1881. J ^t»5 [Chase. 



III. Saturn's satellite system presents two sets of harmonic indications, 



31. The Moons of Uranus. 

 The outer moon of Jupiter, the giant moon of Saturn, and the inner 

 moon of Uranus are the ones w^hich give the most direct testimony to the 

 harmonic influence of planetary oscillations. The primary satellite-har- 

 mony is determined by the joint influence of Jupiter, Earth and Sun, in 

 the systems of Earth and Jupiter ; Saturn, Venus and Sun, in the system 

 of Mars; Jupiter, Saturn and Sun, in the Saturnian system; Jupiter, 

 Uranus and Sun, in the system of Uranus. The nucleal centre has, there- 

 fore, modified all the systems ; the centre of nebulosity, all but the systems 

 of Mars and Neptune ; the centre of planetary inertia, its own system and 

 that of Mars; the centre of condensation, its own system and that of 

 Jupiter. The influence of each planetary radius appears in its own system; 

 the influence of the radius vector also appears, except in the case of Mars, 

 the outer planet of the dense belt, which shows the interaction of mean 

 planetary inertia in the outer belt and internal rupturing tendencies in the 

 inner belt. 



I. The mean rupturing locus of Uranus : Jupiter's mean locus of sub- 

 sidence : : Sun's semi-diameter : Ariel's semi-axis major. 



18.323 : 5.427 : : .00466 : .00138. 



II. The outer moon of the Uranian system represents, within less than 

 two per cent., the retarded extremity of a linear pendulum, of which the 

 inner moon represents the centre of oscillation. The harmonic divisor for 

 the second moon, as in the Jovian system, is of the form 1 + 2 a. The 

 subsequent differences are multiples of 5, the range between 1 + 2 a and 

 1 + 127 a being 5^ a. The harmonic details are shown in the following 

 table : 



