l
kind of oval--the ellipse. Strange that he had not thought of it before.
It was a famous curve, for the Greek geometers had studied it as one of
the sections of a cone, but it was not so well known in Kepler's time.
The fact that the planets move in it has raised it to the first
importance, and it is familiar enough to us now. But did it satisfy the
law of speed? Could the rate of description of areas be uniform with
it? Well, he tried the ellipse, and to his inexpressible delight he
found that it did satisfy the condition of equable description of areas,
if the sun was in one focus. So, moving the planet in a selected
ellipse, with the sun in one focus, at a speed given by the equable area
description, its position agreed with Tycho's observations within the
limits of the error of experiment. Mars was finally conquered, and
remains in his prison-house to this day. The orbit was found.

[Illustration: FIG. 32.]

In a paroxysm of delight Kepler celebrates his victory by a triumphant
figure, sketched actually on his geometrical diagram--the diagram which
proves that the law of equable description of areas can hold good with
an ellipse. The above is a tracing of it.

Such is a crude and bald sketch of the steps by which Kepler rose to his
great generalizations--the two laws which have immortalized his name.

All the complications of epicycle, equant, deferent, excentric, and the
like, were swept at once away, and an orbit of striking and beautiful
properties substituted. Well might he be called, as he was, "the
legislator," or law interpreter, "of the heavens."

[Illustration: FIG. 33.--If _S_ is the sun, a planet or comet moves from
_P_ to _P_1_, from _P_2_ to _P_3_, and from _P_4_ to _P_5_ in
the same time; if the shaded areas are equal.]

He concludes his book on the motions of Mars with a half comic appeal to
the Emperor to provide him with the sinews of war for an attack on
Mars's relations--father Jupiter, brother Mercury, and the rest--but the
death of his unhappy patron in 1612 put an end to all these schemes, and
reduced Kepler to the utmost misery. While at Prague his salary was in
continual arrear, and it was with difficulty that he could provide
sustenance for his family. He had been there eleven years, but they had
been hard years of poverty, and he could leave without regret were it
not that he should have to leave Tycho's instruments and observations
behind him. While he was hesitating what best to d