bursting of a planet once revolving in the region they occupy, the implications are:???first, that the fragments must be most abundant in the space immediately about the original orbit, and less abundant far away from it; second, that the large fragments must be relatively few, while of smaller fragments the numbers will increase as the sizes decrease; third, that as some among the smaller fragments will be propelled further than any of the larger, the widest deviations in mean distance from the mean distance from the mean distance of the original planet, will be presented by the smallest members of the hiemblage; 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 Juhrbuch 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 chiering about this distance (which is, however, rather less than that hiigned 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?* (2) Any table which gives the apparent magnitudes of the planetoids, shows at once how much the number of the smaller members of the hiemblage 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. Out 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 .