Myths and Marvels of Astronomy

Only six years later a discovery was made by two English observers, William and Thomas Ball, which enhanced the mystery. Observing the northern face of the ring, which was at that time turned earthwards, they perceived a black stripe of considerable breadth dividing the ring into two concentric portions. The discovery did not attract so much attention as it deserved, insomuch that when Cassini, ten years later, announced the discovery of a corresponding dark division on the southern surface, none recalled the observation made by the brothers Ball. Cassini expressed the opinion that the ring is really divided into two, not merely marked by a dark stripe on its southern face. This conclusion would, of course, have been an assured one, had the previous observation of a dark division on the northern face been remembered. With the 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 à 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, that arrangement was ordinarily described as probably existing.

At length, however, a discovery was made which caused the whole question to be reopened.

On November 10, 1850, W. Bond, observing the planet with the telescope of the Harvard Observatory, perceived within the inner bright ring a feeble illumination which he was at a loss to understand. On the next night the faint light was better seen. On the 15th, Tuttle, who was observing with Bond, suggested the idea that the light within the inner bright ring was due to a dusky ring inside the system of bright rings. On November 25, Mr. Dawes in England perceived this dusky ring, and announced the discovery before the news had reached England that Bond had already seen the dark ring. The credit of the discovery is usually shared between Bond and Dawes, though the usual rule in such matters would assign the discovery to Bond alone. It was found that the dark ring had already been seen at Rome so far back as 1828, and again by Galle at Berlin in May 1838. The Roman observations were not satisfactory. Those by Galle, however, were sufficient to have established the fact of the ring's existence; indeed, in 1839 Galle measured the dark ring. But very little attention was attracted to this interesting discovery, insomuch that when Bond and Dawes announced their observation of the dark ring in 1850, the news was received by astronomers with all the interest attaching to the detection of before unnoted phenomena.

It may be well to notice under what conditions the dark ring was detected in 1850. In September 1848 the ring had been turned edgewise towards the sun, and as rather more than seven years are occupied in the apparent gradual opening out of the ring from that edge view to its most open appearance (when the outline of the ring-system is an eclipse whose lesser axis is nearly equal to half the greater), it will be seen that in November 1850 the rings were but slightly opened. Thus the recognition of the dark ring within the bright system was made under unfavourable conditions. For four preceding years—that is, from the year 1846—the rings had been as little or less opened; and again for several years preceding 1846, though the rings had been more open, the planet had been unfavourably placed for observation in northern latitudes, crossing the meridian at low altitudes. Still, in 1838 and 1839, when the rings were most open, although the planet was never seen under favourable conditions, the opening of the rings, then nearly at its greatest, made the recognition of the dark ring possible; and we have seen that Galle then made the discovery. When Bond rediscovered the dark ring, everything promised that before long the appendage would be visible with telescopes far inferior in power to the great Harvard refractor. Year after year the planet was becoming more favourably placed for observation, while all the time the rings were opening out. Accordingly it need not surprise us to learn that in 1853 the dark ring was seen with a telescope less than three inches and a half in aperture. Even so early as 1851, Mr. Hartnup, observing the planet with a telescope eight inches and a half in aperture, found that 'the dark ring could not be overlooked for an instant.'

