Forces of the Solar System. 



317 



related as to give Jupiter an inertia-moment, at a centre of 

 spherical gyration, equivalent to that of the remaining mass at 

 the corresponding spherical surface. 



10. Saturn and the Neptune-Uranian belt are so related as 

 to give equal momenta, in reference to a nodal division midway 

 between the lower nebular, or nucleal, radii of Saturn and 

 Uranus. 



11. Jupiter and Sun are so related as to balance each other, 

 in a linear pendulum, of which the geometrical mean planetary 

 radius vector represents a centre of oscillation, and Sun's sur- 

 face represents both a centre of suspension and a fulcrum. 



Late estimates of mass* give the following values, Sun 

 being the unit : — 



Jupiter -0009543269 



Saturn -0002855837 



Uranus -0000454545 



Neptune '0000507614 



Aggregate Planetary mass '0013421925. 



On the basis of these values the following Table is con- 

 structed : — 





A. 



B. 



(A-B)^-A. 



1. h-^X V32 



•0002856 

 •0002856 

 •0002856 

 0002856 

 0002856 

 •0002856 

 •0009543 

 •0009543 

 •0009543 

 0002856 

 0009543 



•0002872 

 •0002839 

 0002856 

 •0002891 

 0002839 

 0002839 

 •0009491 

 •0009488 

 •0009545 

 •0002850 

 •0009571 



-•006 

 +•006 

 -•001 

 -012 

 +•006 

 + •006 

 +•005 

 +•006 

 •000 

 +•002 

 -•003 



2. yi — ^xt+t 



3. h — S X27r 



4. h ~ $ X 48- 16-*- 7*572 



5. T* — -^xt-rtf 



6. \i — -^ Xd^^-d 2 , 



7. ■%— pi. -f- V2 



8. ^ = ©-KV2xfxlll7'9) ... 



9 y-Y^-y---* 



10. h -S"H?x21-15-=-714 



11. -u~- (7) — (4 x 696-54) 





The fourth accordance is computed as follows. The rotation- 

 radii, or the radii of solar nuclei which would rotate synchro- 

 nously with the respective planets, are, for Neptune 4 9 '01 6 8, 

 Uranus 35*006, Saturn 20*726, Jupiter 13*154, Sun's present 

 radius being the unit. Stockwell has found f that the mean 

 perihelion longitudes of Jupiter and Uranus differ by exactly 

 180°, while the mean node longitudes of Jupiter and Saturn 

 also differ by .180°. Therefore, if the two outer tw^o-planet 

 belts were compared before their hypothetical rupture, the 

 rotation-radii, when referred to Jupiter, would be : — 



Saturn =20*726-13*154=7*572; 



Uranus =35*006 + 13*154=48*16. 



* Proc. Amer. Phil. Soc. 1875, p. 3. 



t Smithsonian Contributions, 232, p. xiv. 



