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on the other hand, a disappearance is possible (if the earth be rightly situated) during the whole time of the description
of the arc B D. Now, since SB or SD, the distance of Saturn from the Sun, is to SE or SG, that of the Earth, as 9:54 to 1, the angle CSD or C SB = 6° 1', and the whole angle B SD = 12° 2', which is described by Saturn (on an average) in 359.46 days, wanting only 5.8 days of a complete year. The Earth then describes very nearly an entire revolution within the limits of time when a disappearance is possible; and since, in either half of its orbit EF G or G HF, it may equally encounter the plane of the ring, one such encounter at least is unavoidable within the time specified.
(516.) Let G a be the arc of the Earth's orbit described from G in 5.8 days. Then if, at the moment of Saturn's arrival at B, the Earth be at a, it will encounter the plane of the ring advancing parallel to itself and to B E to meet it, somewhere in the quadrant H E, as at M, after which it will be behind that plane (with reference to the direction of Saturn's motion) through all the arc MEFG up to G, where it will again overtake it at the very moment of the planet quitting the arc B D. In this state of things there will be two disappearances. If, when Saturn is at B, the Earth be anywhere in the arc a H E, it is equally evident that it will meet and pass through the advancing plane of the ring somewhere in the quadrant H E, that it will again
overtake and pass through it somewhere in the semicircle EFG, and again meet it in some point of the quadrant G H, so that three disappearances will take place. So, also, if the Earth be at E when Saturn is at B, the motion of the Earth being at that instant directly towards B, the plane of the ring will for a short time leave it behind; but the ground so lost being rapidly regained as the earth's motion becomes oblique to the line of junction, it will soon overtake and pass through the plane in the early part of the quadrant EF, and passing on through G before Saturn arrives at D, will meet the plane again in the quadrant GH. The same will continue up to a certain point b, at which, if the earth be initially situated, there will be but two disappearances — the plane of the ring there overtaking the earth for an instant, and being immediately again left behind by it, to be again encountered by it in GH. Finally, if the initial place of the earth (when Saturn is at B) be in the arc 6 Fa, there will be but one passage through the plane of the ring, viz., in the semicircle GHE, the earth being in advance of that plane throughout the whole of b G.
(517.) The appearances will moreover be varied according as the Earth passes from the enlightened to the unenlightened side of the ring, or vice versa. If C be the ascending node of the ring, and if the under side of the paper be supposed south and the upper north of the ecliptic, then, when the Earth meets the plane of the ring in the quadrant HE, it passes from the bright to the dark side: where it overtakes it in the quadrant EF, the contrary. Vice versâ, when it overtakes it in FG, the transition is from the bright to the dark side, and the contrary where it meets it in GH. On the other hand, when the earth is overtaken by the ring-plane in the interval Eb, the change is from the bright to the dark side. When the dark side is exposed to sight, the aspect of the planet is very singular. It appears as a bright round disc, with its belts, &c., but crossed equatorially by a narrow and perfectly black line. This can never of course happen when the planet is more than 6° 1' from the node of the ring. Generally, the northern side is enlightened and visible when
the heliocentric longitude of Saturn is between 173° 32' and 311° 30, and the southern when between 353° 32' and 161° 30'. The greatest opening of the ring occurs when the planet is situated at 90° distance from the node of the ring, or in longitudes 77° 31' and 257° 31', and at these points the longer diameter of its apparent ellipse is almost exactly double the shorter.
(518.) It will naturally be asked how so stupendous an arch, if composed of solid and ponderous materials, can be sustained without collapsing and falling in upon the planet ? The answer to this is to be found in a swift rotation of the ring in its own plane, which observation has detected, owing to some portion of the ring being a little less bright than others, and assigned its period at 106 32m 15%, which, from what we know of its dimensions, and of the force of gravity in the Saturnian system, is very nearly the periodic time of a satellite revolving at the same distance as the middle of its breadth. It is the centrifugal force, then, arising from this rotation, which sustains it; and, although no observation nice enough to exhibit a difference of periods between the outer and inner rings have hitherto been made, it is more than probable that such a difference does subsist as to place each independently of the other in a similar state of equilibrium.
