1871.] 165 
[Kirkwood. 
Sp be the distance at which a planetary molecule would revolve in one 
half the period of the planet P. The disturbing effect of P will render 
the orbit of p more and more eccentric. The particle, therefore, must be 
brought into contact, either in aphelion or perihelion, with other parts of 
the ring, thus forming a planetary nucleus at such distance that its period 
would be nearly one-half that of the exterior planet. Similar reasoning 
will apply to the distances at which the ratio of the periods would be 4, 
2, or any simple relation of commensurability. We have thus an ex: 
tremely simple explanation of the facts embodied in the preceding tables. 
Should it be objected that this theory fails to account for the formation 
of the most remote planet, it may be answered that the first separation of 
matter from the condensing nebula probably occurred before the mass 
had assumed a symmetrical form. The successive ratios of the periods 
from Neptune to Jupiter are },}.and2. With Jupiter, “the giant of the 
solar system,’’ the process of planet formation seems to have culminated ; 
the mass of this stupendous globe being nearly three times greater than 
that of all other members of the solar family united. But why have we 
no planet of any considerable magnitude whose period is one-half, one- 
third, or two-fifths that of Jupiter? It may be answered, in the first 
place, that the matter of asteroid ring was so extremely rare that the in- 
tersection of orbits failed to produce large planetary nuclei. The ques- 
tion recurs, however, whence the smali mass of the ring immediately 
interior to the Jargest member of the system? The circumstances of the 
primitive asteroid-ring were different from those of any other. As its 
successive portions were thrown off at the equator of the solar nebula 
they would be liable to great perturbations by Jupiter. The perihelion 
distance of portions of the zone might thus become less than the equato- 
rial radius of the spheroid by which they had been abandoned. <A consid- 
erable proportion of the matter originally separated may have been thus 
re-united to the parent mass.* 
The writer has shown however, that in the distribution of the mean dis- 
tances of the asteroids, we have indications of an order similar to that 
of the exterior planets. This fact is rendered still more conspicuous 
by recent discoveries. The distances at which the periods of asteroids 
would be one-half, two-fifths, and one-third that of Jupiter, are respec- 
tively, 3.2776, 2.8245, and 2.5012. Between the mean distances 3.22 
and 8.82 no asteroid has yet been discovered; while between 3.12 and 
3.22 there are no less than 12. Between 2.78 and 2.88, the interval con- 
taining the distance at which five times the period of a planet would be 
equal to twice that of Jupiter, only two have been detected ; while in the 
equal space immediately interior, from 2.68 to 2.78, there are 21. Finally, 
between 2.45 and 2.55, the space in the middle of which an asteroid’s 
period would be one-third that of Jupiter, the number of known asteroids 
is 4; while in the equal space immediately interior there are 20, and in 
that exterior, 15. These facts are certainly very remarkable, and deserve 
the earnest consideration of astronomers. 
*See Proc, Am. Phil. Soc., Aug. 19, 1870, 
