830 James Elliot on certain 



bodies in which any extreme precision of original adjust- 

 ment has ever been detected : instead of that, they have been 

 subjected to laws by means of which every little displace- 

 ment produces its own remedy, and is its own restoring 

 cause. This rule has been proved, I believe, to hold good 

 throughout all the other motions of the solar system, prin- 

 cipal and subordinate ; and, if this were an exception, it 

 would be the only exception, standing out as a solitary ex- 

 ample of its own kind. No doubt, if any necessary con- 

 nexion could be shown to exist between the displacing and 

 the supposed restoring causes, the general law would, in 

 this instance also, hold good ; but no attempt is made to point 

 out such a connexion ; nor can we even form the least con- 

 ception in what way it can exist. In addition to this, the force 

 necessary to restore an unstable equilibrium is always so im- 

 mensely greater than that which has destroyed it, especially 

 if any considerable time has elapsed in the interval, that a 

 singularity and complexity in the restoring powers would be 

 required, such as is altogether inconsistent with the general 

 character of the planetary motions, if, indeed, it could not be 

 demonstrated to be physically impossible.* No machine can 

 be made to sustain a balanced pole. The exertion of intel- 

 ligence alone can do it. 



But let us examine Laplace's supposed demonstration of 

 the instability of equilibrium of a uniform ring round a centre 

 of attraction, and see what it amounts to, for if not conclu- 

 sive, neither his own hypothesis nor that of Sir John Her- 

 schel will be necessary. After a very elaborate process of 

 computation, to determine the proportion which the thickness 

 of the ring should bear to its breadth, or at least the limit 

 of that ratio, and a much simpler computation of the period 

 of revolution which each ring ought to have in order to main- 

 tain its form by its centrifugal force, showing that that pe- 

 riod must be the same as that of a satellite at the same dis- 

 tance, he proceeds to discuss the question of the stability of 



* I sincerely hope I have not misunderstood the sentiments of Sir John 

 Herschel, an author for whom I entertain the very highest regard. Having 

 examined his expressions carefully and repeatedly, I cannot interpret them in 

 any other sense than that which I have attached to them. 



