par 
1888. ] 265 | Kirkwood. 
distance and 98 exterior to it. The average interval between adjacent 
members is 0.00849, while that containing the distance 2.5012—between 
Thetis and Hestia—is 0.05886, or more than fifteen times the average. Or, 
if we take spaces adjacent to the chasm and of equal breadth with it, we 
find twenty asteroids in the interior and eighteen in the exterior. 
III. Tum pisrance 8.70. 
Kfere five periods of a minor planet would be equal to three of Jupiter. 
The distance falls in the wide hiatus interior to the orbits of Hilda and 
Ismene. 
IV. Tum DISTANCE 2.82. 
At the distance 2.82 five periods of an asteroid would be equal to two 
of Jupiter. The difference between the two terms of the ratio is three, 
and hence the conjunctions would occur at angular intervals of 1209. 
Between the distances 2.758 and 2,803 we find twenty-three minor plan- 
ets. In the next space of equal breadth, containing the distance 2.82, 
there is but one. This is No. 188, Menippe, whose elements are still some- 
what uncertain. Between 2.858 and 2.903 we find ten asteroids. 
Several other gaps have been noticed, but they become less distinctly 
marked as the cases of commensurability become less simple. Those con- 
sidered are the only cases in which the conjunctions would occur at less 
than four points of the asteroid’s orbit. 
The orbit of Tilda is doubtless nearly, if not quite, the outer limit of 
ROE 
the zone. Its mean distance is 8.9528, and in the space immediately be- 
yond—at the distance 3.9683—an asteroid’s period would be two-thirds of 
Jupiter’s. It may be observed, moreover, that at the distance 2.068, just 
within the orbit of Medusa, a minor planet would make four revolutions 
to Jupiter’s one. 
Arp ton Gaps IN THE Zone AccrpENTAL?—In 1870, before half the 
asteroids now known had been discovered, Mr. Proctor, the well-known 
astronomer, wrote : 
“The question may be suggested, however, is it not possible that the 
gaps thus apparent are merely accidental, and their accordance with the 
mean distances simply another accidental coincidence? It may seem, at 
first sight, that we have not as yet determined the orbits of a sufficient 
number of asteroids to decide very positively on this point. If another 
hundred were discovered, it might well happen, one would suppose, that 
the gaps would be filled up. But, in reality, the doctrine of chances is 
wholly opposed to.this supposition. A law, such as that exhibited in the 
figure,* does not present itself without a cause. Irregularity is to be ob- 
served in all chance combinations, and the figure may be said to exhibit 
irregularity. But irregularities resulting purely from accident, never by 
any chance (when a fairly large number of cases is taken) simulates, so 
*Mr. Proctor’s diagram was merely a graphic representation of the groups 
and chasms of the zone, 
PROG. AMBER. PHILOS. SOC, xx1. 114, 2H. PRINTED NOVEMBER 14, 1883. 
