In 1619, the Emperor Matthias died, and was succeeded by Ferdinand III., who retained Kepler in the post he had filled under his two predecessors on the imperial throne. Kästner, in his "History of Mathematics," has corrected a gross error of Hantsch, in asserting that Kepler prognosticated Matthias's death. The letter to which Hantsch refers, in support of his statement, does indeed mention the emperor's death, but merely as a notorious event, for the purpose of recalling a date to the memory of his correspondent. CHAPTER VII. _Kepler publishes his Harmonics—Account of his Astrological Opinions and Discovery of the Law of the Periods of the Planetary Revolutions—Sketch of Newton's proof of Kepler's Laws._ THE "Cosmographical Mystery" was written, as has been already mentioned, when Kepler was only twenty-six, and the wildness of its theories might be considered as due merely to the vivacity of a young man; but as if purposely to shew that his maturer age did not renounce the creations of his youthful fancy, he reprinted the "Mystery" in 1619, nearly at the same time when he published his celebrated work on Harmonics; and the extravagance of the latter publication does not at all lose in comparison with its predecessor. It is dedicated to James I. of England, and divided into five books: "The first, Geometrical, on the origin and demonstration of the laws of the figures which produce harmonious proportions;—the second, Architectonical, on figurate geometry, and the congruence of plane and solid regular figures;—the third, properly Harmonic, on the derivation of musical proportions from figures, and on the nature and distinction of things relating to song, in opposition to the old theories;—the fourth, Metaphysical, Psychological, and Astrological, on the mental essence of harmonies, and of their kinds in the world, especially on the harmony of rays emanating on the earth from the heavenly bodies, and on their effect in nature, and on the sublunary and human soul;—the fifth, Astronomical and Metaphysical, on the very exquisite harmonies of the celestial motions, and the origin of the excentricities in harmonious proportions."