eviations in
mean distance from the mean distance of the original planet, will be
presented by the smallest members of the assemblage; and fourth, that
the orbits differing most from the rest in eccentricity and in
inclination, will be among those of these smallest members. In the
fourth edition of Chambers's _Handbook of Descriptive and Practical
Astronomy_ (the first volume of which has just been issued) there is a
list of the elements (extracted and adapted from the _Berliner
Astronomisches Jahrbuch_ for 1890) of all the small planets (281 in
number) which had been discovered up to the end of 1888. The apparent
brightness, as expressed in equivalent star-magnitudes, is the only
index we have to the probable comparative sizes of by far the largest
number of the planetoids: the exceptions being among those first
discovered. Thus much premised, let us take the above points in order.
(1) There is a region lying between 2.50 and 2.80 (in terms of the
Earth's mean distance from the Sun) where the planetoids are found in
maximum abundance. The mean between these extremes, 2.65, is nearly the
same as the average of the distances of the four largest and
earliest-known of these bodies, which amounts to 2.64. May we not say
that the thick clustering about this distance (which is, however, rather
less than that assigned for the original planet by Bode's empirical
law), in contrast with the wide scattering of the comparatively few
whose distances are little more than 2 or exceed 3, is a fact in
accordance with the hypothesis in question?[24] (2) Any table which
gives the apparent magnitudes of the planetoids, shows at once how much
the number of the smaller members of the assemblage exceeds that of
those which are comparatively large; and every succeeding year has
emphasized this contrast more strongly. Only one of them (Vesta) exceeds
in brightness the seventh star-magnitude, while one other (Ceres) is
between the seventh and eighth, and a third (Pallas) is above the
eighth; but between the eighth and ninth there are six; between the
ninth and tenth, twenty; between the tenth and eleventh, fifty-five;
below the eleventh a much larger number is known, and the number
existing is probably far greater,--a conclusion we cannot doubt when the
difficulty of finding the very faint members of the family, visible only
in the largest telescopes, is considered. (3) Kindred evidence is
furnished if we broadly contrast their mean distances. Ou