larger one in which were set the stars. This was believed to turn all
the others, and was called the _primum mobile_. The whole system was
supposed to produce, in its revolution, for the few privileged to hear
the music of the spheres, a sound as of some magnificent harmony.

[Illustration: FIG. 7.--Order of ancient planets corresponding to the
days of the week.]

The enthusiastic disciples of Pythagoras believed that their master was
privileged to hear this noble chant; and far be it from us to doubt
that the rapt and absorbing pleasure of contemplating the harmony of
nature, to a man so eminently great as Pythagoras, must be truly and
adequately represented by some such poetic conception.

[Illustration: FIG. 8.--Ptolemaic system.]

The precise kind of motion supposed to be communicated from the _primum
mobile_ to the other spheres so as to produce the observed motions of
the planets was modified and improved by various philosophers until it
developed into the epicyclic train of Hipparchus and of Ptolemy.

It is very instructive to observe a planet (say Mars or Jupiter) night
after night and plot down its place with reference to the fixed stars
on a celestial globe or star-map. Or, instead of direct observation by
alignment with known stars, it is easier to look out its right ascension
and declination in _Whitaker's Almanac_, and plot those down. If this be
done for a year or two, it will be found that the motion of the planet
is by no means regular, but that though on the whole it advances it
sometimes is stationary and sometimes goes back.[1]

[Illustration: FIG. 9.--Specimens of Apparent paths of Venus and of Mars
among the stars.]

[Illustration: FIG. 10.--Apparent epicyclic orbits of Jupiter and
Saturn; the Earth being supposed fixed at the centre, with the Sun
revolving in a small circle. A loop is made by each planet every year.]

These "stations" and "retrogressions" of the planets were well known to
the ancients. It was not to be supposed for a moment that the crystal
spheres were subject to any irregularity, neither was uniform circular
motion to be readily abandoned; so it was surmised that the main sphere
carried, not the planet itself, but the centre or axis of a subordinate
sphere, and that the planet was carried by this. The minor sphere could
be allowed to revolve at a different uniform pace from the main sphere,
and so a curve of some complexity could be obtained.

A curve described in spac