rrect 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.

These two laws Kepler published as early as 1609. Many years more of
patient investigation were required before he found out the secret of
the relation between planetary distances and times of revolution which
his third law expresses. In 1618, however, he was able to formulate this
relation also, as follows:

3. The squares of the distance of the various planets from the sun are
proportional to the cubes of their periods of revolution about the sun.

All these laws, it will be observed, take for granted the fact that the
sun is the centre of the planetary orbits. It must be understood, too,
that the earth is constantly regarded, in accordance with the Copernican
system, as being itself a member of the planetary system, subject to
precisely the same laws as the other planets. Long familiarity has made
these wonderful laws of Kepler seem such a matter of course that it is
difficult now to appreciate them at their full value. Yet, as has been
already pointed out, it was the knowledge of these marvellously simple
relations between the planetary orbits that laid the foundation for the
Newtonian law of universal gravitation. Contemporary judgment could not,
of course, anticipate this culmination of a later generation. What it
could understand was that the first law of Kepler attacked one of the
most time-honored of metaphysical conceptions--namely, the Aristotelian
idea that the circle is the perfect figure, and hence that the planetary
orbits must be circular. Not even Copernicus had doubted the validity of
this assumption. That Kepler dared dispute so firmly fixed a belief,
and one that seemingly