But while this increase in the distinctness of the dark ring was to be expected, from the mere fact that the ring was discovered under relatively unfavourable conditions, yet the fact that Saturn was thus found to have an appendage of a remarkable character, perfectly obvious even with moderate telescopic power, was manifestly most surprising. The planet had been studied for nearly two centuries with telescopes exceeding in power those with which the dark ring was now perceived. Some among these telescopes were not only of great power, but employed by observers of the utmost skill. The elder Herschel had for a quarter of a century studied Saturn with his great reflectors eighteen inches in aperture, and had at times turned on the planet his monstrous (though not mighty) four-feet mirror. Schröter had examined the dark space within the inner bright ring for the special purpose of determining whether the ring-system is really disconnected from the globe. He had used a mirror nineteen inches in aperture, and he had observed that the dark space seen on either side of Saturn inside the ring-system not only appeared dark, but actually darker than the surrounding sky. This was presumably (though not quite certainly) an effect of contrast only, the dark space being bounded all round by bright surfaces. If real, the phenomenon signified that whereas the space outside the ring, where the satellites of the planet travel, was occupied by some sort of cosmical dust, the space within the ring-system was, as it were, swept and garnished, as though all the scattered matter which might otherwise have occupied that region had been either attracted to the body of the planet or to the rings.36 But manifestly the observation was entirely inconsistent with the supposition that there existed in Schröter's time a dark or dusky ring within the bright system. Again, the elder Struve made the most careful measurement of the whole of the ring-system in 1826, when the system was as well placed for observation as in 1856 (or, in other words, as well placed as it can possibly be); but though he used a telescope nine inches and a half in aperture, and though his attention was specially attracted to the inner edge of the inner bright ring (which seemed to him indistinct), he did not detect the dark ring. Yet we have seen that in 1851, under much less favourable conditions, a less practised observer, using a telescope of less aperture, found that the dark ring could not be overlooked for an instant. It is manifest that all these considerations point to the conclusion that the dark ring is a new formation, or, at the least, that it has changed notably in condition during the present century.

I have hitherto only considered the appearance of the dusky ring as seen on either side of the planet's globe within the bright rings. The most remarkable feature of the appendage remains still to be mentioned—the fact, namely, that the bright body of the planet can be seen through this dusky ring. Where the dark ring crosses the planet, it appears as a rather dark belt, which might readily be mistaken for a belt upon the planet's surface; for the outline of the planet can be seen through the ring as through a film of smoke or a crape veil.

Now it is worthy of notice that whereas the dark ring was not detected outside the planet's body until 1838, nor generally recognised by astronomers until 1850, the dark belt across the planet, really caused by the dusky ring, was observed more than a century earlier. In 1715 the younger Cassini saw it, and perceived that it was not curved enough for a belt really belonging to the planet. Hadley again observed that the belt attended the ring as this opened out and closed, or, in other words, that the dark belt belonged to the ring, not to the body of the planet. And in many pictures of Saturn's system a dark band is shown along the inner edge of the inner bright ring where it crosses the body of the planet. It seems to me that we have here a most important piece of evidence respecting the rings. It is clear that the inner part of the inner bright ring has for more than a century and a half (how much more we do not know) been partially transparent, and it is probable that within its inner edge there has been all the time a ring of matter; but this ring has only within the last half-century gathered consistency enough to be discernible. It is manifest that the existence of the dark belt shown in the older pictures would have led directly to the detection of the dark ring, had not this appendage been exceedingly faint. Thus, while the observation of the dark belt across the planet's face proves the dusky ring to have existed in some form long before it was perceived, the same fact only helps to render us certain that the dark ring has changed notably in condition during the present century.

The discovery of this singular appendage, an object unique in the solar system, naturally attracted fresh attention to the question of the stability of the rings. The idea was thrown out by the elder Bond that the new ring may be fluid, or even that the whole ring-system may be fluid, and the dark ring simply thinner than the rest. It was thought possible that the ring-system is of the nature of a vast ocean, whose waves are steadily advancing upon the planet's globe. The mathematical investigation of the subject was also resumed by Professor Benjamin Pierce, of Harvard, and it was satisfactorily demonstrated that the stability of a system of actual rings of solid matter required so nice an adjustment of so many narrow rings as to render the system far more complex than even Laplace had supposed. 'A stable formation can,' he said, 'be nothing other than a very great number of separate narrow rigid rings, each revolving with its proper relative velocity.' As was well remarked by the late Professor Nichol, 'If this arrangement or anything like it were real, how many new conditions of instability do we introduce. Observation tells us that the division between such rings must be extremely narrow, so that the slightest disturbance by external or internal causes would cause one ring to impinge upon another; and we should thus have the seed of perpetual catastrophes.' Nor would such a constitution protect the system against dissolution. 'There is no escape from the difficulties, therefore, but through the final rejection of the idea that Saturn's rings are rigid or in any sense a solid formation.'

