1873.] ±lO [Chase. 



hypothesis, we may perhaps regard it as indicative of the initial tendency 

 to planetary aggregation, iuasmnch as we may reasonahly suppose that 

 the phyllotactic, or "distributive," ratio was most operative when the 

 nebulous diffusion was greatest. 



Bode's series, like Kepler's laws, seems to have been at first merely 

 empirical. But if we conceive a rotating nebulous mass, with a slight 

 equatorial nucleus of condensation, the line of particles between the 

 nucleus and the centre will be influenced by tendencies to two different 

 kinds of motion : first, as portions of a rotating mass, with velocities 

 varying as the distance ; second, as revolving particles, with velocities 

 varying inversely as the square root of the distance. The first of these 

 tendencies, combined with the moment of inertia, would urge such par- 

 ticles as were free to move, towards the linear centre of oscillation. If 

 Mercury's mean distance be taken as the point of suspension, Uranus is 

 situated approximately at Neptune's linear centre of oscillation, and each 

 of the planets between Uranus and Yenus, is at the linear centre of 

 oscillation between the next superior and the next inferior planet. 



My own series is based on the hypothesis that undulations excited in 

 the elastic aither, like those of air, strings, and other elastic bodies, tend 

 to produce harmonic as well as equivalent undulations. The orbital 

 motions of planets, may be regarded as tangential undulations which 

 have been deflected into circles by the continual influence of gravity, 

 and the equivalent radial undulations seem to have determined the - 

 series of groupings in planetary pairs, while the harmonic undulations 

 have been most operative within the planetary belt, where the planetary 

 and aethereal vibrations are in constant mutual inter-action. It will be 

 seen that the mean error of Bode's eight terms (.0022), is more than 

 seven times as great as that of my sixteen terms (.0003), and nearly 

 twenty-seven times as great as that of the eight terms in my series which 

 are directly comparable to his (.0000822). I can think of no mode of 

 gravitating action which will account for such close accordance, as well 

 as for the modifications of the harmonic series by planetary mass and the 

 confirmation of my harmonic prediction, except the one I have already 

 mentioned, the influence of equivalent and harmonic vibrations in an 

 indefinitely elastic sether. 



All of the terms in each series, except the Bodeian term for Neptune, 

 represent actual planetary positions, or positions within the secular vari- 

 ations of planetary eccentricity. Stockw ell's discussion of the secular 

 variations of the orbital elements of the eight principal planets, has 

 shown that the most important of the correlated apsides are the same as 

 are represented in my harmonic series, for he has pointed out the follow- 

 ing curious relations : 



"I. The mean motion of Jupiter's perihelion is exactly equal to the 

 mean motion of the perihelion of Uranus, and the mean longitudes of 

 those perihelia differ by exactly 180°. II. The mean motion of Jupiter's 

 node on the invariable plane is exactly equal to that of Saturn, and the 

 mean longitudes of these nodes differ by exactly 180°." 



