237 



Ilay land 16, 1873.] *-' J * [Uhase 



COSMICAL AND MOLECULAR HARMONIES, NO. II. 



By Pliny Earle Chase, 

 Professor of Physics in Hayerford College, 



(Bead before the American Philosophical Society, May 2 and 16, 1873.) 



I. Harmonic Indications of Intra-Mercurial Planets. 



The modification of the planetary harmonic series, by the inertia of 

 large planetary masses, is perhaps, no less interesting than the primitive 

 series themselves. 



If we take the Neptunian radius vector as our unit, the linear centre 

 of oscillation as our prime determinant, and the oscillatory ratio, 3, as 

 our harmonic difference, we obtain the harmonic series, 



¥ I I § I A &c. 



The first term of this series represents the secular mean aphelion of 

 Uranus ; the second, Saturn's mean aphelion ; the third, Saturn's aphelion 

 centre of linear oscillation, as well as the mean centre of gravity of the 

 planetary system ; the fourth, Jupiter's mean perihelion. Jupiter's mean 

 perihelion is at the octave node of Saturn's mean aphelion, and their 

 joint harmonic importance has been amply illustrated in my previous 

 papers. 



The regularity of this series is interrupted by the influence of the great 

 masses of Saturn and Jupiter, and although inferior planetary positions 

 may be approximately represented by subsequent terms, they are found 

 only at every eighth term of the Neptunian, or at every term of the sim- 

 ple Jupiter series. 



")/ A A i A 1 J i i 



■y- l 3 5 7 a TT T3 T7 



nv XU 2 _ 2 _ _2_ _2 2 2 2 2 



ul > T 1J 36 60 S¥ TUT 132 1?6 TsO" 



These terms represent, in regular succession, Jupiter's mean perihelion ; 

 the mean aphelion of Mars ; the mean distances of Earth and Venus ; the 

 mean octave node of Venus and Mercury ; Mercury's mean aphelion ; 

 Mercury's mean distance ; and the Earth's reverse centre of linear oscil- 

 lation. 



The complete continuity of this series, like that of the foregoing, is 

 broken by the combined disturbance of Earth and Venus, but its thir- 

 teenth term (^ ^ or T fe tj?) approximates quite nearly to Kirkwood's 

 estimated mean distance of Vulcan (.209 ©). A still closer accordance 

 is afforded by the following harmonic series, which assumes Earth's mean 

 distance as the unit. 



