12 D. Kirkwood on certain Harmonies of the Solar System. 
a 
the third; the earth and Venus, the fourth; finally, Mercury is 
without a known companion. It was also remarked that in each 
of the three complete pairs, the first, second and fourth, the 
densities of the members are to each other very nearly as their | 
volumes; and that the facts seemed to indicate “a similarity in 
the original constitution of the members of each pair, and an 
intimate mutual dependence or connection in their primitive 
condition.” It appeared not improbable that in the first stages 
of their history, Neptune and Uranus constituted a system of 
closely associated rings; Saturn and Jupiter, another, &c., and 
that the law of planetary distances might be found in the relative 
situations of the centers of gyration of those binary rings. In short, 
my researches on the subject led to the hypothesis that the differ- 
ences of the radii of gyration of the primitive rings form a geomet- 
rical series ; or that 
d= 4 k= dk? =da ko =...= dink? 3 
where & = a constant; 
ee Deny, Ug) + + Gly = M%yy— May M2 Ns» Maan KC, respect 
ively ; 
4 
D?2,+D3 , : 
13) a se £ 2 ite the radius of gyration of the first pair, Neptune 
and Uranus; 
Diy» Dia» &c. = the distances of Neptune, Uranus, &c., from the sun ; 
Tay 73) &c., = the radii of gyration of the successive binary rings ; 
Examination of this Hypothesis. 
— values of r,,,, & and D,,, are thus computed: Having 
un 
vr, 1) 25°20061 
1 4)== 0'87270 
d, D— 17°51756 
sy “eee y (1) 
Secsaed oath k= 17-51756, (2 
?4)—0°87270) & = 768305 —7,,,, tS} 
we have the equations 
k = 3°34189 log = 0°5239916 
eee tay =e 244123 log = 0°3876087 
oe Ds =3'09800 . 
