]8To.] 629 [Chase. 



The connection of the two-planetary with the single-planet series, 

 which adds to the general harmony the local harmony of equal differences 

 on each side of the respective perihelion planets, is initiated by the rela- 

 tion of Uranus to Neptane, in other words by the simple harmonic which 

 most nearly denotes the ratio of circular orbital velocity to the velocity 

 from infinite fall. The repetition of the harmonic couplet, ?, f, both in 

 the Jovian and in the Telluric belt, is also a consequence of the same 

 initiative. If we look merely to the differences between the mean and 

 the harmonic positions, Saturn and Earth are most disturbed by the ac- 

 tion of Jupiter, Mars has fallen slightly towards Earth, Jupiter towards 

 Saturn, Venus and Mercury towards Sun. Even the greatest differences 

 are less than half of the mean eccentricities, so that the harmonic posi- 

 tions are exactly rex^resented, and traversed by each planet in each orbital 

 half-revolution. Moreover, since the geometrical mean of the actual 

 mean radii, differs by less than jV of oi^e per cent, from the geometrical 

 mean of the harmonic radii, the evidence of primitive harmonic influence 

 modified by mutual perturbations, seems irresistible. Deviation within 

 prescribed limits, allowing liberty in subordination to law, pei-vades all 

 nature, and is the source of manifold supplementary harmonies and 

 aesthetic gratifications, which would be impossible under a more rigid 

 code. 



Although the harmonic action is most simple and most striking in the 

 rotation radii, in consequence of the greater determining influence of the 

 nucleus, the action does not cease even after the withdrawal of all the 

 immediate effects of nebular condensation. We accordingly find such 

 additional rhythmical relations as are indicated by "Bode's Law," 

 "Kirk wood's Analogy," Peirce's Phyllotactic Planetotaxy, Alexander's 

 radial ratios, and the various accordances which I have hitherto commu- 

 nicated to the Society. Perhaps the most important exemplification of 

 varied influence may be found in the mutual relations of the principal 

 planetary masses ; Neptune and Saturn being of such magnitudes as to 

 equalize their inertia-iuoments near the lower nebular, or nucleal radii; 

 Saturn and Jupiter having equal moments near the upper nebular, or 

 vector-radii ; Saturn and Uranus having equal momenta with reference to 

 Jupiter, in the primitive arrangement of nticleal points ; and Jupiter 

 balancing Sun, in a linear pendulum, of which the geometrical mean 

 planetary rotation radius represents a centre of oscillcition, and Sun's 

 surface represents both a centre of suspension and a fulcrum. 



The first break in the Jovian belt appears to have separated the three 

 outer planets from Jupiter, the mass of Jupiter being such as to give the 

 same moment of inertia at a centre of spherical gyration as the remain- 

 ing mass would have at the corresponding spherical surface. The outer 

 belt subdivided in such manner that its middle planetary moment was 

 determined by Satiirn, while Saturn's was determined by Sun, the mo- 

 mentum depending on Sun, Jupiter, and Saturn, as already stated. The 

 equality of the Saturuian and Neptunian rotation-moments completed the 

 harmony of Chladni aggregation. 



