D. Kirkwood on certain Harmonies of the Solar System. 5 
then (2) becomes 
2 
z ae hdd ee ey ose 
(=) : (3) ::D?:D’8; or, by Kepler's third law, 
3 
dz qi n 
qedigg i? DE +s 
whence 
ae. 
# 3 2 33 (5): : (5) (3) 
or, assuming the trath of proportion (1), 
d\3 \ 3 
ee oe a z . Se, 
miei: (5): (5 (4) 
It is seen on the slightest examination that in the solar nebula, 
as well as in each of the gaseous planets, the ratio of the revolv- 
ing or equatorial radius to the radius of gyration hi through- 
out the entire process of condensation: in other words, that the 
rate of variation of density from surface to center was cont 
changing. Were the solar mass expanded so as to fill the 
earth’s orbit, the rate of variation of density remaining the 
same, the period of rotation would not be 365 days, but 5457, 
The diameter corresponding to one revolution in a sidereal year 
would be only 12,720,000 miles. If we compute the values : 
the principal radius of gyration when the spheroid extend 
the present planetary orbits respectively, we find that the sae 
mass had reached a high degree of central condensation before t 
s separation, We find, moreover, that the 
near the surface of the contracting mass. Probably it 
so great as to produce chemical action, thus forming an 
in a state of igneous fluidity by the precipitation of ‘the praia 
portion of the ynebula, long before the exterior parts had passed 
from their original gaseous condition. 
It is not necessary to ee are om as has been eel fe 
history than some = ay the sun. The formation of a single 
planet from matter diffused around the circumference of a larger 
circle, would undoubtedly require more time than the aggrega- 
tion of a ring of smaller dimensions. Possibly there may be 
4 Since writing the —s we have been favored with the reading of nig highly 
” interesting researches on the nebular hypothesis, by Davin Teowsriper, Esq., 
Perry City, N. Y. These ped thematical en sustain the probability of 
the synchronous formation of different members of the solar system. We are grat- 
ified to know that Mr. T. is preparing a realise on this subject for the press, and 
trust it may soon be given to the public. 
