OjV THE FORMATION OF NEBULA. 341 



of the internal gravity, produced by the same operation. By such 

 action as this the icy globe should be quickly torn into pieces and dis- 

 tributed around its primary in the form of a ring of fragments. 



Prof. Daniel Vaughan has shown that such is the origin of the rings 

 of Saturn, and ascribed the close approach of the two satellites which 

 formed them to the action of a resisting medium. 1 



If this were a globe of water instead of ice, it is very evident that 

 much less disruptive energy would be required to tear it to pieces, on 

 account of the greater mobility of its parts ; most probably not more 

 than one-seventh of the above-named force would be required to accom- 

 plish this result. 



If this force be sufficient, and the globe of water be made to revolve 

 around any large planet in fifteen hours or less, the tidal energy will 

 tear it into atoms by virtue of the following law : 



It can be demonstrated 1. That the tidal energy generated on a 

 spherical satellite of small but constant mass, when revolving around 

 a large primary, varies directly as its diameter ; 2. That it varies, 

 also, inversely as the square of its periodic time ; and 3. That the 

 ability of the same satellite to resist the disruptive tendency of this 

 tidal energy varies inversely as the square of its diameter ; provided 

 there be no cohesive force to aid in resisting this tendency, and in a 

 nebulous satellite there would be none to do so. 



As the first and third propositions relate to the diameter, they may 

 be included in one, and then the law may be stated as follows : 



The disruptive ability of the tidal energy of a primary planet on a 

 nebidous satellite of small but unvarying mass varies directly as the 

 cube of the diameter and inversely as the square of the periodic time. 

 Let us apply this law to the case in hand. To do this it may be very 

 safe to estimate that a ten-mile globe of water, while yet in the state of 

 a nebulous satellite, would occupy the globular space of at least one 

 hundred miles in diameter. This would give it a density of only i( * - 6 

 of that of water, which, however, would still be millions of times greater 

 than that of the original nebula out of which the entire system was 

 made. 



According to the above law, the disruptive ability of the tidal en- 

 ergy on the nebulous satellite must be 10 s , or 1,000 times as effective 

 as on the ten-mile liquid one, if revolving in the same time. Now, to 

 find the shortest time by the above law in which this nebulous globe 

 could revolve around its primary without disruption, we must multiply 

 the fore-named fifteen hours by the square root of 10 3 ; the product of 

 this multiplication amounts to about 19f days. As this is the short- 

 est time in which any small nebulous satellite of this density can re- 

 volve around any large primary without disruption, it becomes very 

 evident that nearly all the solid ones in our system must have been 



1 " Popular Physical Astronomy," by Prof. Daniel Vaughan. Cincinnati : Freeman & 

 Spofford. 1858. 



