But, through some error of
calculation, no common relation was found between them. Finding it
impossible, however, to banish the subject from his thoughts, he tells
us, that on the 8th of the following May he renewed the last of these
comparisons, and, by repeating his calculations with greater care,
found, with the highest astonishment and delight, that the ratio of the
squares of the periodical times of any two planets was constantly and
invariably the same with the ratio of the cubes of their mean distances
from the sun. Then it was that he burst forth in his memorable
rhapsody:--"What I prophesied twenty-two 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 contemplation,--at length I have brought to light, and
have recognized its truth beyond my most sanguine expectations.
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