ature of which may be imagined when
it is stated that he published thirty-three separate works, besides
leaving behind twenty-two volumes of manuscript.

During his researches on the motions of Mars, Kepler discovered that the
planet sometimes travelled at an accelerated rate of speed, and at
another time its pace was diminished. At one time he observed it to be
in advance of the place where he calculated it should be found, and at
another time it was behind it. This caused him considerable perplexity,
and, feeling convinced in his mind that the form of the planet's orbit
could not be circular, he was compelled to turn his attention to some
other closed curve, by which those inequalities of motion could be
explained.

After years of careful observation and study, Kepler arrived at the
conclusion that the form of the planet's orbit is an ellipse, and that
the Sun occupies one of the foci. He afterwards determined that the
orbits of all the planets are of an elliptical form.

Having discovered the true form of the planetary orbits, Kepler next
endeavoured to ascertain the cause which regulates the unequal motion
that a planet pursues in its path. He observed that when a planet
approached the Sun its motion was accelerated, and as it receded from
him its pace became slower.

This he explained in his next great discovery by proving that an
imaginary line, or radius-vector, extending from the centre of the Sun
to the centre of the planet 'describes equal areas in equal times.' When
near the Sun, or at perihelion, a planet traverses a larger portion of
its arc in the same period of time than it does when at the opposite
part of its orbit, or when at aphelion; but, as the areas of both are
equal, it follows that the planet does not always maintain the same rate
of speed, and that its velocity is greatest when nearest the Sun, and
least when most distant from him.

By the application of his first and second laws Kepler was able to
formulate a third law. He found that there existed a remarkable
relationship between the mean distances of the planets and the times in
which they complete their revolutions round the Sun, and discovered
'that the squares of the periodic times are to each in the same
proportion as the cubes of the mean distances.' The periodic time of a
planet having been ascertained, the square of the mean distance and the
mean distance itself can be obtained. It is by the application of this
law that the dista