Chase.] -^44 [May 2 and 16, 



satisfactory evidences are deducible from such comparisons of uniform 

 and variable motions as are naturally suggested by the foregoing investi- 

 gations. 



Among the correlations in the preceding article, the following seem 

 peculiarly significant : 



1. The close coincidence between the vectorial ratio of Jupiter to the 

 half-modulus of light, and that of Sun's radius to Earth ; Jupiter and 

 Earth being the controlling masses of their respective planetary belts. 



2. The ratio which connects the velocity of light, the proportionate 

 masses of Sun and Planets, the velocity of planetary revolution about 

 the Sun, the variations of position in the center of gravity of the two 

 principal masses of the System (0, 2/), and the consequent orbital eccen- 

 tricity of Jupiter. 



3. The comparative cominensurability of the Jovian and Telluric Sys- 

 tems, Sun's radius and Earth's radius vector. 



13. The mean proportionality of Sun's radius between the radius of its 

 centre of gyration and the radius of the centre of gravity of the three 

 principal masses of the System (Q, %., b_ ). 



n, re 1 . The ratios which fix the elliptical orbits of the relative mean 

 aphelia and perihelia of Jupiter and Saturn and the eccentricity of 

 Mars, the planet which links the Telluric to the asteroidal belt. 



I have already invited attention to the approximate mean proportion- 

 ality betweeu the distances of Mercury and Neptune from the Sun's 

 surface, and to the resemblances between the gamuts of sound and light. 

 If we regard the condensation of planets and the gaseous elasticity of 

 their envelopes as both resultants of ^ethereal elasticity, we may naturally 

 look to logarithmic curves of the second order for some interesting com- 

 parisons. 



If we divide the planetary octave into twenty-four (= 3 >( 2 3 ) quarter 

 tones and consider Jupiter's mean perihelion as occupying the logarith- 

 mic centre of oscillation (2 3 -log. $ ), we obtain the geometrical series of 



logarithms in column Id of the following table, the ratios of the loga- 



ix 

 , rithms being represented by the gamut ratios (2)2*. For comparison, I 



have also given the logarithms of actual distance, W ; the theoretical and 



actual distances, d, d l ; and the proportionate wave-lengths of the eight 



principal Fraunhofer lines Fr. Planetary perihelion, mean, and aphelion 



distances are represented, respectively by p, m, a, in accordance with 



Stockwell's estimates of the secular mean values. 



Logarithmic Planetary Gamut. 



$m 



