Myths and Marvels of Astronomy

knowledge which we now possess, indeed, the darkness of the seeming stripe would be sufficient evidence that there must be a real division there between the rings; for we know that no mere darkness of the ring's substance could account for the apparent darkness of the stripe. It has been well remarked by Professor Tyndall, that if the moon's whole surface could be covered with black velvet, she would yet appear white when seen on the dark background of the sky. And it may be doubted whether a circular strip of black velvet 2000 miles wide, placed where we see the dark division between the rings, would appear nearly as dark as that division. Since we could only admit the possibility of some substance resembling our darker rocks occupying this position (for we know of nothing to justify the supposition that a substance as dark as lampblack or black velvet could be there), we are manifestly precluded from supposing that the dark space is other than a division between two distinct rings. Yet Sir W. Herschel, in examining the rings of Saturn with his powerful telescopes, for a long time favoured the theory that there is no real division. He called it the 'broad black mark,' and argued that it can neither indicate the existence of a zone of hills upon the ring, nor of a vast cavernous groove, for in either case it would present changes of appearance (according to the ring's changes of position) such as he was unable to detect. It was not until the year 1790, eleven years after his observations had commenced, that, perceiving a corresponding broad black mark upon the ring's southern face, Herschel expressed a 'suspicion' that the ring is divided into two concentric portions by a circular gap nearly 2000 miles in width. He expressed at the same time, very strongly, his belief that this division was the only one in Saturn's ring-system. A special interest attached at that time to the question whether the ring is divided or not, for Laplace had then recently published the results of his mathematical inquiry into the movements of such a ring as Saturn's, and, having _proved_ that a single solid ring of such enormous width could not continue to move around the planet, had expressed the _opinion_ that Saturn's ring consists in reality of many concentric rings, each turning, with its own proper rotation rate, around the central planet. It is singular that Herschel, who, though not versed in the methods of the higher mathematics, had considerable native power as a mathematician, was unable to perceive the force of Laplace's reasoning. Indeed, this is one of those cases where clearness of perception rather than profundity of mathematical insight was required. Laplace's equations of motion did not express all the relations involved, nor was it possible to judge, from the results he deduced, how far the stability of the Saturnian rings depended on the real structure of these appendages. One who was well acquainted with mechanical matters, and sufficiently versed in mathematics to understand how to estimate generally the forces acting upon the ring-system, could have perceived as readily the general conditions of the problem as the most profound mathematician. One may compare the case to the problem of determining whether the action of the moon in causing the tidal wave modifies in any manner the earth's motion of rotation. We know that as a mathematical question this is a very difficult one. The Astronomer Royal, for example, not long ago dealt with it analytically, and deduced the conclusion that there is no effect on the earth's rotation, presently however, discovering by a lucky chance a term in the result which indicates an effect of that kind. But if we look at the matter in its mechanical aspect, we perceive at once, without any profound mathematical research, that the retardation so hard to detect mathematically must necessarily take place. As Sir E. Beckett says in his masterly work, _Astronomy without Mathematics_, 'the conclusion is as evident without mathematics as with them, when once it has been suggested.' So when we consider the case of a wide flat ring surrounding a mighty planet like Saturn, we perceive that nothing could possibly save such a ring from destruction if it were really one solid structure. To recognise this the more clearly, let us first notice the dimensions of the planet and rings. We have in Saturn a globe about 70,000 miles in mean diameter, an equatorial diameter being about 73,000 miles, the polar diameter 66,000 miles. The attractive force of this mighty mass upon bodies placed on its surface is equal to about one-fifth more than terrestrial gravity if the body is near the pole of Saturn, and is almost exactly the same as terrestrial gravity if the body is at the planet's equator. Its action on the matter of the ring is, of course, very much less, because of the increased distance, but still a force is exerted on every part of the ring which is comparable with the familiar force of terrestrial gravity. The outer edge of the outer ring lies about 83,500 miles from the planet's centre, the inner edge of the inner ring (I speak throughout of the ring-system as known to Sir W. Herschel and Laplace) about 54,500 miles from the centre, the breadth of the system of bright rings being about 29,000 miles. Between the planet's equator and the inner edge of the innermost bright ring there intervenes a space of about 20,000 miles. Roughly speaking, it may be said that the attraction of the planet on the substance of the ring's inner edge is less than gravity at Saturn's equator (or, which is almost exactly the same thing, is less than terrestrial gravity) in about the proportion of 9 to 20; or, still more roughly, the inner edge of Saturn's inner bright ring is drawn inwards by about half the force of gravity at the earth's surface. The outer edge is