DISTRIBUTION OF SATELLITES. 273 



to explain the fact that Uranus has but half as many moong 

 as Saturn, though he is at double the distance ? While, 

 however, the current j^resumption is untenable, the Nebu- 

 lar Hypothesis furnishes us with an explanation. It actually 

 enables us to predict, by a not very complex calculation, 

 where satellites will be abundant and wdiere they will be 

 absent. The reasoning is as follows. 



In a rotating nebulous spheroid that is concentrating 

 into a planet, there are at work two antagonist mechanical 

 tendencies — the centripetal and the centrifugal. While 

 the force of gravitation draws all the atoms of the spheroid 

 together, their tangential momentum is resolvable into two 

 parts, of which one resists gravitation. The ratio which 

 this centrifugal force bears to gravitation, varies, other 

 things equal, as the square of the velocity. Hence, the 

 aggregation of a rotating nebulous spheroid will be more 

 or less strongly opposed by this outward impetus of its 

 particles, according as its rate of rotation is high or low : 

 the opposition, in equal spheroids, being four times as great 

 when the rotation is twice as rapid ; nine times as great 

 when it is three times as rapid ; and so on. Now, the de- 

 tachment of a ring from a planet-forming body of nebulous 

 matter, implies that at its equatorial zone the centrifugal 

 force produced by concentration has become so great as to 

 balance gravity. Whence it is tolerably obvious that the 

 detachment of rings will be most frequent from those 

 masses in wdiich the centrifugal tendency bears the greatest 

 ratio to the gravitative tendency. Though it is not possi- 

 ble to calculate what proportions these two tendencies had 

 to each other in the genetic spheroid which produced each 

 planet ; it is possible to calculate where each was the great- 

 est and where the least. While it is true that the ratio 

 which centrifugal force now bears to gravity at the equa- 

 tor of each planet, differs widely from that which it bore 

 iuring the earlier stages of concentration ; and while it is 

 12* 



