lard 
1878. ] 307 [Chase. 
called attention five or six yearsago.* Hethus obtains a planetary series of 
great symmetry and beauty, but it is neither so close in its general approxi- 
mations, so broad in its indications, norso simple in its law, as my series of 
harmonic nodes, determined by the overshadowing influence of Jupiter. + 
His figures, however, in connection with my own, show that the law of 
simple harmonic interferences is universally operative, between adjacent 
planets and satellites, as well as in the systematic subordination of whole 
groups to more widely controlling masses. 
I quite agree with Professor Alexander, in thinking that the relations of 
the mean distances, detailed in his ‘‘ Harmonies,’’ { belong to a very 
ancient and probably formative state of the system ; while those of the ex- 
treme distances, as also Stockwell’s curious relations between the perihelia 
and nodes of the outer planets, § have been brought about by subsequent 
perturbations. According to the nebular hypothesis, we might naturally 
look, when rotation was first established, for arrangements determined by 
centres of spherical gravity, inertia and oscillation. But as soon as 
nucleal points appeared, corresponding linear centres began to be operative, 
and their influence must have become more and more prevalent as conden- 
sation went on, leading to the many consequences which I have already 
pointed out, as well as to many others, the discovery of which will doubt- 
less reward the labors of future investigators. Evidences of perturbative 
action originating since the establishment of the terrestrial nucleus, 
seem to be given by the following equations : 
N 0; 
he = tes (7) 
0.2 1 
(= Ca (8) 
1 
In these equations n, = the special coefficient of Jupiter's dissociative 
velocity (m, = 1/ fir) : ©, = Jupiter’s secular perihelion distance from the 
Sun ; 0, = Uranus’s mean distance from Sun ; Chirp? = limit of satellite- 
velocity at Jupiter. In view of the many pointings which we thus find 
towards the limiting velocity of light, it seems probable that the solar-dis- 
sociative velocity is still continually efficient, through the combined in- 
fluences of virtual fall and elasticity, in maintaining the gaseous structure 
of the Sun. Alexander’s relations between Saturn’s moons and belts indi- 
cate a similar gaseous structure in the belted planet; but even in the 
Saturnian system my harmonic series gives closer approximations to actual 
lunar distances, except in the cases of Titan and Tethys, than Alexander’s 
series, which represents centres of atmospheric dissociation, thus doubly con - 
firming the hypothesis that centres of spheroidal activity are first operative, 
and that afterwards, linear centres modify and extend the primitive har- 
monies. Titan is Saturn’s giant moon. The ratio of distance to planetary 
radius, for Tethys, is the same as the ratio between the limiting satellite- 
velocities of Jupiter and Earth. 
* Ante, vols. xii, 403-7, 412, 520; xiii, 146, 196 (11); xiv, 655, ete. 
+Ante, xiii, 196 (11); 237-9. 
{Smithsonian Contributions, 280. 
$Smithsonian Contributions, 232, p. xiv. 
