276 G. Hinrichs on Planetology. 
Art. XXXIV.—Introduction to the Mathematical Principles of the 
Nebular Theory, or Planetology ; by Gustavus Hinricus, Pro- 
fessor of Physics and Chemistry, Iowa State University. 
(Concluded from p. 150.) 
§ 14.-The Lunar Distances. 
As Kepler’s third law was deduced from the planetary orbits 
alone, so was the law of Titius. But it was shown to be a con- 
sequence of the law of universal gravitation, and therefore itself 
universal and applicable to any system—hence, also to the lunar 
systems. Now the law of Titius, as modified above, has been 
found to be identical with the equality of the intervals of time im 
the history of any system. Therefore, also, this law (88) must 
apply to the lunar systems. This we now will show. 
A. The Lunar System of Jupiter. 
The Jovial World is the youngest of those great lunar systems 
that adorn the exterior planets. (This Journal, xxxvij, p. 45.) 
Therefore, it is the most regular yet of any, and our law (38) 
must very closely harmonize with the actual distances of Jupi- 
ter’s moons. It is easily found that y=2, again, as 10r 
planetary distances; and that «=4 and @=8 radii of Jupiter. 
Thus (88) is for the Jovial World, 
O28 $300 Se 
Distance, 
t. Calculated. Observed. Fall. 
Moon I. 0 3 6049 951 
reps 8s HY | 10 9°623 377 
* JIE -¢ 16 15350 650 
Sas, See 28 26°998 1°002 
The “fall” of a moon is the distance it has fallen toward the 
planet in virtue of the resisting ether. That this fall correspo 
to the age, mass and density of the different moons as 
shown in our previous article. (This Journal, xxxvil, 45.) 
he calculation of ¢ from the observed distances gives ne 
‘2d, 8d and 4th, respectively, -907, 1°92, and 2°94, which, only | 
are 
deviate by 09, 08 and -06 from the theoretical values 1, 
; and all values being too small shows that these nee 
correspondingly nearer the primary, having approached so 
on account of the etherial resistance. 
B. The lunar world of Saturn 
is next in age, hence not quite so regular as th 
t of Jupiter: 
a fe. 
if 
Rs: find that (38) represents the distances of the eight moons 
are 
ax 4-4+-0°3 5x g' giiee et ere eres . 
as will be seen from the following table: i 
