G. Hinrichs on Planetology: 145 
this particle and the time ¢, we need only to substitute the different 
intervals corresponding to the formation of the different planets 
in order to obtain their distances. But as the evolution is regu- 
larly periodical (§ 10), it is most probable that these intervals are 
al; comparison with observation shows tiis to be the case. 
But the motion of such a particle in so rare a nebula is regu- 
lated by the attraction of the whole nebula and the resistance of 
the ether. The first of these forces is inversely proportional to 
the square of the distance a, since the mass remains sensibly 
the same, and the particle is considered as on the equatorial sur- 
face of the nebula. In other words, the force of attraction on the 
particle is the same as the force of gravitation acting upon a 
planet. Resistance of the ether will necessarily follow the same 
law, whether a single particle or a planet be subject to it. But 
then our analysis* of the motion of a planet toward the sun is 
directly applicable to the motion of the superficial particle in its 
fall toward the center of the nebula. Formula (10) of that ar- 
ticle shows the distance a (radius of the nebula) to be 
a Acere eg? ah OD 
where A is the original distance (or radius of the nebula) and ¢ 
the time of falling from A to a. Or, if a represent the distance 
of the planet that separated from the principal nebula at a time ¢ 
earlier than the now nearest planet—i.e. the age of the planet as 
counted from Mercury,—the above (85) becomes 
OAS Se a eS 
where @ and y are constants. But ih the analysis leading to (35) 
the coéfficient » of resistance 
—y é 
: "gp pod ag ge{ Oey 
has been considered constant; here we cannot do so, for though 
the density 5 of the ether and the radius ¢ of the particle may 
considered constant, the density 4 of the particle varies very 
much, about inversely as the cube of the radius of the (homo- 
geneous) nebula. If therefore, »’ be the value of » correspond- 
ing to the particle at the distance 30°0 of Neptune, »’ the same 
atthe distance 0-4 of Mercury, we have for a homogeneous 
nebula 
vf zy! == (-4)3: (30°0)% = 1: 422000 
hearly. If 4 increases toward the center this proportion would 
be diminished ; but still we see that ¥ decreases toward the inte- 
or. The formula (36) can therefore only express the principal 
Part of the law; how (36) has to be amended in order to take 
; On the Density, Rotation and relative Age of the Planets. This Journal, 1864, 
2), zxxvii, 36. 
