Chase.] 1^^ [May 15, 



and the determination of orbital eccentricities by the blending iufinence 

 of linear, circular, spherical, and harmonic undulations. § 



It is evident that every planet, satellite, or other rotating and revolv- 

 ing globe, may have its principal motions formulated by the continued 

 proportion, 



— : i/2gr : : \/2gr : (v — ^ ) •, v^ being constant for each body, 



under every possible variation of g, r, and i". The various primary 

 cosmical velocities having been determined by the general aethereal undu- 

 lations, and the arrangement of the planets being dependent on subor- 

 dinate harmonic undulations, we may reasonably look for various second- 

 ary values of v^ having a similar dependence, indicating a relation- 

 ship to solar centrifugal impulsion, analogous to that of the primary 

 velocities to tethereal centripetal impulsion, and marking a further pro- 

 gress in development. 



The equilibrium of solar centrifugal and centripetal forces, indicated 

 by the equation v = -\/gr, is a maximum at the Sun's surface. This 

 maximum velocity is equivalent to the constant determining velocity 



(»*) for Jupiter and Earth, the controlling j)lanets of the extra-aster- 

 oidal and intra-asteroidal belts. 



There is still some uncertainty about the value of f for any planet 

 but the Earth. But Proctor's discussions seem to leave no room for 

 any important error in the case of Mars, and the lengths of days at 

 Jupiter, Saturn, Venus and Mercury, are known accurately enough to 

 furnish data for satisfactory comparisons. If we compute the values 



at" * 

 of v^ = "^ from the commonly accepted elements, and regard dimin- 

 ishing velocity as an evidence of increasing inertia and lapse of time, the 

 order of planetary development, after the two principal planetary 

 centres had been fixed, appears to have been Venus, Mercury, Saturn, 

 Mars, the inner system, as a whole, being older than the outer. 



Evidences of increasing complexity are found, not only in the varied 

 simple relationships to the primary radiiis,f but also in mutual planetary 

 associations. The points at whi jh the reactionary centrifugal undula- 

 tions would have communicated velocities equivalent to ■y^ for Jupiter, 

 Earth, Venus, and Mercury, are all within the asteroidal belt. The car- 

 dinal point, that for Jnpiter and Earth, is near the outer asteroidal limit, 

 nearly midway between the orbits of those two controlling planets, and 

 at nearly a mean proportionate distance between the Sun's surface and 

 Saturn, as well as between Mercury's perihelion and Neptune's aphelion. 

 Venus and the Moon are related to the Earth, nearly as Neptune and 



* If m = mass of any planet or satellite, in units of Sun's mass, we have the gene- 



ral formula g = -py- , t" being time of solar rotation for radius r. 

 t xiii. 246-8. § xiii. 471, sqq. 



