1873.] —"il [Chase. 



4. The aggregate mass of the principal planetary pair in the extra- 

 asteroidal belt (71, b_ ), is to the mass of the principal planetary pair in 

 the intra-asteroidal belt (0, J ), as the Earth's distance from the Sun, is 

 to solar radius. 



5. The aggregate mass of the exterior planetary pair (ttf, § ), is to the 

 mass of Saturn, as Saturn's mean aphelion distance, is to Neptune's 

 mean distance from the Sun. 



6. The aggregate mass of the smaller planetary pair in the terrestrial 

 belt (rf, $ ), is to the mass of the larger pair (0, 9 )? as the force of 

 solar gravitation in any planetary orbit, is to the force at the planet's re- 

 verse centre of linear oscillation (1 : 9). 



7. The aggregate mass of the inner planetary pair of the terrestrial 

 belt ( 9 , £ ), is to the mass of the outer pair (0, ^ ), as twice the square 

 of the radius of spherical gyration, is to the square of the equatorial 

 radius. The uncertainty as to the mass of Mercury, renders the last two 

 ratios more doubtful than the three preceding. In order to make them 

 equally satisfactory, it may be necessary to take account of intra-Mer- 

 curial planets or planetoids. 



8. The mean annual motion of Neptune's perihelion, is one-sixth of 

 that of Uranus ; that of Uranus being one-sixth of that of Saturn. The 

 mean perihelion distance of Mars, is one-sixth of the distance of mean 

 centre of gravity of Neptune and Uranus at their opposition. Its 

 mean distance is one sixth of Saturn's mean perihelion distance ; its mean 

 aphelion distance, one-sixth of Saturn's mean distance. 



9. Terrestrial superficial gravity, is to solar superficial gravity, as Sun's 

 radius, is to one-third of the mean distance of Mercury from the Sun's 

 surface. 



10. There are numerous relations between the varying positions of the 

 center of gravity of Saturn and Jupiter, which seem to corroborate the 

 nebular hypothesis and to encourage careful investigation. 



11. The aggregate mass of Jupiter and Mars, is to the aggregate mass 

 of Saturn and Earth, as the quotient of Saturn's aphelion by Earth's 

 mean distance, is to the quotient of Jupiter's perihelion by Mars's 

 aphelion. 



12. The aggregate mass of Earth and Mercury, is to the aggregate 

 mass of Venus and Mars, as the quotient of Mars' s mean aphelion by the 

 radius of spherical gyration in Earth's orbital sethereal sphere, is to the 

 quotient of Earth's perihelion distance by Mercury's aphelion distance. 

 This proportion, like the fourth and fifth, is affected by the uncertainty 

 of Mercury's mass. 



13. The Sun's radius is a mean proportional between its centre of gyra- 

 tion and the conjunctive centre of gravity of Sun, Jupiter's perihelion, 

 and Saturn's perihelion. 



14. The quotient of Sun's mass by Jupiter's mass, is to the fourth 

 power of the quotient of the time of planetary revolution by the time 

 of fall to the orbital center, as the mean perihelion distance of the center 

 of gravity of Sun and Jupiter, is to Sun's radius. 



a. p. s. — vol. xni. 2e 



