rse.

But we have as yet only partly enunciated the first discovery of Kepler.
We have seen that a planet revolves in an ellipse around the sun, and
that the sun is, therefore, at some point in the interior of the
ellipse--but at what point? Interesting, indeed, is the answer to this
question. We have pointed out how the foci possess a geometrical
significance which no other points enjoy. Kepler showed that the sun
must be situated in one of the foci of the ellipse in which each planet
revolves. We thus enunciate the first law of planetary motion in the
following words:--

_Each planet revolves around the sun in an elliptic path, having
the sun at one of the foci._

We are now enabled to form a clear picture of the orbits of the planets,
be they ever so numerous, as they revolve around the sun. In the first
place, we observe that the ellipse is a plane curve; that is to say,
each planet must, in the course of its long journey, confine its
movements to one plane. Each planet has thus a certain plane
appropriated to it. It is true that all these planes are very nearly
coincident, at least in so far as the great planets are concerned; but
still they are distinct, and the only feature in which they all agree is
that each one of them passes through the sun. All the elliptic orbits of
the planets have one focus in common, and that focus lies at the centre
of the sun.

It is well to illustrate this remarkable law by considering the
circumstances of two or three different planets. Take first the case of
the earth, the path of which, though really an ellipse, is very nearly
circular. In fact, if it were drawn accurately to scale on a sheet of
paper, the difference between the elliptic orbit and the circle would
hardly be detected without careful measurement. In the case of Venus the
ellipse is still more nearly a circle, and the two foci of the ellipse
are very nearly coincident with the centre of the circle. On the other
hand, in the case of Mercury, we have an ellipse which departs from the
circle to a very marked extent, while in the orbits of some of the minor
planets the eccentricity is still greater. It is extremely remarkable
that every planet, no matter how far from the sun, should be found to
move in an ellipse of some shape or other. We shall presently show that
necessity compels each planet to pursue an elliptic path, and that no
other form of path is possible.

Started on its elliptic path, the planet