Here, again, in his search for the unknown law, Kepler had no
accurate dynamical principles to guide his steps. Of course, we now
know not only what the connection between the planet's distance and
the planet's periodic time actually is, but we also know that it is a
necessary consequence of the law of universal gravitation. Kepler,
it is true, was not without certain surmises on the subject, but they
were of the most fanciful description. His notions of the planets,
accurate as they were in certain important respects, were mixed up
with vague ideas as to the properties of metals and the geometrical
relations of the regular solids. Above all, his reasoning was
penetrated by the supposed astrological influences of the stars and
their significant relation to human fate. Under the influence of
such a farrago of notions, Kepler resolved to make all sorts of
trials in his search for the connection between the distance of a
planet from the sun and the time in which the revolution of that
planet was accomplished.
It was quite easily demonstrated that the greater the distance of the
planet from the sun the longer was the time required for its
journey. It might have been thought that the time would be directly
proportional to the distance.
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