blished his work
entitled "On the Motion of Mars." This was the result of an attempt,
upon which he had been engaged since the beginning of the century, to
reconcile the motions of that planet to the hypothesis of eccentrics and
epicycles. It ended in the abandonment of that hypothesis, and in the
discovery of the two great laws now known as the first and second laws
of Kepler. They are respectively that the orbits of the planets are
elliptical, and that the areas described by a line drawn from the planet
to the sun are proportional to the times.

In 1617 he was again rewarded by the discovery which passes under the
designation of Kepler's third law: it expresses the relation of the mean
distances of the planets from the sun with the times of their
revolutions--"the squares of the periodic times are in the same
proportion as the cubes of the distances." In his "Epitome of the
Copernican Astronomy," published 1622, he showed that this law likewise
holds good for the satellites of Jupiter as regards their primary.

[Sidenote: His remonstrance with the Church.] Humboldt, referring to the
movement of Jupiter's satellites, remarks: "It was this which led
Kepler, in his 'Harmonices Mundi,' to state, with the firm confidence
and security of a German spirit of philosophical independence, to those
whose opinions bore sway beyond the Alps, 'Eighty years have elapsed
during which the doctrines of Copernicus regarding the movement of the
earth and the immobility of the sun have been promulgated without
hindrance, because it was deemed allowable to dispute concerning natural
things and to elucidate the works of God, and, now that new testimony is
discovered in proof of the truth of those doctrines--testimony which was
not known to the spiritual judges, ye would prohibit the promulgation of
the true system of the structure of the universe.'"

[Sidenote: Rectification of the Copernican theory.] Thus we see that the
heliocentric theory, as proposed by Copernicus, was undergoing
rectification. The circular movements admitted into it, and which had
burdened it with infinite perplexity, though they had hitherto been
recommended by an illusive simplicity, were demonstrated to be
incorrect. They were replaced by the real ones, the elliptical. Kepler,
as was his custom, ingenuously related his trials and disappointments.
Alluding on one occasion to this, he says: "My first error was that the
path of a planet is a perfect circle--an opinion