68 D. Kirkwood on Planetary Distances, 
the orbits of the innermost satellites. If the radius of gyration | 
for Mimas and Enceladus was diminished in a ratio equal to 
f Jupiter 
interpolating the two missing terms, we have the following 
ments conforming to our hypothesis: 
SATELLITES OF SATURN. 
Names. Distances. nage tneban rt. of Intervals. 
§ Japetus, 64359 : 
L ———— | 436208 649764 32-0070 
§ Hyperion 25°029 a 
I.) titen, — | 90-106 22-9604 12-4154 
Saidseds 12 21088 
iil Rhea, 8-932 106540 48156 
{ Dione, 6°399 “ 
. Tethys, 49926 5°7390 18670 
neeladus, 4:0319 : ae. 
V. 9 Mimas, 3:1408 red 
de, 00000 
Limit=2-6862 
The ratio of the ascending series of intervals is 2°578 
These ratios in the systems of Jupiter and Saturn are to each 
other inversely as the orbital velocities of the two planets. Thi 
distance from the center of Saturn at which a satellite would 
complete its orbital revolution in the present period of 
planet's rotation is 20075. The distance at which the nuel 
, then, the arrangements of the Saturnian System should 
not be admitted as confirmatory of the empirical order of dis 
tances, we may at least conclude that it is not incompatible with 
it. The eract coincidences are of course produced by the inter 
polation of the two terms. With these, our formula gives th 
ere with three unknown quantities, and, consequently, — 
whatever the distances of the known satellites, the roots of these 
equations, whether real or imaginary, must, in an algebraic sens? _ 
satisfy the conditions. At the same time it is easy to perceil 
that these algebraic results might be decidedly unfavorable 1 
the proposed hypothesis. PQ 
_ The tendency in a rotating nebula to unequal angular velocr 
ties, resulting from the increased rapidity of condensation from 
the 2 toward the center, may, perhaps, also account 
the p t 
‘ 
lished before the centrifugal force becomes equal to the centri 
etal, a spiral convergence, like that of No. 51 in Messier’s 
e, would naturally ensue. 
