Chase] 4o4 rj an . 2) 



vector-radii of the centre of inertia and the centre of nebulosity. For, 



9 .2 



if we take a locus at - of p 6 , p b is at - of the locus, or at the centre of sub- 



11 o 



sidence collision and the centre of linear oscillation, while the locus 

 itself is at the centre of projection due to Saturn's spherical vis viva 



\ 11 11/ 



— of 9.5388 = 5.20298 (15. ) 



11 v ; 



This approximation gives a value for Jupiter's mean radius-vector which 



is only about of one per cent, too large. 

 J 290 f 



In the dense belt, the moment of rotary inertia (,"■,"") of Mars (7,500) is 



-1 of Earth's (30,600), while that of Venus (12,246) is .4 of Earth's, thus 

 4 



indicating the influence of Sun's mean spherical moment of inertia, when 

 expanded to Earth's orbit. The uncertainty with regard to Mercury's mass 

 is too great to warrant any present speculation as to its origin, or its in- 

 fluence on the stability of the system. 



The principal considerations, involved in these approximations, are : 



1. Fouiier's theorem, that every periodic vibratory motion can always 

 be regarded as the sum of a certain number of pendulum vibrations. 



2. The natural alternation of radial and tangential oscillations, in elastic 

 media surrounding centres of inertia. 



3. Maxwell's theorem of equality between vires vivce of translation and 

 vires vivce of rotation. 



4. Equality of action and reaction, especially in centripetal and centrifugal 

 tendencies. 



5. Perihelion indications of primitive centrifugal or rupturing force, and 

 aphelion indications of primitive centripetal "subsidence." 



6. Synchronism of rectilinear (4r) and circular (2~r) orbits. 



7. The tendency of nodes in elastic media to establish harmonic nodes. 



8. The laws of elasticity which connect arithmetical ratios of distance, 

 with geometric and harmonic ratios of density. 



9. The different variability, in condensing nebula;, of times of rotation 



:; 



(oc r 2 ) and times of revolution (cc r-). 



10. Laplace's limitation of rotating elastic stress, by the radius of equal 

 times of rotation and revolution. 



11. The counteraction of the cyclical variations of stress, during each 

 half-rotation, by the central force \g), after the analog}' of projectiles from 

 the Earth's surface. 



12. The constancy, at the nuclcal surface of any expanding or contract- 

 ing nebula, of the stress-opposing value eL # 



13. The tendency, in the primitive rupture of a nebula, to rotations in 

 opposite directions. 



