He had invented but not
published several powerful mathematical methods (one of them now known
as "the method of least squares"), and he applied them to Piazzi's
observations. He was thus able to calculate an orbit, and to predict a
place where, by the end of the year, the planet should be visible. On
the 31st of December of that same year, very near the place predicted by
Gauss, von Zach rediscovered it, and Olbers discovered it also the next
evening. Piazzi called it Ceres, after the tutelary goddess of Sicily.

Its distance from the sun as determined by Gauss was 2.767 times the
earth's distance. Bode's law made it 2.8. It was undoubtedly the missing
planet. But it was only one hundred and fifty or two hundred miles in
diameter--the smallest heavenly body known at the time of its discovery.
It revolves the same way as other planets, but the plane of its orbit is
tilted 10 deg. to the plane of the ecliptic, which was an exceptionally
large amount.

Very soon, a more surprising discovery followed. Olbers, while searching
for Ceres, had carefully mapped the part of the heavens where it was
expected; and in March, 1802, he saw in this place a star he had not
previously noticed. In two hours he detected its motion, and in a month
he sent his observations to Gauss, who returned as answer the calculated
orbit. It was distant 2.67, like Ceres, and was a little smaller, but it
had a very excentric orbit: its plane being tilted 34-1/2 deg., an
extraordinary inclination. This was called Pallas.

Olbers at once surmised that these two planets were fragments of a
larger one, and kept an eager look out for other fragments.

In two years another was seen, in the course of charting the region of
the heavens traversed by Ceres and Pallas. It was smaller than either,
and was called Juno.

In 1807 the persevering search of Olbers resulted in the discovery of
another, with a very oblique orbit, which Gauss named Vesta. Vesta is
bigger than any of the others, being five hundred miles in diameter, and
shines like a star of the sixth magnitude. Gauss by this time had become
so practised in the difficult computations that he worked out the
complete orbit of Vesta within ten hours of receiving the observational
data from Olbers.

For many weary years Olbers kept up a patient and unremitting search for
more of these small bodies, or fragments of the large planet as he
thought them; but his patience went unrewarded, and he died in 1840