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G. P. Bond on the Rings of Saturn. 99 



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that to set aside these appearances by referring them to some op- 

 tical deception on the part of the observer, or to some defect ni 

 his instrument, is an explanation altogether insufficient and un- 

 satisfactory. On the other hand, we know that some of the best 

 telescopes in the world, in the hands of Struve, Bessel, Sir John 

 Herschel, and others, have given no indication of more than one 

 division, when the planet has appeared under the most perfect 

 definition. The fact, also, that the divisions on both rings have 

 not usually been visible together, and that the telescopes which 

 ^ * have shown distinctly several intervals in the old ring have failed 



i^ to reveal the new inner ring, while the latter is now seen, but 



not the former, may be taken as some evidence that the difference 

 is not probably owing to any extraordinary tranquillity or purity 

 of the atmosphere, nor to any peculiarly favorable condition of 

 the eye or instrument, but rather to some real alterations in the 

 disposition of the material of the rings. 



Admitting this, the idea that they are in a fluid state, and with- 

 m certain limits change their form and position in obedience to 

 the laws of equilibrium of rotating bodies, naturally suggests it- 

 self. There are considerations to be drawn from the state of the 

 forces acting on the rings which favor this hypothesis. For in- 

 ^ stance, on the assumption that the matter of which the ring is com- 



posed is in a solid state, we may compute for any point on its sur- 

 face the sum of the attractions of the whole ring and of Saturn. 

 The centrifugal force, generated by its rotation, may then be de- 

 termined from the condition that the particle must remain on the 

 surface. Now in the case of a solid ring, particles on the inner 

 and outer edges must have the same period of rotation. This 

 condition limits the breadth of the ring, for if it be found neces- 

 sary for the inner and outer edges to have different times of rota- 

 tion, this can be accomplished only by a division of the ring into 

 two or more parts. In this way Laplace has inferred the neces- 

 sity of there being several rings. From a more exact analysis, 

 M. Plana, in the Mem. Acad. Turin, vol. xxiv, concludes that 

 / more than one ring is not essential. The data which he assumed 



we now know to have been very wide of the truth, as regards 

 the mass and thickness of the ring. 



Vessel's last determination of the mass derived from the pro- 

 gressive motion of the line of apsides of the satellite Titan, 

 which amounts to a very sensible quantity, makes that as- 

 sumed by Plana at least thirty times too large. If Bessel's mass 

 oe received, the necessity of numerous rings can scarcely be 

 questioned. 



If the density of the ring be the same with that of Saturn, 

 ^d Its matter uniformily distributed with Bessel's mass =j\-, of 

 Saturn's, its thickness, seen from the earth, would only subtend 

 an angle of ^^ of a second of arc. It is a confirmation of the 



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