The idea that the ring-system may be fluid came naturally next under mathematical scrutiny. Strangely enough, the physical objections to the theory of fluidity appear to have been entirely overlooked. Before we could accept such a theory, we must admit the existence of elements differing entirely from those with which we are familiar. No fluid known to us could retain the form of the rings of Saturn under the conditions to which they are exposed. But the mathematical examination of the subject disposed so thoroughly of the theory that the rings can consist of continuous fluid masses, that we need not now discuss the physical objections to the theory.

There remains only the theory that the Saturnian ring-system consists of discrete masses analogous to the streams of meteors known to exist in great numbers within the solar system. The masses may be solid or fluid, may be strewn in relatively vacant space, or may be surrounded by vaporous envelopes; but that they are discrete, each free to travel on its own course, seemed as completely demonstrated by Pierce's calculations as anything not actually admitting of direct observation could possibly be. The matter was placed beyond dispute by the independent analysis to which Clerk Maxwell subjected the mathematical problem. It had been selected in 1855 as the subject for the Adams Prize Essay at Cambridge, and Clerk Maxwell's essay, which obtained the prize, showed conclusively that only a system of many small bodies, each free to travel upon its course under the varying attractions to which it was subjected by Saturn itself, and by the Saturnian satellites, could possibly continue to girdle a planet as the rings of Saturn girdle him.

It is clear that all the peculiarities hitherto observed in the Saturnian ring-system are explicable so soon as we regard that system as made up of multitudes of small bodies. Varieties of brightness simply indicate various degrees of condensation of these small satellites. Thus the outer ring had long been observed to be less bright than the inner. Of course it did not seem impossible that the outer ring might be made of different materials; yet there was something bizarre in the supposition that two rings forming the same system were thus different in substance. It would not have been at all noteworthy if different parts of the same ring differed in luminosity—in fact, it was much more remarkable that each zone of the system seemed uniformly bright all round. But that one zone should be of one tint, another of an entirely different tint, was a strange circumstance so long as the only available interpretation seemed to be that one zone was made (throughout) of one substance, the other of another. If this was strange when the difference between the inner and outer bright rings was alone considered, how much stranger did it seem when the multitudinous divisions in the rings were taken into account! Why should the ring-system, 30,000 miles in width, be thus divided into zones of different material? An arrangement so artificial is quite unlike all that is elsewhere seen among the subjects of the astronomer's researches. But when the rings are regarded as made up of multitudes of small bodies, we can quite readily understand how the nearly circular movements of all of these, at different rates, should result in the formation of rings of aggregation and rings of segregation, appearing at the earth's distance as bright rings and faint rings. The dark ring clearly corresponds in appearance with a ring of thinly scattered satellites. Indeed, it seems impossible otherwise to account for the appearance of a dusky belt across the globe of the planet where the dark ring crosses the disc. If the material of the dark ring were some partly transparent solid or fluid substance, the light of the planet received through the dark ring added to the light reflected by the dark ring itself, would be so nearly equivalent to the light received from the rest of the planet's disc, that either no dark belt would be seen, or the darkening would be barely discernible. In some positions a bright belt would be seen, not a dark one. But a ring of scattered satellites would cast as its shadow a multitude of black spots, which would give to the belt in shadow a dark grey aspect. A considerable proportion of these spots would be hidden by the satellites forming the dark ring, and in every case where a spot was wholly or partially hidden by a satellite, the effect (at our distant station where the separate satellites of the dark ring are not discernible) would simply be to reduce pro tanto the darkness of the grey belt of shadow. But certainly more than half the shadows of the satellites would remain in sight; for the darkness of the ring at the time of its discovery showed that the satellites were very sparsely strewn. And these shadows would be sufficient to give to the belt a dusky hue, such as it presented when first discovered.37