508 Prof. P. E. Chase on Planetary Interaction. 



those masses*, from Neptune's satellite and from perturba- 

 tions of Uranus, the equation gives two values for Saturn's 

 mass, one of which is slightly larger, the other slightly smaller 

 than Bessel's value. There are, however, other relations of a 

 similar character which can be measured with great accuracy. 



Laplace found that if the mass of each planet be multiplied 

 by the product of the square of the eccentricity and the square 

 root of the mean distance, the sum of all the products will 

 always retain the same magnitude ; also that if each of the 

 masses be multiplied by the product of the square of the orbital 

 inclination and the square root of the mean distance, the sum 

 of the products will always remain invariable. Now the square 

 root of the mean distance varies inversely as the velocity of 

 circular revolution at the mean distance, or inversely as the 

 square root of the velocity of nucleal rotation at the same dis- 

 tance. It is therefore probable that the primitive nucleal un- 

 dulations, to which I have hypothetically attributed both the 

 relative positions and the relative masses of the planetary orbs, 

 may have left their record in many other directions than those 

 which I have already pointed out. 



Stockwell has found f the following 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°." 



If the four great planets were ranged in a line, Jupiter on 

 one side of the sun and the remoter planets on the other, the 

 tidal influences, relatively to the nucleal centre of inertia, 

 would drive Jupiter, Uranus, and Neptune to their respective 

 aphelia. Those positions would accord with Stockwell's two 

 theorems, they would approximate the planetary centre of 

 inertia very closely to Saturn's mean radius vector, and they 

 would make the above equation of the products of triangular 

 powers applicable to vector radii as well as to masses ; for 

 the logarithms of mean vector radii and of their designated tri- 

 angular powers, according to Stockwell I, are : — 

 Neptune, mean aphelion ... 1*481951 (Neptune) 1 1*481951 

 Uranus, „ „ ... 1*301989 (Uranus) 3 3*905967 

 Jupiter, „ „ ... -734588 (Jupiter) 6 4*407528 

 • 10) 9*795446 



Saturn, mean -979496 Saturn -979545 



* "The Uranian and Neptunian Systems," Washington Obs. for 1873, 

 App. I. 



t Smithsonian Contributions, 232, p. xiv. X Ibid. P- 5. 



