Chase.] 1J4 [April 4, 



I. Alternate Planetary Series. 



Theoretic. Observed. Ratio. Mus. Interval.* 



Neptune'. 30.043 30.037 3.149 3.174 



Saturn 9.563 9.539 3.130 3.174 



Mean Asteroid 3.044 3.047 3.047 2.996 



Earth, perihelion 969 .966 3.137 3.174 



Mercury, " 308 .319 



Earth, mean 1.000 1.000 



Uranus 19.231 19.183 3.687 3.776 



Jupiter 5.196 5.203 3.416 3.364 



Mars 1.522 1.524 2.106 2.118 



Venus 711 .723 



The closeness of approximation between the theoretic and observed 

 values, and the near accordance of the ratios to musical intervals, in- 

 duced me to apply the test of a harmonic progression, based upon the 

 centre of linear oscillation (§), the general expression for the several 



terms being _ . I found that the mean planetary positions could be in- 



dicated by terms of such a progression, even more precisely than by 

 Bode's law, inasmuch as the asteroidal belt is skipped, and additional 

 light is thrown upon planetary eccentricities. 



We have therefore three coordinate agencies, one of centrifugal oscilla- 

 tion, represented by my modification of Bode's law ; one of centripetal 

 oscillation, represented by the above harmonic law ; and one of uniform 

 gravitating oscillation, combined with the square of the ratio of the time 



_« 

 of fall to the time of revolution, represented by - — • The two former 



series seem to be attributable to the combined centripetal and centrifugal 

 activities, at the two principal centres of inertia in our system, Sun and 

 Jupiter. I therefore take the mean perihelion distance of Jupiter as the 

 'point (V appui of my harmonic series, and construct the Bode series in 

 such manner that its sum shall be equivalent to the corresponding har- 



-n 

 monic sum. The importance of the series, is obvious at a glance. 



o* 



The doubling of the second term of that series, to give the bracketed 

 mean distance of Uranus, and the halving of the third term, to give the 

 bracketed mean distance of Mars, are curiously suggestive. 



In the following table, m denotes mean distance ; p, perihelion ; a, 

 aphelion. The musical intervals represent the number of semitones in 

 the ideal scale, proportionate to the corresponding theoretic planetary 

 distances from Jupiter's mean perihelion. The planetary eccentricities 

 are subject to such variations, that it is obviously important, in a pre- 

 liminary comparison of this kind, to consider the secular mean aphelia 

 and perihelia. 



♦According to the ideal scale in which each semitone is 12 t/ 2. 



