could avail most for a mind which, like Kepler's, tended
instinctively to the formulation of theories. When Tycho Brahe
died, in 1601, Kepler became his successor. In due time he
secured access to all the unpublished observations of his great
predecessor, and these were of inestimable value to him in the
progress of his own studies.

Kepler was not only an ardent worker and an enthusiastic
theorizer, but he was an indefatigable writer, and it pleased him
to take the public fully into his confidence, not merely as to
his successes, but as to his failures. Thus his works elaborate
false theories as well as correct ones, and detail the
observations through which the incorrect guesses were refuted by
their originator. Some of these accounts are highly interesting,
but they must not detain us here. For our present purpose it must
suffice to point out the three important theories, which, as
culled from among a score or so of incorrect ones, Kepler was
able to demonstrate to his own satisfaction and to that of
subsequent observers. Stated in a few words, these theories,
which have come to bear the name of Kepler's Laws, are the
following:

1. That the planetary orbits are not circular, but elliptical,
the sun occupying one focus of the ellipses.

2. That the speed of planetary motion varies in different parts
of the orbit in such a way that an imaginary line drawn from the
sun to the planet--that is to say, the radius vector of the
planet's orbit--always sweeps the same area in a given time.