G. Hinrichs on Planetology. 53 
inductive, reasonings with our senses. Thus, in the Jatter, we 
see the plane of the oscillations rotate, but conclude it to be the 
earth. It requires at least as much mental effort to apprehend 
its true bearing as the simple reference to the diurnal motion of 
sun, moon, and stars. 
§5. How far the nebular theory accounts for the stability of the system. 
The theory of gravitation can never, therefore, account for 
the stability of the solar system. How far, then, does the nebu- 
ar theory explain those great fundamental conditions of the 
system that ensure not only the harmony of the solar world but 
even make this harmony (almost) permanent 
In order to invite physicists and astronomers to the perusal of 
the following introduction, we will try to give a simple answer 
to this most important question. 
I. The plane of all planetary orbits must be nearly the same (see 
§1, 9, and § 8, 4, also § 10). 
_ This theorem has been clearly seen by Kant and Laplace; it 
is the most immediate expression of the hypothesis. Mr. Trow- 
bridge has recently pointed out™ to us a very interesting conse- 
quence hereof, viz: the most distant planet must move in the in- 
variable plane ; and, indeed, the inclination of the orbit of Nep- 
tune is 1° 47’, that of the invariable plane 1° 41’. 
IL. The direction of all planetary revolutions must be the same ; 
— <a consequence of the hypothesis accounts for § 3, 3, 
and §1, 10. 
Ill. The eccentricity of the planetary orbits must be very small— 
accounting for observation, §1, 11, and condition of stability, 
§3, 5 and § 10. 
This proposition has been deduced in general reasonings by 
Kant and Laplace; in the following we will try to give a dem- 
onstration of it. 
. The planetary distances are such that the successive planets 
were evolved at equal intervals of time; or if t=1, 2, 8, .... Te 
spectively for Mercury, Venus, Earth ...., then the distance is’ 
; qaae+ py So... ee ee ) 
where «, 6, y are constants, and ¢ the age of the planets above that 
of ereury. From this follows the condition of stability that 
the periodic times are incommensurable (§ 8,1). Besides, it is seen 
that this law accounts for the empirical law of Bode (§ 1, 8). : 
The analytical demonstration of this law is one of the princi- 
pal objects attempted in the present introduction. (See § 13.) 
V. The mass of the more distant planets ts the greater, on account 
of the greater space from which the material of the planet was 
Condensed (space increasing according to IV). This is confirmed 
* On the Nebular Hypothesis, $24; this Journal, November, 1864, page 355. 
