have no ascertainable apparent diameter. The sixth, treating the satellite nearest to the planet as the first, and the most distant as the seventh or last, is the largest, and was first discovered. It was first observed by Huygens, and is thence called the Huygenian satellite. It is seen without much difficulty in a common telescope. The others are more difficult of observation; the first and second were never discovered till Dr. Herschel observed them; the others were discovered at different periods between the eras of Huygens and Herschel. Difficult, however, as they are of observation, one of them, the seventh, furnishes a very remarkable result. Its light, whenever it is to the east of Saturn, becomes so faint that the satellite cannot be seen without great difficulty, much exceeding that presented at other times. As in the case of the satellites of Jupiter, this cannot proceed from any phases presented by the satellite to the earth; it must, therefore, depend on some variation of its surface. We are thus enabled to conclude that this satellite has a motion of rotation round an axis, and that this motion, like the corresponding motions of Jupiter's satellites, is performed in its periodic time. We have no means of making similar observations on the other satellites; but as far as our observations go, it appears to be a fact common to all sateliltes, that they do revolve on an axis, and that the period of their revolution is the same with their periodic time. This offers a remarkable analogy, and also a remarkable contrast, to the facts stated in the table in page 122, with respect to the planets; an analogy in the existence of motions of rotation, a contrast in the circumstance that the period of rotation appears in the case of satellites to be uniformly the same with the periodic time, while in the case of the planets it evidently is unconnected with it. The most remarkable appearance presented by Saturn remains to be described. Galileo observed that Saturn did not appear spherical, but seemed to have two small bodies adhering to, or closely accompanying him; not moving round him like satellites, but continuing, at least for a considerable period of time, to hold the same position with respect to him. Some time afterwards, when the construction of telescopes was considerably improved, Huygens discovered that these were not separate bodies, but the two sides of a ring, which encompasses the planet. By minute observation, it has been ascertained that the plane of this ring is inclined at an angle of 31° 32' to that of the ecliptic, and that it exactly corresponds with the plane of the equator of the planet itself. It is found that the thickness of the ring is very small, probably not more than 1000 miles, while its outer diameter is about 200,000 miles, (its apparent diameter at the mean distance of Saturn being 47,") and its inner diameter about 161,000; the width of the whole ring being, therefore, about 20,000 miles. On more minute observation, however, it is found that the ring is divided about 6700 miles from its outer edge, and that there is then an interval of about 3800 miles in width; so that it really consists of two concentric rings, an outer and an inner one, lying in the same plane. It has even been supposed from some faint appearances of division on its surface, that it consists of a greater number of these concentric rings. These minute observations are principally due to Dr. Herschel, who has also ascertained, by the observation of some brilliant points on its surface, that it has a motion of rotation from West to East round an axis perpendicular to its plane, and passing through the centre of Saturn, and consequently coinciding with the axis of rotation of Saturn himself. The period of this rotation is .437 of a day, very nearly the same as that of the rotation of Saturn himself. A more remarkable observation is this, that the period of rotation of the ring, is that which would be the period of rotation of a satellite whose orbit was the mean circumference of the ring, deducing that period from those of the actually existing satellites, according to the law that the periodic times vary as the square root of the cubes of the distances. The plane of the ring being inclined to the ecliptic, and the earth being in the plane of the ecliptic, and Saturn never far distant from it, the plane of the ring can never be perpendicular to the line joining Saturn with the Earth. The ring, therefore, will always be seen obliquely. Now a circle, when viewed obliquely, at a considerable distance, assumes to the eye the appearance of an ellipse, an ellipse being the projection of a circle; and the more obliquely the circle is presented to the eye, or the smaller the angle made by the plane of the circle with the line joining the eye and its centre, the more excentric is the ellipse. When this line coincides with the plane of the circle, the circle assumes the appearance of a straight line. Now as the centre of the earth is a point in the ecliptic, it may evidently happen that the common section of the plane of the ring and the ecliptic, which is a line in the plane of the ecliptic, may pass through the earth; and in this case, as the same common section is a line in the plane of the ring also, the circle, which forms the ring, would be seen as a straight line. When this is the case, the edge of the ring only is presented to the spectator, and as that edge is comparatively very thin, it