AND THEORY OF THE HEAVENS. 127 



subject which offers the greatest prospect of important 

 discoveries. 



But if Saturn has been so fortunate as to acquire a 

 ring, why then has no other planet come to participate 

 in this advantage? The reason is clear. Since a ring 

 must arise from the evaporations of a planet which has 

 exhaled them in its crude state, and as its axial rotation 

 must give them the impulsion which they have only to 

 carry on when they have reached that height at which 

 they can just attain to equilibrium with this implanted 

 motion of gravitation towards the planet, it can be easily 

 determined by calculation to what height the vapours of 

 a planet must ascend, if they are to maintain themselves 

 in free circular motion by the movements which they had 

 about its equator, when we know the diameter of the 

 planet, the period of its rotation, and the gravity of 

 bodies at its surface. According to the law of the central 

 motion the distance of a body which can revolve freely 

 in a circle around a planet with a velocity equal to its 

 axial rotation will be in the same ratio to the semi- 

 diameter of the planet as the centrifugal force at its 

 equator is to the gravity. For these reasons the distance 

 of the inner border of Saturn's ring is as 8, if its semi- 

 diameter is taken as 5, which two numbers are in the 

 same ratio as 32 : 20, which, as we have formerly observed, 

 expresses the proportion between the gravity and the 

 centrifugal force at the equator. For the same reasons, if 

 it is supposed that Jupiter were to have a ring produced 

 in this way, its least semi-diameter would exceed the 

 semi-diameter of Jupiter ten times, which would coincide 

 with the distance at which its outmost satellite revolves 

 around it ; and hence both from these reasons and be- 



