Chase.] 



(J54: 



[Oct. 15 and Dec. 3, 



The difference between the actual value of loof. 



I2 r. vec, and the value 

 10 



as found by the foregolnop equation, tp X S X 2/ = I2 ^"5 is therefore, 

 only .000049, representing a numerical difference of only gL of one per 

 cent. 



When the hypothetical nebular condensation had proceeded so far as to 

 show the controlling planetary influence of Jupiter's mass, the mean peri- 

 helia of Saturn and Uranus were so fixed as to establish the following 

 relationships of harmonic powers : 



?3 

 §lJ 



X 



S3 

 »21J 



X 



Is 



1; 



Stockwell's logarithmic values are 



Neptune, 

 Uranus, 



a 



Saturn, 

 Jupiter, 



tp. 



'^2 

 SlJ 



X 



U 





^2 

 •^1 



=1 



1.473337 



S3 

 ^1 

 2/3 



1.481951 a 



1.363996 ,3 



1.301989 Y 



.957973 d 



.734588 £ 



1 (a-/5) + 1 (r-8) + (e-d^) = -000085 



i («'-;5) + i ir-s) + (-^'-'0 = -000383 



The theoretical differ from the actual values, by less than J^ of one 

 per cent, in the first, and by less than j\ of one per cent, in the second 

 equation. 



At the hypothetical limit of struggle between opposing forces,- which 

 we are now considering, I have shown that the ratio between the velocity of 

 incipient dissociation and the velocity of incipient aggregation is 1 : -. 

 This ratio is found to prevail in a comparison of the vector-radii of the 

 aphelion planets in each of the aphelion or supra-asteroidal two-planet 

 belts, with the vector-radii of the perihelion planets in each of the peri- 

 helion or infra-asteroidal belts, as is shown in the following table. The 

 tabular unit is Sun's radius: 



The close accordance between the deviation of I2 X --^ and 0's mean 

 eccentricity, connects the supra-asteroidal with the infra-asteroidal 

 planets, in a manner which is still further illustrated by the Neptunian, 

 Jovian, and Telluric harmonic series of planetary positions*. 



In the harmonic series of differences between perihelion nucleal pen- 

 ■dulums (If), (If), (If), (ft), (f i)t the inter-telluric terms were ^ Venus 

 * Ante, xiii, 239. 1 Ante, xiv, 628. 



