6 OD. Kirkwood on certain Harmonies of the Solar System. 
rings exterior to Neptune still in the nebular state, or at least 
not yet collected about a single nucleus. 
It has been shown that, according to the nebular theory, a 
planet’s time of rotation ought to be some function of the ratio 
of the radius of its orbit to the diameter of its sphere of attrac- 
tion. Those ratios are very nearly equal in the case of Jupiter 
and Saturn; the periods of rotation are also nearly identical: 
the ratio, however, is somewhat greater in the case of Saturn; 
so also is the time of rotation. The ratios again are not ver 
different in the cases of Mercury, Venus, the Earth and Mars; 
and again in each instance a greater ratio corresponds to a slower 
rotation. The form of the function as expressed by the equation, 
-—z =a constant, 
s 
iD? 
was found by a tentative process. 
This analogy indicates, as we have stated, a longer period of 
rotation for Uranus than had been conjectured by some astrono- 
mers. It assigns, however, a physical cause for this slow revo- 
lution ; while the short period of nine hours and a half, assumed 
some writers, has no such basis. The best observers have 
failed to detect any such polar compression of the planet as 
89, 
equal to that of Jupiter or 
so great, especially in the case of 
nized. The preponderance of evi- 
: -* Main's Rudimentary Astronomy, p. 130. 
