Caiase.] ^*^ [April 15, 



Solving the proportions, we find the following accordances : 



;.o = 16.467 



The same principles are further illustrated in the following comparative 

 table : 



Harmonic Harmonic 



Exponents and Divisors. Roots. Observed. Quotients. Observed. 



1.0000 6441.4 6441.4 Neptune, 7612 7612 A. 



1.05355=1+ f X .0153 412-5.1 4118.9 Uranus, 



1.1071 1 -I- 7 X .0153 2757.7 2742.6 " c. o., 



1.1530 1 + 10 X -0153 2011.8 2045.6 Saturn, 



1.1989 1 -I- 13 X .0153 1503.5 1510.7 Geom. mean, 



1.2448 1 + 16 X .0153 1148.0 1115.7 Jupiter, 



1.2907 1 + 19 X .0153 893.6 892.6 | " 



1.3366 1 + 22 X .0158 707.6 707.6 



1.3825 1 + 25X.0153 569.1 569.2 



1.4284 1 + 28 X .0153 464.1 457.2 @ 



1.4743 1 + 31X.0153 383.4 383.3 v 



1.5202 1 + 34 X .0153 320.3 326.8 > Mars, 



1.5661 1 -f 37 X .0153 270.5 270.3* 



The "exponents and divisors " are terms of an arithmetical progression, 

 as was shown in the foregoing note, the common diiference (.0153 ; Note 

 36) representing a differential action of Sun and Jupiter, the two controlling 

 masses of the system. Therefore, all the roots which are obtained from 

 6441.4 by using the series as exponential denominators, are harmonic roots, 

 and all the quotients which are obtained from 7612, by using the series as di- 

 visors, are harmonic quotients. The "observed" roots represent the mean 

 planetary distances, if n = 214.45 ; the "observed " wave-lengths are given 

 by Gibbs, in the American Journal of Science,* except a, which is inter- 

 polated from Angstrom's table. It is, therefore, evident that the external 

 planetary positions and the most prominent spectral lines are both influ- 

 enced by the same harmonic oscillations in the aether, modified by the law 

 of density in the planetary nodes, and by the law of simple distance in the 

 excursions of wave-lengths. 



Harmonic influence is also shown in the roots which correspond to 

 TJranus's linear centre of oscillation, the geometrical mean between the 



* [2] xliii, 4. 



