G, Hinrichs on Planetology. 141 
or the squares of the times of rotation of the different rings are as the 
cubes of their radit. 
If we remember that the possible ellipsoids reach to a propor- 
tion of 1 to about 3 between polar and equatorial diameters of 
_ the nebula, we can be sure that this covers the principal god of 
the metamorphosis ; hence, (26) is rigorously proved for the 
greatest part of the condensation intervening between the forma- 
tion of two successive rings; the nebula acquires its principal 
dimensions while changing in accordance with the ellipsoidic 
figure, and when abandoning this it quickly passes to the form 
of aslightly oblate spheroid and aring. The interruption in 
our strictly mathematical demonstration cannot, therefore, seri- 
ously interfere with (26). But then this or Kepler’s third law is 
a consequence of the nebular hypothesis, or the observations embodied 
in this law sustain equally the nebular hypothesis and gravitation. 
gain, inductively, we may conclude from Kepler’s third law 
that the interruption in our analytical deductions occasioned by 
our ignorance of the exact mechanical laws of the metamorpho- 
_ S18 of the ellipsoid into the globe ring (we might in reference to 
Saturn find the expression Kronion-form convenient) is not of 
Serious conseqnences. 
‘hus we may at least conclude from the third of Kepler's 
‘great laws that the development of the planets was periodical ; 
s a this law being a fact, and (25) being rigorously true, we must 
ave 
a= constant Pe yp a ke 
_ but, as remarked before, M remains essentially constant, hence 
_ # or what is the same 4, i.e, the ellipticity ¢ of the nebula cor- 
_ Fesponding to the different planets, must have been the same at 
Corresponding epochs, just as we assumed above. mee 
Bat # the metamorphosis of the nebula has been periodic, and 
hot simultaneous, we must ascertain whether the successive inter- 
vals of time were equal or not. We shall find that they were equal, 
_ Just as it would be the most natural or the simplest to assume. 
§ 12. Spiral Nebula. 
ru. 