drawn towards Saturn by a force less than terrestrial gravity in the proportion of about 3 to 16--say roughly that the force thus exerted by Saturn on the matter of the outer edge of the ring-system is equivalent to about one-fifth of the force of gravity at the earth's surface. It is clear, first, that if the ring-system did not rotate, the forces thus acting on the material of the rings would immediately break them into fragments, and, dragging these down to the planet's equator, would leave them scattered in heaps upon that portion of Saturn's surface. The ring would in fact be in that case like a mighty arch, each portion of which would be drawn towards Saturn's centre by its own weight. This weight would be enormous if Bessel's estimate of the mass of the ring-system is correct. He made the mass of the ring rather greater than the mass of the earth--an estimate which I believe to be greatly in excess of the truth. Probably the rings do not amount in mass to more than a fourth part of the earth's mass. But even that is enormous, and subjected as is the material of the rings to forces varying from one-half to a fifth of terrestrial gravity, the strains and pressures upon the various parts of the system would exceed thousands of times those which even the strongest material built up into their shape could resist. The system would no more be able to resist such strains and pressures than an arch of iron spanning the Atlantic would be able to sustain its own weight against the earth's attraction. It would be necessary then that the ring-system should rotate around the planet. But it is clear that the proper rate of rotation for the outer portion would be very different from the rate suited for the inner portion. In order that the inner portion should travel around Saturn entirely relieved of its weight, it should complete a revolution in about seven hours twenty-three minutes. The outer portion, however, should revolve in about thirteen hours fifty-eight minutes, or nearly fourteen hours. Thus the inner part should rotate in little more than half the time required by the outer part. The result would necessarily be that the ring-system would be affected by tremendous strains, which it would be quite unable to resist. The existence of the great division would manifestly go far to diminish the strains. It is easily shown that the rate of turning where the division is, would be once in about eleven hours and twenty-five minutes, not differing greatly from the mean between the rotation-periods for the outside and for the inside edges of the system. Even then, however, the strains would be hundreds of times greater than the material of the ring could resist. A mass comparable in weight to our earth, compelled to rotate in (say) nine hours when it ought to rotate in eleven or in seven, would be subjected to strains exceeding many times the resistances which the cohesive power of its substance could afford. That would be the condition of the inner ring. And in like manner the outer ring, if it rotated in about twelve hours and three-quarters, would have its outer portions rotating too fast and its inner portions too slowly, because their proper periods would be fourteen hours and eleven hours and a half respectively. Nothing but the division of the ring into a number of narrow hoops could possibly save it from destruction through the internal strains and pressures to which its material would be subjected. Even this complicated arrangement, however, would not save the ring-system. If we suppose a fine hoop to turn around a central attracting body as the rings of Saturn rotate around the planet, it may be shown that unless the hoop is so weighted that its centre of gravity is far from the planet, there will be no stability in the resulting motions; the hoop will before long be made to rotate eccentrically, and eventually be brought into destructive collision with the central planet. It was here that Laplace left the problem. Nothing could have been more unsatisfactory than his result, though it was accepted for nearly half a century unquestioned. He had shown that a weighted fine hoop may possibly turn around a central attracting mass without destructive changes of position, but he had not proved more than the bare possibility of this, while nothing in the appearance of Saturn's rings suggests that any such arrangement exists. Again, manifestly a multitude of narrow hoops, so combined as to form a broad flat system of rings, would be constantly in collision _inter se_. Besides, each one of them would be subjected to destructive strains. For though a fine uniform hoop set rotating at a proper rate around an attracting mass at its centre would be freed from all strains, the case is very different with a hoop so weighted as to have its centre of gravity greatly displaced. Laplace had saved the theoretical stability of the motions of a fine ring at the expense of the ring's power of resisting the strains to which it would be exposed. It seems incredible that such a result (expressed, too, very doubtingly by the distinguished mathematician who had obtained it) should have been accepted so long almost without question. There is nothing in nature in the remotest degree resembling the arrangement imagined by Laplace, which indeed appears on _a priori_ grounds impossible. It was not claimed for it that it removed the original difficulties of the problem; and it introduced others fully as serious. So strong, however, is authority in the scientific world that none ventured to express any doubts except Sir W. Herschel, who simply denied that the two rings were divided into many, as Laplace's theory required. As time went on and the signs of many divisions were at times recognised, it was supposed that Laplace's reasoning had been justified; and despite the utter impossibility of the arrangement he had suggested,