lled the Deferent. If for any reason
the earth had to be placed out of the centre, the main planetary orbit
was called an Excentric, and so on.

But although the planetary paths might be roughly represented by a
combination of circles, their speeds could not, on the hypothesis of
uniform motion in each circle round the earth as a fixed body. Hence was
introduced the idea of an Equant, _i.e._ an arbitrary point, not the
earth, about which the speed might be uniform. Copernicus, by making the
sun the centre, had been able to simplify a good deal of this, and to
abolish the equant.

But now that Kepler had the accurate observations of Tycho to refer to,
he found immense difficulty in obtaining the true positions of the
planets for long together on any such theory.

He specially attacked the motion of the planet Mars, because that was
sufficiently rapid in its changes for a considerable collection of data
to have accumulated with respect to it. He tried all manner of circular
orbits for the earth and for Mars, placing them in all sorts of aspects
with respect to the sun. The problem to be solved was to choose such an
orbit and such a law of speed, for both the earth and Mars, that a line
joining them, produced out to the stars, should always mark correctly
the apparent position of Mars as seen from the earth. He had to arrange
the size of the orbits that suited best, then the positions of their
centres, both being supposed excentric with respect to the sun; but he
could not get any such arrangement to work with uniform motion about the
sun. So he reintroduced the equant, and thus had another variable at his
disposal--in fact, two, for he had an equant for the earth and another
for Mars, getting a pattern of the kind suggested in Fig. 29.

The equants might divide the line in any arbitrary ratio. All sorts of
combinations had to be tried, the relative positions of the earth and
Mars to be worked out for each, and compared with Tycho's recorded
observations. It was easy to get them to agree for a short time, but
sooner or later a discrepancy showed itself.

[Illustration: FIG. 29.--_S_ represents the sun; _EC_, the centre of the
earth's orbit, to be placed as best suited; _MC_, the same for Mars;
_EE_, the earth's equant, or point about which the earth uniformly
revolved (_i.e._ the point determining the law of speed about the sun),
likewise to be placed anywhere, but supposed to be in the line joining
_S_ to _EC_; _ME_,