Chase.] UO [April 4, 



8. The mean perihelion distance of Jupiter corresponds with the dis- 

 tance of a planetary revolution which would be synchronous with the 

 mean sun-spot period. The mean perihelion of Saturn (9.078), corres- 

 ponds with the mean perihelion centre of planetary inertia (9.039). 



- n 



9. The eighth term of the - - series (2.137 X solar radius), is equiva- 

 lent to about twice the distance of the solar-jovian centre of gravity 

 (1.006). The third term of the same series is about twice the mean radius 

 vector of Mars. 



10. The Saturnian year is to the terrestrial year, nearly as the solar 

 rotation is to terrestrial rotation, or as solar is to terrestrial superficial 

 gravity. 



11. The harmonic series between Jupiter and the inner limit of the 

 planetary belt (J, \, \, I, i, T \, T \, T V), is remarkably simple. If we in- 

 terpolate as many harmonic means between each of the terms, as are 

 equivalent to the number of remaining planets (7), the series may be ex- 

 tended to the outer planetary limit. 



12. The ultra-jovian series (2, 4, G, 2/ ; or I, f, § t};) renders each of the 

 supra-asteroidal planets subservient to the stability of the system. For 

 if all the "exterior planets were in conjunction, Jupiter would be near the 

 centre of linear oscillation, between their centre of gravity and the Sun ; 

 when Jupiter and Saturn are in opposition, Saturn, moving more slowly 

 than Jupiter, may be regarded as somewhat pivotal, and the Sun is near 

 the centre of linear oscillation ; the Sun is also near the centre of linear 

 oscillation when Saturn and Uranus are in opposition ; Uranus is near 

 Neptune's centre of linear oscillation, when those two planets are in con- 

 junction, and the time of luminous oscillation between Uranus and the 

 Sun's surface, appears to be precisely coincident with the time of planet- 

 ary oscillation at the Sun's surface. 



13. The Bodeian, Circular, and Harmonic Series, all concur in indica- 

 ting alternate planetary positions, except in the asteroidal belt, which is 

 at the extremity of linear oscillation when Jupiter and the Sun are re- 

 garded as fixing the length of the simple pendulum. 



14. The eccentricity indicated within the asteroidal belt [ (3.044—2.832) 

 -=- 2.832], is nearly equivalent to the mean eccentricity of Mars (.079). 

 The Bodeian asteroidal term represents twice the mean perihelion dis- 

 tance, while the circular term represents twice the mean distance, of Mais 

 (2.8317,2.8004; 3.044, 3.047), and, very nearly, the ratio of Jupiter's 

 mean perihelion to Mars' s mean distance (3.028). 



15. The inner limit of the asteroidal belt is near the linear centre of 

 oscillation of the outer limit. 



1G. The musical intervals are generally such as to produce chords 

 between any two adjacent theoretical planetary positions. But where 

 quarter-tones occur, the discordant vibrations seem to have broken up or 

 disturbed the tendencies to planetary aggregation, aiding in producing 

 the asteroidal belt, giving Mars and Mercury their great eccentricity, and 

 obliterating the planet between Mercury and Venus. 



