t of the 13
largest planetoids whose apparent brightnesses exceed that of a star of
the 9.5 magnitude, there is not one having a mean distance that exceeds
3. Of those having magnitudes at least 9.5 and smaller than 10, there
are 15; and of these one only has a mean distance greater than 3. Of
those between 10 and 10.5 there are 17; and of these also there is one
exceeding 3 in mean distance. In the next group there are 37, and of
these 5 have this great mean distance. The next group, 48, contains 12
such; the next, 47, contains 13 such. Of those of the twelfth magnitude
and fainter, 72 planetoids have been discovered, and of those of them
of which the orbits have been computed, no fewer than 23 have a mean
distance exceeding 3 in terms of the Earth's. It is evident from this
how comparatively erratic are the fainter members of the extensive
family with which we are dealing. (4) To illustrate the next point, it
may be noted that among the planetoids whose sizes have been
approximately measured, the orbits of the two largest, Vesta and Ceres,
have eccentricities falling between .05 and .10, whilst the orbits of
the two smallest, Menippe and Eva, have eccentricities falling between
.20 and .25, and between .30 and .35. And then among those more recently
discovered, having diameters so small that measurement of them has not
been practicable, come the extremely erratic ones,--Hilda and Thule,
which have mean distances of 3.97 and 4.25 respectively; AEthra, having
an orbit so eccentric that it cuts the orbit of Mars; and Medusa, which
has the smallest mean distance from the Sun of any. (5) If the average
eccentricities of the orbits of the planetoids grouped according to
their decreasing sizes are compared, no very definite results are
disclosed, excepting this, that the eight Polyhymnia, Atalanta,
Eurydice, AEthra, Eva, Andromache, Istria, and Eudora, which have the
greatest eccentricities (falling between .30 and .38), are all among
those of smallest star-magnitudes. Nor when we consider the inclinations
of the orbits do we meet with obvious verifications; since the
proportion of highly-inclined orbits among the smaller planetoids does
not appear to be greater than among the others. But consideration shows
that there are two ways in which these last comparisons are vitiated.
One is that the inclinations are measured from the plane of the
ecliptic, instead of being measured from the plane of the orbit of the
hypothetical pla