ercury, Venus, Earth, Mars, Jupiter, Saturn.

_The five regular solids, in appropriate order--_
Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube.

_Table illustrating Kepler's third law._

+---------+---------------+-----------+---------------+----------------+
| | Mean distance | Length | Cube of the | Square of the |
| Planet. | from Sun. | of Year. | Distance. | Time. |
| | D | T | D^3 | T^2 |
+---------+---------------+-----------+---------------+----------------+
| Mercury | .3871 | .24084 | .05801 | .05801 |
| Venus | .7233 | .61519 | .37845 | .37846 |
| Earth | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| Mars | 1.5237 | 1.8808 | 3.5375 | 3.5375 |
| Jupiter | 5.2028 | 11.862 | 140.83 | 140.70 |
| Saturn | 9.5388 | 29.457 | 867.92 | 867.70 |
+---------+---------------+-----------+---------------+----------------+

The length of the earth's year is 365.256 days; its mean distance from
the sun, taken above as unity, is 92,000,000 miles.

LECTURE III

KEPLER AND THE LAWS OF PLANETARY MOTION

It is difficult to imagine a stronger contrast between two men engaged
in the same branch of science than exists between Tycho Brahe, the
subject of last lecture, and Kepler, our subject on the present
occasion.

The one, rich, noble, vigorous, passionate, strong in mechanical
ingenuity and experimental skill, but not above the average in
theoretical and mathematical power.

The other, poor, sickly, devoid of experimental gifts, and unfitted by
nature for accurate observation, but strong almost beyond competition in
speculative subtlety and innate mathematical perception.

The one is the complement of the other; and from the fact of their
following each other so closely arose the most surprising benefits to
science.

The outward life of Kepler is to a large extent a mere record of poverty
and misfortune. I shall only sketch in its broad features, so that we
may have more time to attend to his work.

He was born (so his biographer assures us) in longitude 29 deg. 7', latitude
48 deg. 54', on the 21st of December, 1571. His parents seem to have been of
fair condition, but by reason, it is said, of his becoming surety for a
friend, the father lost all hi