218 COSMICAL ARRANGEMENTS. 



would float about with no principle of coherence 

 or stability : they would obey the general law of 

 the system, but would acknowledge no particular 

 relation to the earth. We can hardly pretend to 

 judge of the abstract possibility of such a system 

 of things ; but it is clear that it could not exist 

 without an utter subversion of all that we can 

 conceive of the economy and structure of the 

 world which we inhabit. 



With any other direct law of force, we should 

 in like manner lose gravity, without gaining the 

 theoretical regularity of the planetary motions 

 which we have described in the case just con- 

 sidered. 



2. Among inverse laws of the distance, (that is 

 those according to which the force diminishes as 

 the distance from the origin of force increases,) all 

 which diminish the central force faster than the 

 cube of the distance increases are inadmissible, 

 because they are incompatible with the perma- 

 nent revolution of a planet. Under such laws it 

 would follow, that a planet would describe a spiral 

 line about the sun, and would either approach 

 nearer and nearer to him perpetually, or perpe- 

 tually go further and further off : nearly as a 

 stone at the end of a string, when the string is 

 whirled round, and is allowed to wrap round the 

 hand, or to unwrap from it, approaches to or 

 recedes from the hand. 



If we endeavour to compare the law of the 

 inverse square of the distance, which really regu- 



