in 1780 had appeared to indicate the possibility that other divisions besides the great one exist in the ring; and Laplace-his inferior as a practical astronomer, but his superior as a mathematician-had asserted that such divisions are absolutely necessary to the stability of the formation. Herschel maintained, however, and with some reason, that observation afforded no support to the theories of the French mathematician. Confident that his 20-feet reflectors were equal, if not superior, in power to the best telescopes of his day, he refused to put faith in the records of observations which his own telescopes failed to verify; and the idea of the temporary existence of such lines either never occurred to him, or was rejected as improbable.* His observations of the broad black mark,' as he at first spoke of the great division, were conducted with his usual accuracy and clearsightedness. He found that the outer and inner boundaries of this mark are both ellipses, concentric with and similar to the boundaries of the rings. He argued that the black stripe could not be the shadow of hills on the surface of the ring, since such a shadow would vary with the position of Saturn in his orbit, and when Saturn is in opposition no shadow would be visible at the ends of the longer axis of the elliptical mark, whereas it is precisely at these points that the mark is broadest. For similar reasons he rejected the idea that the line indicates the existence of a vast cavernous groove on the northern surface of the ring.

On the reappearance of the ring in the winter months of 1789-90,† he examined its southern face with his 40-feet reflector, and after carefully measuring the stripe on this face, he found that it corresponds exactly in form and dimensions with the stripe on the northern face. Accordingly, in the year 1790, he announced his suspicion that the formation is divided into two rings by a vast circular gap of uniform width-at the same time recording his opinion that this is the only division existing in the system.

On August 19th, 1787, Herschel thought he could detect a sixth satellite attending on Saturn. He remained uncertain as

* He has, in fact, recorded his opinion that the rings are undoubtedly solid formations, since they cast a strong shadow on the body of the planet.'

†The disappearances and reappearances of the rings in the years 1789-1790 are considered in Appendix II. See explanation of Table X.

to the existence of this body until the completion of his 40-feet reflector.* On August 27th, 1789, the first evening after the completion of this powerful instrument, he directed it towards Saturn. No sooner had he brought the planet into the field of view than he plainly saw six stars shining round its disc. Five of these were the satellites already discovered; it remained to be seen whether the sixth were a satellite or a fixed star. Saturn was then not far from opposition, and retrograding at the rate of 4' 30" daily; thus the motion of his system was carrying him across the celestial sphere, slowly indeed, but with a motion readily detected, even in a short time, by a telescope of such power as Herschel's. Thus, 2 hours after the first observation, Herschel found all the six stars had accompanied Saturn in his slow motion across the celestial sphere-all, therefore, were satellites.

Herschel found that the orbit of the newly-discovered satellite is within those of the other five. It is less conspicuous, and, therefore, probably smaller than any of the satellites that had hitherto been discovered. It revolves about Saturn in rather less than one day and nine hours, at a distance of about 148,000 miles from Saturn's centre, or about 112,000 miles from the surface of the planet.

While continuing his observations of this satellite, and within three weeks of its discovery, Herschel detected a seventh satellite, about as small-or, at least, as little conspicuous-as the other, and following a smaller orbit. This satellite moves at a distance of rather more than 115,000 miles from Saturn's centre, or about 79,000 miles from his surface. Its mean distance from the outer edge of the ring is less than 32,000 miles. It accomplishes a revolution around Saturn in about 22 hours-a period of revolution shorter than that of any known satellite in our system. Herschel published tables of the motions of the two satellites he had discovered. He found that the planes in which they move are either absolutely coincident with the plane of the ring, or so nearly so that no difference can be detected. Owing to this coincidence, as well as to their minuteness at so vast a distance from the earth,

This splendid telescope, only exceeded in size by the great Parsonstown reflector, had a speculum four feet in diameter. It will serve to give an idea of the patience and energy of Herschel to record that, between the years 1775 and 1781, he cast, ground, and polished 80 specula of 23 feet, 150 of 10 feet, and 200 of 7 feet focal length.

they are not favourably seen, even in the most powerful telescopes, except when the ring is very nearly closed, as was the case at the time of their discovery.

Herschel examined the belts on Saturn's surface with great care. He found that their outlines are straight lines when the rings are invisible, and change into ellipses of less and less eccentricity as the rings open more and more; that, in fact, these outlines are always similar to the outlines of the rings. From this observation it follows, assuming that the belts are due to the rotation of the planet on an axis, that the axis of rotation is perpendicular to the plane of the ring; or, in other words, that the plane of the planet's equator coincides with the plane of the ring, as had been already suggested by Dr. Halley. Herschel established beyond doubt the connection between the belts and the rotation of the planet, by the discovery of certain spots on Saturn's surface. Carefully observing the motions of these spots for some time, he found that Saturn rotates upon his axis in 10 hours, 29 minutes, 16.8 seconds. This rotation, like that of the earth, is from west to east; so that to the Saturnians the sun appears to travel across the sky from east to west, as with us. Instead of 365 days, however, the Saturnian year contains no less than 24,618 Saturnian days.

