D. Kirkwood on certain Harmonies of the Solar System. 15 
according to this series, is precisely where Bond’s ring is situa- 
ted, between the body of the planet and the inner bright ring. 
The interpolated distances are 12°43 and 35°32 respectively. 
The radii of gyration of the pairs, together with their differ- 
ences, are as follows :— 
Names of Satellites. Rad. of Gyr Differences. 
I. Mimas and Enceladus, 3°61 2°13 
II. Tethys and Dione, 5°74 5°08 
If. Rhea and —— 10°82 12°13 
IV. Titan and Hyperion, 22°95 28°96 
Vv. —— and Iapetus, 51°91 | 
These differences form a geometrical series whose ratio is 
2:385. The sum of the series = 50°59, which substracted from 
51-91 gives 1:32 as the limit. The series indicates the abandon- 
ment of an indefinite number of satellites or rings in close prox- 
imity to each other, between Mimas and this limit. Now Pro- 
fessor Vaughan has shown that neither a gaseous nor a liquid 
satellite, of considerable magnitude, would be stable so near the 
primary.” Hence the probable origin of Saturn’s rings. 
IL—THE SATELLITES OF JUPITER, 
If we suppose the third and fourth satellites of Jupiter to 
have originally constituted one ring, or syste ociated 
rings, the first and second, another, and that the ratio of the 
differences of the radii of gyration was the same as in the pri- 
mary system, we shall find 
1,4) = 21°960 equatorial radii of the planet, 
No) = ‘036 = . -y 
a5 isgie * ¢ ne 
d,) = 4166 “ . 
dk 
_ = 6 “ “cc “ 
se 19°869 
and 21-960 — 19°869 = 2°091 = the distance from the center of 
the primary, within which no rings could have been formed. 
This again is nearly equal to the distance (2:299) of the point 
of equilibrium between the centripetal and centrifugal forces. 
sat we discover no decided indications of the binary arrange- 
ment in the Jovian system. Is a similar relationship then to be 
found between the respective distances of the satellites them- 
selves? ‘The four satellites of Jupiter,” says Humboldt, “ pre- 
sent a certain regularity in their distances, forming nearly the 
series, 8, 6,12. The distance of the second from the first, ex- 
pressed in diameters of Jupiter, is 3-6; the distance of the third 
_ the second, 5°7; and that of the fourth from the third, 
® Proc. Am. Assoc. for the Adv. of Sci. 1856, p. 111. 
