50 A. Hinrichs on the Density, Rotation, and Age of the Planets, 
If we only take the column of means—having again neglected — 
to take the difference of mass into account, and not having 
searched for the true formula, but only having accepted the most — 
simple form (15) satisfying (14)—we see the age of the planets 
again regularly increasing with the distance, very nearly accord: — 
ing to the law eS 
. oe eas (17) 
r=V200=142.... (18) 
i.e., about equally distant from Uranus and Saturn. 
It m e remembered that we did not try to give a useful 
interpolation,” neither do we pretend to have found the exact 
law ; yet we think that we have shown, that the nebular hypo 
thesis, if duly considered, is in complete accordance with expel 
ence. ‘The contradiction between theory and observation 80 | 
long insisted on appears to have been occasioned by neglecting — 
the most important element of dynamics, time. This elemem 
makes the planetary density increase” after a certain minimum 
has been attained. 
The Law of Rotation.—To find the velocity of rotation from 
_the primary nebulous globe is undoubtedly most difficult; but 
if we wish merely to determine the direction of rotation, and 00+ 
its amount, the following simple analysis will prove sufficient. 
The principal part of motion in the planetary ring is p@ 
to the orbit of the future planet; hence the direction will be 
defined by its equatorial part. : é 
Let then dm be the mass of a particle in the plane of the orbit, 
a+aand 6 its polar codrdinates, a the radius of orbit, 4° 
density and v the velocity in the orbit; then 
fa (19) 
a Pray ae 
will always be but a small fraction at the time of rupture, SiN@ 
the ring passes through a process of condensation previous to it 
—and as the distance to the next planet is never greater bt 
a, § will never exceed one half. Within each nebulous T0g bane 
may assume the density to vary according to _ 
dat anatse, (20) : | 
__ % Such a formula is given by Babinet, /’ Institut, 1857, p. 94. Yet for Neptun’ 
his formula a 
; A=1-2754 —0-2935.a+0-01831 .a? : 
deviating by 8 units from the true density. nat 
i i nt 14 or equal amr 
gives a result 
__.% The density of Neptune is sometimes stated to be b 
¥ Saturn ; Hambokdt, Cosmos, iv, 178 (Harper's) gives “28 as the most 
Sy, OR ee 
