clination may be produced. I made a similar research a few years ago concerning eccentricities, and found a region of instability corresponding with a still smaller distance from the sun, 1⋅83. The perturbations caused by Jupiter and Saturn must therefore be regarded as insufficient to explain the considerable values of the eccentricities and inclinations of so many asteroids. These values were never small, and consequently the conditions in which Laplace's nebula existed were not the same at the times of the formation of the asteroids as they were when the old planets were fixed. An interesting cosmological question is presented here, and the accumulation of new discoveries of asteroids can only facilitate its solution.
The distribution of the asteroids, according to their mean distances from the sun, or (which amounts to the same thing) according to their mean diurnal motions,[1] offers some curious facts. A table showing this factor for all the asteroids but three presents the striking feature of accumulations of minor planets about the mean motions 640", 780", and 815", with which correspond the mean distances 3·13, 2·75, and 2·67. Two principal voids may also be recognized, about 600" and 900", or the mean distances 3·27 and 2·50 from the sun. The mean diurnal motion of Jupiter is 299·42" or very nearly 300". The voids that have been pointed out thus correspond with regions where the mean motion of the planet would be exactly double or triple that of Jupiter. There are other less well-defined voids, in which the relation of the mean motions to that of Jupiter, instead of being 2 or 3, would be represented by one of the fractions 53, 73, 52, and 72 Prof. Kirkwood first brought out this fact in 1866, and generalized it by saying that the parts of the zone of the asteroids in which exists a simple relation of commensurability between the period of revolution of a minor planet and that of Jupiter are represented by gaps like the intervals between the rings of Saturn. "We remark in addition that the gaps are less sharply marked than in the case of the rings of Saturn, in that after a void the number of asteroids does not increase suddenly, but gradually, till it regains its normal value.
Can the voids be accounted for by the theory of perturbations? We should have a very simple explanation if we could show that two planets, the durations of whose revolutions are in a simple commensurable relation, exist for that reason in an eminently unstable condition which they are liable to abandon at any moment. If these conditions are realized, the usual theory of perturbations defaults; but we can not conclude that instability would result from it. Recent calculations seem rather to lead to opposite con-
- ↑ The mean diurnal motion is the quotient of the division of the number of seconds (1,296,000) in the circumference by the number of days of the planet's revolution.