(519.) Although the rings are, as we have said, very nearly concentric with the body of Saturn, yet micrometrical measurements of extreme delicacy have demonstrated that the coincidence is not mathematically exact, but that the center of gravity of the rings oscillates round that of the body describing a very minute orbit, probably under laws of much complexity. Trifling as this remark may appear, it is of the utmost importance to the stability of the system of the rings. Supposing them mathematically perfect in their circular form, and exactly concentric with the planet, it is demonstrable that they would form a system in a state of unstable equilibrium, which the slightest external power would subvert—not by causing a rupture in the substance of the rings—but by precipitating them, unbroken, on the surface of the planet. For the attraction of such a ring or rings on a point or sphere excentrically within them, is not the same in all directions, but tends to draw the point or sphere towards the nearest part of the ring, or away from the center. Hence, supposing the body to become, from any cause, ever so little excentric to the ring, the tendency of their mutual gravity is not to correct but to increase this excentricity, and to bring the nearest parts of them together. Now, external powers, capable of producing such excentricity, exist in the attractions of the satellites, as will be shown in Chap. XII.; and in order that the system may be stable, and possess within itself a power of resisting the first inroads of such a tendency, while yet nascent and feeble, and opposing them by an opposite or maintaining power, it has been shown that it is sufficient to admit the rings to be loaded in some part of their circumference, either by some minute inequality of thickness, or by some portions being denser than others. Such a load would give to the whole ring to which it was attached somewhat of the character of a heavy and sluggish satellite maintaining itself in an orbit with a certain energy sufficient to overcome minute causes of disturbance, and establish an average bearing on its center. But even without supposing the existence of any such load, — of which, after all, we have no proof, - and granting, in its full extent, the general instability of the equilibrium, we think we perceive, in the rapid periodicity of all the causes of disturbance, a sufficient guarantee of its preservation. However homely be the illustration, we can conceive nothing more apt, in every way, to give a general conception of this maintenance of equilibrium under a constant tendency to subversion, than the mode in which a practised hand will sustain a long pole in a perpendicular position resting on the finger by a continual and almost imperceptible variation of the point of support. Be that, however, as it may, the observed oscillation of the centers of the rings about that of the planet is in itself the evidence of a perpetual contest between conservative and destructive powers — both extremely feeble, but so antagonizing one another as to prevent the latter from ever acquiring an uncontrollable ascendancy, and rushing to a catastrophe.
(520.) This is also the place to observe, that as the smallest difference of velocity between the body and the rings must infallibly precipitate the latter on the former, never more to separate (for they would, once in contact, have attained a position of stable equilibrium, and be held together ever after by an immense force); it follows, either that their motions in their common orbit round the sun must have been adjusted to each other by an external power, with the minutest precision, or that the rings must have been formed about the planet while subject to their common orbitual motion, and under the full and free influence of all the acting forces.
(521.) [The exterior ring of Saturn is described by many observers as rather less luminous than the interior, and the inner portion of this latter than its outer. On the night of Nov. 11. 1850, however, Mr. G. B. Bond, of the Harvard Observatory (Cambridge, U. S.), using the great Fraunhofer equatorial of that institution, became aware of a line of demarcation between these two portions so definite, and an extension inwards of the dusky border to such an extent (one fifth, by measurement, of the joint breadth of the two old rings), as to justify him in considering it as a newly-discovered ring. On the nights of the 25th and 29th of the same month, and without knowledge of Mr. Bond's observations, Mr. Dawes, at his observatory at Wateringbury, by the aid of an exquisite achromatic by Merz, of 64 inches aperture, observed the very same fact, and even more distinctly, so as to be sure of a decidedly darker interval between the old and new rings, and even to subdivide the latter into two of unequal degrees of obscurity, separated by a line more obscure than either.
(522.) Dr. Galle of Berlin, however, would appear to have been the first to notice (June 10. 1838), a faint extension of the inner ring towards the body of the planet, to about half the interval between the then recognised inner ring and the body, as shown by micrometrical measures. But this result remained unpublished, (or at least not generally