al to the cubes of their mean distances.

For purposes of illustration let us take the earth and the planet Venus
and compare these two. The periodic time of the earth is 365 days,
omitting the quarter day. The periodic time of Venus is 224 days
approximately. Now, according to Kepler's Third Law, the square of 365
is to the square of 224, as the cube of the earth's mean distance is to
the cube of Venus's mean distance, which are 92.7 millions of miles and
67 millions of miles respectively. The problem may be thus stated--

As 365^2: 224^2:: 92.7^3: 67^3:

This worked out gives--

133,225: 50,176: 796,597.982: cube of Venus's mean distance.

So that by Kepler's Third Law, if we have the periodic time of any two
planets, and the mean distance of either, we can find out the mean
distance of the other by simple proportion.

In making astronomical calculations, the distances of the planets are
generally obtained by means of Kepler's Third Law, as the periodic time
of the planet is a calculation that may be made by astronomers with
great certainty, and when once the periodic times are found, and the
mean distance of a planet, as our earth for example, is known, the mean
distances of all the other planets in the solar system may soon be
obtained.

In like manner this Third Law of Kepler's is equally applicable to the
satellites of any planet. For example, when the periodic time of both of
Mars' satellites, Phobos and Deimos, are known, being about 8 hours and
30 hours respectively, and the distance of either is known, as Phobos
with a mean distance of 5800 miles, then the mean distance of Deimos can
easily be calculated by this law, and is found to be 14,500 miles.

As discovered by Kepler, the Third Law was simply the result of
observation. He was unable to give any mathematical basis for its
existence. The Laws as they were given to the world by Kepler were
simply three great truths which had been discovered by observation. It
rested with Newton to show how these laws could be accounted for on a
mathematical basis, and to show how they all sprang from one and the
same source, namely the universal Law of Gravitation. In his
_Principia_, he proved that all Kepler's Laws were fully expounded and
explained by his great discovery of Universal Gravitation.

Now what Newton has done for Kepler's Laws from the mathematical
standpoint, we propose to do from the physical standpoint. In the
development of the physical agency