ON THE STABILITY OF THE MOTION OF SATURN'S RINGS. 291 



mankind. The theory of the Moon's inequalities, though in its first stages it 

 presents theorems interesting to all students of mechanics, has been pursued into 

 such intricacies of calculation as can be followed up only by those who make 

 the improvement of the Lunar Tables the object of their lives. The value of 

 the labours of these men is recognised by all who are aware of the importance 

 of such tables in Practical Astronomy and Navigation. The methods by which 

 the results are obtained are admitted to be sound, and we leave to professional 

 astronomers the labour and the merit of developing them. 



The questions which are suggested by the appearance of Saturn's Kings 

 cannot, in the present state of Astronomy, call forth so great an amount of 

 labour among mathematicians. I am not aware that any practical use has been 

 made of Saturn's Rings, either in Astronomy or in Navigation. They are too 

 distant, and too insignificant in mass, to produce any appreciable effect on the 

 motion of other parts of the Solar system ; and for this very reason it is diffi- 

 cult to determine those elements of their motion which we obtain so accurately 

 in the case of bodies of greater mechanical importance. 



But when we contemplate the Rings from a purely scientific point of view, 

 they become the most remarkable bodies in the heavens, except, perhaps, those 

 still less useful bodies the spiral nebulae. When we have actually seen that 

 great arch swung over the equator of the planet without any visible connexion, 

 we cannot bring our minds to rest. We cannot simply admit that such is the 

 case, and describe it as one of the observed facts in nature, not admitting or 

 requiring explanation. We must either explain its motion on the principles of 

 mechanics, or admit that, in the Saturnian realms, there can be motion regu- 

 lated by laws which we are unable to explain. 



The arrangement of the rings is represented in the figure (l) on a scale 

 of one inch to a hundred thousand miles. S is a section of Saturn through 

 his equator, A, B and C are the three rings. A and B have been known for 

 200 years. They were mistaken by Galileo for protuberances on the planet itself, 

 or perhaps satellites. Huyghens discovered that what he saw was a thin flat 

 ring not touching the planet, and Ball discovered the division between A and B. 

 Other divisions have been observed splitting these again into concentric rings, 

 but these have not continued visible, the only well-established division being one 

 in the middle of A. The third ring C was first detected by Mr Bond, at 

 Cambridge U.S. on November 15, 1850; Mr Dawes, not aware of Mr Bond's 

 discovery, observed it on November 29th, and Mr Lassel a few days later. It 



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