16 



STATEMENT AND EXPOSITION OF 



System of Uranus. 



Table (E). 

 (21) A-pproximate Arrangement. 



Oberon 

 Titania 

 Umbriel 



Ariel 



Mean Distance 

 from Planet. 



22.56 



lfi.92 



10.82 



7.40 



1..3333 



(1.3913)1 

 1.3932 



; 1.6411 



Here r — r'J, or r = rl; and the value of r increases; as r did (but regularly) 

 -n the planetary system. 



Summing up of Relations of Mean Eistances from their Respective Centres. 



{fl'l) \\\ the Planetary Sysiem the value of the leading ratio r is at first 1.7770, 

 and the regularly progressive increase of its value afterwards, from term to term 

 = 0.0138. Also r = r\ ; and r" = ?•'. 



In the System of Saturn r= 1.28273, r' = r% and r" = r\; and all the ratios 

 are constant. Moreover, for the two outermost rings, r'" = r\ = (r!)-- 



In the System of Jupiter we have / = rl ; r', at first, = 1.6007 ; and the regu- 

 larly progressive decrease of its value = 0.0051. 



In the System of Uranus r' = 7-1 ; and the value of r shows an increase from 

 term to term. 



Additional Feature of Resemblance of Two Half-Planets. 



(23) The inclination of the equator of Yenus to the plane of that planet's orbit, 

 does not seem to have been accurately determined, but it is usually stated to be 

 nearly 72°; the rotation of the planet (as is usually the case) being direct. 



In the Montldy Notices of the Royal Asfronomical Society, vol. xxiii. p. 166 (Jan. 

 1873), W. B'uffham, Esq., as a merely approximate result as yet, makes the incli- 

 nation of the equator of Uranus 80°.* "Movement direct." 



The orbits of the satellites are inclined to the ecliptic at an angle of about 79°; 

 and their motion is retrograde. 



These two half-planets, then, though near to the two extremes of the system, 

 are again alike; viz., in the great inclinations of their equators, as well as in the 

 direction of their rotations. 



' Inclination, viz., to the plane of the ecliptic. The inclination to the plane of the planet's own 

 orbit is about 794°. 



