Binary Star and its attendants. 31 



6. The mean proportional between these valnes of rh and r, 

 as well as between Sun's radius and modulus, is 688*3 solar 

 radii, or 3*203 times Earth's mean radius vector, which is 

 near the outer limit of the asteroidal belt. This agrees very 

 closely with the secular range of Uranus (2*991 11); and the 

 relation is still closer to the ratio between the gravitating 



radii of Saturn and Uranus f ^ =3*209 j. The positions of 



the principal masses in the three chief companion planetary 

 pairs, iudicate 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 

 (30*46955). Neptune's secular perihelion (29*598) is within 

 one per cent, of 6 x Jupiter's secular perihelion, or in inverse 

 ratio of the indices in my equation of products of figurate 

 powers (^x&'x ^ 6 =V°). 



7. The nodal influence of linear centres of oscillation on 

 material particles which are subjected to radial " lines of 

 force " is shown in the vector radii of the three outer planets 

 (Saturn, mean aphelion, 10 ; Uranus, mean aphelion, 20*014 ; 

 Neptune, mean, 30*034). This 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 (n + 1), (n + 1) 2 , (n + 1) 3 , 

 as w r ell as the arithmetical pendulum progression 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 difference* of 180°, serve to connect these accordances 

 with the figurate equation. 



8. As further clues to the significance of the figurate equa- 

 tion, it may be well to note the closeness of the accordance 

 between the mass-ratios O : 1£, 6, or : V-, and the distance- 

 ratio (V- : ©) 6 ? as well as Stockwell's ratios* of mean peri- 

 helion- and node-motion. 



9. The radial light-oscillation which is synchronous with 

 the present limit of possible circular revolution is 10020 s *25 

 -7-497*825 = 20*128 Earth's vector radii, which is also the 

 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 rela- 

 tively to the nebular planetary centre of inertia) being 



* Stockwell, op. cit. p. xiv. 



