Chase.] 186 [April 21, 



and Uranus I " — := 3.209 \ . The positions of the principal masses in 

 L1824 J 



the three cljief companion planetary pairs, indicate the same law of mean 

 proportionality, between interior and exterior rupturing tendencies. For 

 Jupiter's secular aphelion (5.5193) is at the geometrical mean (5.5195) 

 between Earth's mean distance and Neptune's secular aphelion (80.46955). 

 Neptune's secular perihelion (29.598) is within one per cent, of G X Jupi- 

 ter's secular perihelion, or in inverse ratio of the indices in my equation 

 of products of ligurate powers, (y;i X 6^ X ^® = i?^")- 



7. The nodal influence of linear centres of oscillation, on material parti- 

 cles which are subjected to radial " lines of force," is shown in the .vector- 

 radii of the three outer planets, (Saturn, mean aphelion, 10; Uranus, jnean 

 aphelion, 20.044; Neptune, 7nea7i, 30.034). Tliis tendency would be aided 

 by the apparent primitive interposition of Sun between Jupiter and the 

 exterior planets; for Saturn's vector-radius is so small, in comparison with 

 modulus, that the above positions represent the geometrical progression, 

 (?!. -f 1), (n + 1)'^ (n -f l)^ as well as the arithmetical peudulum progres- 

 sion, 1, 2, 3, thus satisfying the requirements, both of elastic media and of 

 simple force-lines. The many indications that Jupiter and Saturn were 

 once parts of the same nebular belt, with a mean nodal diircrence* of 180°, 

 serve to connect those accordances with the figurate equation. 



8. As further clews to the significance of the figurate equation, it maybe 

 well to note the closeness of the accordance between the mass-ratios Q : tj;^ 

 6 ~ O : 2/, and the distance-ratio (2/ : ©)•*; as wellas Stockwell's ratios* of 

 mean perihelion and node-motion. 



9. The radial light oscillation which is synchronous with the present 

 limit of possible circular revolution, is 10020.^25 -- 497.''825 = 20.128 

 Eartli's vector-radii, which is also tlie rupturing radius of the retrograde- 

 satellite and the direct-satellite planets, the difference between the secular 

 aphelia of Saturn and Neptune, (or the vector-radius of Neptune relatively 

 to the nebular planetary centre of inertia), being 20.126; the mean aphelion 

 vector-radius of Uranus == 20.044; llie major axis of the November meteors, 

 and the secular aphelion of Uranus, each = 30.68; twice Saturn's secular 

 aphelion = 20.69; the original nebular activity thus combining witii the 

 satellite influences, in maintaining Saturn's rings. Moreover, Neptune's 

 secular perihelion ::= 1.4313 X the secular aphelion of Uranu.s, (the "kinetic 

 radius" or the limiting radius of equality, towards which I have shown 

 that all central forces mathematically tend, being 1.4232). 



10. The sum of Uranus's mean, and Earth's secular perihelion vector- 

 radius — 20.0158. The importance of Earth's position, the near approxi- 

 mation of this sum to the cardinal light oscillation (9), and the indications 



of a somewhat shorter major-axis for the inner meteors of tlie November 

 stream, encourage us to look for still further evidences of continuing 

 nebular activity, in our own orbit as well as in that of Saturn. If Earth 

 and Uranus were once parts of an elliptical ring, or meteor current, with 



Stockwell, op, cit, p. xiv. 



