must have remained buried in darkness; not Saturn predominating Mercury,
but my lords the Emperors Rudolph and Matthias, not Capricorn the house
of Saturn but Upper Austria, the house of the Emperor, and the ready and
unexampled bounty of his nobles to my petition. Here is that corner, not
the western one of the horoscope, but on the earth whither, by
permission of my Imperial master, I have betaken myself from a too
uneasy Court; and whence, during these years of my life, which now tends
towards its setting, emanate these Harmonics and the other matters on
which I am engaged."

The fifth book contains a great deal of nonsense about the harmony of
the spheres; the notes contributed by the several planets are gravely
set down, that of Mercury having the greatest resemblance to a melody,
though perhaps more reminiscent of a bugle-call. Yet the book is not all
worthless for it includes Kepler's Third Law, which he had diligently
sought for years. In his own words, "The proportion existing between the
periodic times of any two planets is exactly the sesquiplicate
proportion of the mean distances of the orbits," or as generally given,
"the squares of the periodic times are proportional to the cubes of the
mean distances." Kepler was evidently transported with delight and
wrote, "What I prophesied two and twenty years ago, as soon as I
discovered the five solids among the heavenly orbits,--what I firmly
believed long before I had seen Ptolemy's 'Harmonics'--what I had
promised my friends in the title of this book, which I named before I
was sure of my discovery,--what sixteen years ago I urged as a thing to
be sought,--that for which I joined Tycho Brahe, for which I settled in
Prague, for which I have devoted the best part of my life to
astronomical computations, at length I have brought to light, and have
recognised its truth beyond my most sanguine expectations. Great as is
the absolute nature of Harmonics, with all its details as set forth in