by the admission of
many, where room could, according to old-fashioned rules, only be found
for one. A daring hypothesis of Olbers's invention provided an exit from
the difficulty. He supposed that both Ceres and Pallas were fragments of
a primitive trans-Martian planet, blown to pieces in the remote past,
either by the action of internal forces or by the impact of a comet; and
predicted that many more such fragments would be found to circulate in
the same region. He, moreover, pointed out that these numerous orbits,
however much they might differ in other respects, must all have a common
line of intersection,[206] and that the bodies moving in them must
consequently pass, at each revolution, through two opposite points of
the heavens, one situated in the Whale, the other in the constellation
of the Virgin, where already Pallas had been found and Ceres recaptured.
The intimation that fresh discoveries might be expected in those
particular regions was singularly justified by the detection of two
bodies now known respectively as Juno and Vesta. The first was found
near the predicted spot in Cetus by Harding, Schroeter's assistant at
Lilienthal, September 2, 1804; the second by Olbers himself in Virgo,
after three years of persistent scrutiny, March 29, 1807.

The theory of an exploded planet now seemed to have everything in its
favour. It required that the mean or average distances of the
newly-discovered bodies should be nearly the same, but admitted a wide
range of variety in the shapes and positions of their orbits, provided
always that they preserved common points of intersection. These
conditions were fulfilled with a striking approach to exactness. Three
of the four "asteroids" (a designation introduced by Sir. W.
Herschel[207]) conformed with very approximate precision to "Bode's law"
of distances; they all traversed, in their circuits round the sun,
nearly the same parts of Cetus and Virgo; while the eccentricities and
inclinations of their paths departed widely from the planetary
type--that of Pallas, to take an extreme instance, making with the
ecliptic an angle of nearly 35 deg. The minuteness of these bodies
appeared further to strengthen the imputation of a fragmentary character.
Herschel estimated the diameter of Ceres at 162, that of Pallas at 147
miles.[208] But these values are now known to be considerably too small.
A suspected variability of brightness in some of the asteroids, somewhat
hazardously expl