On the stability of the motion of Saturn's Rings

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Macmillan & Company, 1859 - Saturn (Planet) - 71 pages
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Contents

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V
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VIII
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IX
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XXVIII
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XXX
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XXXI
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XVIII
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XXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XXXIX
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XL
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XLI
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XLII
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Page iii - Prize be open to the competition of all persons who have at any time been admitted to a Degree in this University. 4. That the successful Candidate receive two years...
Page iii - PRIZE," be awarded every two years to the author of the best Essay on some subject of Pure Mathematics, Astronomy, or other branch of Natural Philosophy. 2.
Page 67 - The final result, therefore, of the mechanical theory is, that the only system of rings which can exist is one composed of an indefinite number of unconnected particles, revolving round the planet with different velocities according to their respective distances.
Page 67 - If the satellites are unequal, the propagation of the waves will no longer be regular, but disturbances of the ring will in this, as in the former case, produce only waves, and not growing confusion. Supposing the ring to consist, not of a single row of large satellites, but of a cloud of evenly distributed unconnected particles, we found that such a cloud must have a very small density in order to be permanent, and that this is inconsistent with its outer and inner parts moving with the same angular...
Page iii - ... The problem may be treated on the supposition that the system of rings is exactly or very approximately concentric with Saturn, and symmetrically disposed about the plane of his equator, and different hypotheses may be made respecting the physical constitution of the rings. It may be supposed, (1.) that they are rigid ; (2.) that they are fluid, or in part aeriform ; (3.) that they consist of masses of matter not mutually coherent. The question will be considered to be answered by ascertaining,...
Page 67 - We are not able to ascertain by observation the constitution of the two outer divisions of the system of rings; but the inner ring is certainly transparent, for the limb of Saturn has been observed through it. It is also certain that, though the space occupied by the ring is transparent, it is not through the material parts of it that Saturn was seen, for his limb was observed without distortion; which shows that there was no refraction, and therefore that the rays did not pass through a medium at...
Page 45 - On that evening, Mr. Morgan, at my request, made a drawing of the form, which on comparison coincided very closely with a drawing made independently by myself. The ratio of the diameter of the Ring to that of the Planet, as measured from the drawings, is about that of 3 to 2. The angle made by the axis of the Ring with a parallel of declination, in • the south-preceding or north-following quarter, I estimated at 60'.
Page 67 - These particles may be arranged in series of narrow rings, or they may move through each other irregularly. In the first case the destruction of the system will be very slow, in the second case it will be more rapid, but there may be a tendency towards an arrangement in narrow rings, which may retard the process.
Page 3 - We may draw the conclusion more formally as follows : — If the rings were solid and uniform, their motion would be unstable, and they would be destroyed ; but they are not destroyed, and their motion is stable, therefore they are either not uniform or not solid.
Page 1 - 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.

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