PLANETARY SYSTEMS. 81 



second of Jupiter's moons is actually denser than that great 

 planet itself. Amongst the fourteen satellites, that have been 

 investigated with any degree of certainty, the system of the 

 seven satellites of Saturn presents an instance of the greatest 

 possible contrast, both in absolute magnitude, and in distance 

 from the central body. The sixth of these satellites is probably 

 not much smaller than Mars, whilst our moon has a diameter 

 which does not amount to more than half that of the latter 

 planet. With respect to volume, the two outer, the sixth 

 and seventh of Saturn's satellites, approach the nearest to the 

 third and brightest of Jupiter's moons. The two innermost 

 of these satellites belong perhaps, together with the remote 

 moons of Uranus, to the smallest cosmical bodies of our solar 

 system, being only made visible under favourable circum- 

 stances by the most powerful instruments. They were first 

 discovered by the forty-foot telescope of William Herschel 

 in 1789, and were seen again by John Herschel at the Cape 

 of Good Hope, by Vico at Rome, and by Lament at Munich. 

 Determinations of the true diameter of satellites, made by the 

 measurement of the apparent size of their small discs, are sub- 

 jected to many optical difficulties ; but numerical astronomy, 

 whose task it is to predetermine by calculation the motions 

 of the heavenly bodies as they will appear when viewed from 

 the Earth, is directed almost exclusively to motion and mass, 

 and but little to volume. The absolute distance of a satellite 

 from its central body is greatest in the case of the outermost 

 or seventh satellite of Saturn, its distance from the body 

 round which it revolves amounting to more than two millions 

 of miles, or ten times as great a distance as that of our moon 

 from the Earth. In the case of Jupiter we find that the 

 outermost or fourth attendant moon is only 1,040,000 miles 

 from that planet, whilst the distance between Uranus and its 

 sixth satellite (if the latter really exist) amounts to as much 

 as 1,360,000 miles. If we compare, in each of these subordi- 

 nate systems, the volume of the main planet with the distance 

 of the orbit of its most remote satellite, we discover the exis- 

 tence of entirely new numerical relations. The distances of 

 the outermost satellites of Uranus, Saturn and Jupiter are, 

 when expressed in semi-diameters of the main planets, as 

 91, 64, and 27. The outermost satellite of Saturn appears, 

 therefore, to be removed only about one-fifteenth further from 



