks after the formulation of that law the book was finished. He set about the printing at once, in a kind of panic, as if fire or flood, his greatest fears, or some other hobgoblin, might strike him down before he could make public his testament. Besides, the printing was a kind of work, and how could he simply stop? The trajectory he had long ago entered on would take time to run down, would sweep him through further books, the scrag-ends of his career. And even if he had been capable of rest, rest was not permissible, for then he would have had to face, in the dreadful stillness, the demon that has started up at his back, whose hot breath was on his neck.

For years the World Harmony had obsessed him, a huge weight pinning him down; now he was aware of a curious feeling of lightness, of levity almost, as if he had drunk again a dose of Wincklemann's drugged wine. That was the demon. He recognised it. He had known it before, the selfsame feeling, when, in the Astronomia nova, he had blithely discarded years of work for the sake of an error of a few minutes of arc, not because he had been wrong all those years-though he had-but in order to destroy the past, the human and hopelessly defective past, and begin all over again the attempt to achieve perfection: that same heedless, euphoric sense of teetering on the brink while the gleeful voice at his ear whispered jump.

 her and far less inviting precipices appeared under his feet. The world that once had seemed so wide was becoming narrower daily. The Palatinate's army had been crushed in the battle of Weisser Berg and Bohemia regained by the Catholics, but the war of the religions still raged. The Empire was ablaze and he was on the topmost storey. He could hear the flames roaring behind him, the crash of masonry and splintering timber as another staircase gave way. Before him there was only the shivered window and the sudden chill blue air. When in the autumn of 1619 the Elector Frederick and his wife Princess Elizabeth entered Prague to accept the crown offered him by the Bohemian Protestants, the World Harmony had been on the presses, and Kepler had had time to suppress only in a few final copies the dedication to James of England, the Princess's father. He had not needed that connection to mark him out as suspect. Even his attacks on the brotherhood of the Rosy Cross, and his dispute with the English Rosicrucian Robert Fludd, had won him no praise: the imperial parties, so he heard, were asking what he had to hide, that he should flaunt this too enthusiastic loyalty to his Catholic Emperor Ferdinand. He despaired, he was no good at politics. He was not even sure any longer who was fighting whom in the war. The Bohemian barons had not accepted the defeat of Weisser Berg, but they were a local disturbance: now there was talk of French and even Danish involvement. Kepler was baffled. Could these far-off kingdoms really care so much for religion and the fate of little Bohemia? It must be all a conspiracy. The Rosicrucians were to blame, or the Vatican.

Presently, as he knew it would, the old wheel turned: all Lutherans were ordered out of Linz. As the Emperor's mathematician, in title at least, Kepler could hope for immunity. He gave up his pilgrimages to Wincklemann's deserted shop, and stayed away from religious services. But the invisible plotters would not be thus easily put off. His library was confiscated by the Catholic authorities. He bitterly admired the accuracy of their aim; it was a hard blow to bear. And then, it was almost comic, Lutheranism threw up a tormentor of its own in the shape of Pastor Hitzler. Kepler felt himself backed into a corner, an old, puzzled rat.

The public turmoil was matched in the darkness of his heart, where a private war was raging. He could not tell what was the cause of battle, nor what the prize that was being fought for. On one side was all that he held precious, his work, his love for wife and children, his peace of mind; on the other was that which he could not name, a drunken faceless power. Was it still, he wondered, the demon that had risen up out of the closing pages of the Harmonia mundi, grown fat on the world's misfortunes? That was when he began to suspect a connection between his inner ragings and Europe 's war, and feared for his sanity. He fled from the battlefield into the numbing grind of the Tabulae Rudolphinae. There, among the orderly marching columns of Tycho Brahe's lifework, he could hide. But not for long. Soon that manoeuvre was exhausted. Then he embarked on the first of his strange frantic wanderings. On the road he felt easier, the clash of battle within him stilled for a while by the pains and frustration of travel. It seemed to be what the demon wanted.

He used as excuse the moneys owed him by the crown. The printing of the Tables would be a costly business. He set out for Vienna and Ferdinand's court. After four months of haggling there he won a grudging part settlement of 6,000 florins. The Treasury, however, cleverer and more careful than the Emperor, immediately transferred responsibility for the payment to the three towns of Nuremberg, Kempten and Memmingen. Once more Kepler set off, seeming to hear Vienna break out in general hilarity behind him. By the end of winter he had collected from the tight-fisted trinity of towns 2,000 florins. It would buy the paper for the Tables. The effort had exhausted him, and he turned wearily towards home.

When he got to Linz he found the city transformed into a military camp. The Bavarian garrison sent in by the Emperor was billeted everywhere. At Plank the printer's a squad of soldiers was sprawled at feed among the presses, their stink overlaying the familiar smells of ink and machine oil. All work had stopped. They watched him incuriously as he danced before them in helpless rage. He might have dropped into their midst from another planet. They were for the most part the sons of poor farmers. When the printing got under way at last they began to display a childlike interest in the work: few of them had ever seen a machine working before. They would gather about Plank's men in silent groups, staring and softly breathing like cattle at a stile. The sudden white flourish of a pulled proof never failed to call forth a collective sigh of surprise and pleasure. Later on, when the amazing fact had soaked into their understanding that Kepler was the sole cause of all this mighty effort, they turned their awed attention on to him. They would jostle to get near him at the benches or the readers' desk, trying to sift out of his talk of fonts and colophons and faces some clue to the secret of his wizardry. And occasionally they would pluck up courage enough to offer him a mug ofbeer or a twist of tobacco, grinning furiously, at their boots and sweating. He grew accustomed to their presence, and ceased to heed them, except that now and then something spoke to him, at once faint and insistent, out of this warm noisome mass of life pressing at his back. Then he would fly into a rage again, and yell into their stunned faces, and stamp out of the shop, waving his arms.