The investigations of Laplace into the stability of a solid flat ring (such as Saturn's was supposed to be) about a central attracting body, had led that distinguished mathematician to the conclusion that Saturn's rings must rotate about the planet in their own plane. In July, 1789, when the edge of the ring was turned directly towards the earth,† Herschel observed that it continued visible as a broken line of light when viewed through one of his 20-feet reflectors, and that certain spots of light were carried along this line as if by the rotation of the ring in its own plane. Continuing his observations, he found that the spots of light travelled nearly to the ends of the ansæ, so that he concluded they belonged to the outer ring. He found that they occupied 5 hours, 16 minutes, 7.5 seconds in travelling from end to end of the fine line presented

* Herschel first gave for this period 10 hours, 16 minutes, 0'44 seconds. †The ring at this time was reappearing; the earth which for a few weeks before had been on the unilluminated side of the ring passing to the illuminated side. See explanation of Table X, Appendix II.

by the ring, and he therefore announced that the outer ring rotates in its own plane in 10 hours, 32 minutes, 15 seconds. *

Herschel's measurements of the diameters of the planet and rings are somewhat in excess of the measurements now generally adopted as the most trustworthy. He considered that the breadth of the system of rings was about one-fourth greater than the breadth of the space between the inner edge of the inner ring and the planet's equator. It will be remembered that Huygens considered those breadths equal. Pound, with the same telescope as Huygens, and using an excellent micrometer, considered that the breadth of the ring-system was even somewhat less than the breadth of the space between the planet and the rings. So remarkable a discrepancy can hardly be ascribed to errors of observation, and it will presently be seen that the change which would thus appear to have taken place in the shape of the rings between the years 1659 and 1790, was part of a progressive increase of the breadth of the system, that has continued to our own time.

Herschel at first considered the form of the planet to be spheroidal, and the polar axis shorter than an equatorial diameter in about the proportion of 10 to 11. He subsequently changed his opinion as to the form of the planet, concluding, from observations taken in April, 1805, that the outline of the planet's disc is not a regular curve. He compared its form to that of a parallelogram with rounded corners, whose longest diagonal iş inclined at an angle of 43° 20' to the equatorial diameter, while its shortest diagonal is the polar axis of the planet. Subsequent observation has not confirmed this view, which probably arose from an optical illusion. At the time of observation the ring was not favourably situated for the measurement of the planet's disc. For this purpose the ring should be altogether, or very nearly closed. In April, 1805, the line of sight from the observer was inclined at an angle of about 13° to the plane of the ring, so that the ring was sufficiently open to

* Doubt has been thrown on this conclusion, since Schroeter, at the next disappearance of the ring in 1802-3, and Bond in 1848, observed that spots and irregularities along the thin line of light maintain their positions absolutely unchanged for hours. The positive evidence of the ring's rotation afforded by Herschel's observation, is not affected, however, by the observations of Schroeter and Bond. The spots seen by these astronomers have been satisfactorily explained by the latter as belonging to the general configuration of the rings, not to irregularities of form at particular parts of the rings' surface.

interfere with the measurement of the disc, an operation at all times sufficiently difficult.

From a series of observations made in the years 1789-1790, during which the earth passed three times through the plane of the ring, Herschel arrived at the conclusion that the ring must be very thin. When the edge was turned directly towards the earth, the ring continued visible in his 20-feet reflectors as a fine line of light; and in his great reflector the ring was visible even when the earth and sun were on opposite side of the ring's plane,—that is, when the unilluminated side of the ring was turned towards the earth. Along the fine line of light visible in the former case, the satellites appeared to move 'like golden beads upon a wire,' as Herschel has described the phenomenon. He did not, however, conclude from this circumstance alone that the ring's thickness is necessarily less than the diameter of the least of the satellites; for he considered that the disc of the satellite might be rendered visible on both sides of the ring by refraction through an atmosphere which he supposed might envelope the ring. He was doubtful whether the fact that the ring is visible when its dark side is turned towards the earth is due to the partial illumination of that side of the ring by light reflected from Saturn and from his satellites, or whether he only saw the illuminated edge of the ring. He judged that the edge of the ring is not perpendicular to the faces of the ring (so as to be part of a cylinder of very short axis), but that it is rounded (so as to form part of the surface of an oblate spheroid, whose axis is very short compared with its other dimensions); or, as he expressed it, that the edge of the ring is not flat but spheridical.'

*

Herschel found that when the satellites are occulted by Saturn, they appear both at ingress and egress to cling to his disc for a longer time than would be due to the dimensions of their own

* The supposition has not been confirmed by observation, however. To produce the effects described, the atmosphere of the ring must cling round the edges of the ring, since the mere presence of an atmosphere on the flat surfaces of the rings could have no other effect than to dim the lustre of the satellites. Now, it is plain that as the satellites reached (apparently) the ends of the line presented by the ring, their motion would appear to be considerably modified by refraction round the ring's edge; they would, in fact, appear to cling to the extreme end of the line for an appreciable interval: this is not the case, however; their apparent motions along and beyond the line being exactly those due to their motions in their orbits.