egion, and would be again confounded
with the stars which it so closely resembled. How, then, was the planet
to be pursued through its period of invisibility and identified when it
again came within reach of observation?

This difficulty attracted the attention of astronomers, and they sought
for some method by which the place of the planet could be recovered so
as to prevent Piazzi's discovery from falling into oblivion. A young
German mathematician, whose name was Gauss, opened his distinguished
career by a successful attempt to solve this problem. A planet, as we
have shown, describes an ellipse around the sun, and the sun lies at a
focus of that curve. It can be demonstrated that when three positions of
a planet are known, then the ellipse in which the planet moves is
completely determined. Piazzi had on each occasion measured the place
which it then occupied. This information was available to Gauss, and the
problem which he had to solve may be thus stated. Knowing the place of
the planet on three nights, it is required, without any further
observations, to tell what the place of the planet will be on a special
occasion some months in the future. Mathematical calculations, based on
the laws of Kepler, will enable this problem to be solved, and Gauss
succeeded in solving it. Gauss demonstrated that though the telescope of
the astronomer was unable to detect the wanderer during its season of
invisibility, yet the pen of the mathematician could follow it with
unfailing certainty. When, therefore, the progress of the seasons
permitted the observations to be renewed, the search was recommenced.
The telescope was directed to the point which Gauss's calculations
indicated, and there was the little Ceres. Ever since its re-discovery,
the planet has been so completely bound in the toils of mathematical
reasoning that its place every night of the year can be indicated with a
fidelity approaching to that attainable in observing the moon or the
great planets of our system.

The discovery of one minor planet was quickly followed by similar
successes, so that within seven years Pallas, Juno, and Vesta were added
to the solar system. The orbits of all these bodies lie in the region
between the orbit of Mars and of Jupiter, and for many years it seems to
have been thought that our planetary system was now complete. Forty
years later systematic research was again commenced. Planet after planet
was added to the list; gradually the d