is not of sufficient magnitude to be visible except by telescopes of very great power. Herschel, however, succeeded in seeing it even under these circumstances, and found it, as it would naturally appear, in the form of a straight line. At different inclinations, the ellipse would of course appear of different width; but the inclination never much exceeding 30°, the minor axis of the ellipse will never be more than about half the major. These appearances may be advantageously represented by figures, of which fig. 33 represents Saturn with Fig. 33. the ring and the planet, through which stars have occasionally been seen. Again, the sun is in the plane of the ecliptic; and therefore, on the same principle as before, the common section of the ring and ecliptic may pass through it. In this case, therefore, the rays of the sun will fall only on the edge of the ring. When they do so, the ring is found to disappear to common observation; but a line of shadow, corresponding with the position of its plane, is found crossing the disk of the planet. The conclusion is obvious, that both Saturn and the ring shine only by reflected light; for the ring becomes invisible when the rays of the sun do not fall on it, which it would not do if it shone by its own light; and Saturn is darkened where the rays of the sun are intercepted from it, which also would not be the case if it were itself luminous. The very edge of the ring, however, which in this case would receive the rays of the sun, would still be illuminated; but as in the case when the edge only is turned to us, it is invisible, except with telescopes of very great power. With these Dr. Herschel succeeded in observing it. Besides these disappearances, however, which last for a comparatively short time, there are others of more importance. In fig. 35, let S represent the place of the sun, the circle described about it the orbit of Saturn, h any position of Saturn, and Ah B (a line drawn through ) the intersection of the plane of the ring with the plane of the ecliptic. Let XY be drawn through S, parallel to A h B, and meeting the orbit in X and Y. The plane Fig. 35. several intersections of that plane with the plane of the ecliptic will always be parallel. When, therefore, the planet is at X and Y, this intersection will coincide with the lines X S, Y S, joining the centre of the ring and the sun. This, therefore, must happen twice in each revolution of the planet round the sun; and on these occasions the disappearances of the ring, of which we have last spoken, will occur, the edge of the ring being then turned towards the sun. Besides this, it is plain that one side of the ring will be turned towards the sun throughout that half of the orbit which lies from X through to Y; and the other side, throughout the remaining half; and consequently that the opposite sides of the ring will be illumined during each of these periods; and that one side will always be light, and the other dark, except on the occasions when the edge of the ring only is presented to the sun, and both the sides are deprived of his light. Now the earth is at a considerable distance from the sun, though that distance is small when compared with its distance from Saturn. It may easily, therefore, happen that the plane of the ring passes between the earth and the sun, and consequently that the opposite sides of the ring are presented to those bodies. The dark side, therefore, will be presented to the earth, and the ring will, on that account, be invisible. The very edge, indeed, of the ring would not be absolutely turned away either from the sun or the earth; it would therefore be illumined, and this illuminated edge might be visible; and here again Dr. Herschel, with the assistance of his very powerful instruments, has succeeded in seeing this small portion of the ring, when it was invisible to all other observers. Generally speaking, however, the ring may be considered as invisible during this period; and Galileo was led for a time to doubt the correctness of his discovery, from the disappearance of the ring from this cause after he had for some months observed it. Its nature and the laws of its motion were not then sufficiently ascertained to enable him to account for this disappearance, and the correctness of his original observations appeared doubtful, until the re-appearance of the ring, when the sun and earth again were on the same side of its plane, confirmed them. tion of the line in which the plane of the ring intersects the ecliptic; for this plane then passes through the earth, and the line joining Saturn and the earth is the line of intersection required. This line always moves parallel to itself. When, therefore, it is ascertained by observation that the edge of the ring is presented to the sun, in which case we have already seen that this line of intersection must pass through the sun, the position of this line is known. The position of the line joining the earth and sun may be observed at the same period; and consequently the angle between these two lines known. The elongation, also, of Saturn from the sun, as seen at the earth, may be observed. As in the case of Jupiter, therefore, we know the angles of the rectilineal triangle formed by lines joining the sun, the earth, and Saturn; and we can, therefore, ascertain the distances of Saturn from the Sun, and from the earth; and from the latter, and the apparent magnitude at the time, we can ascertain the real magnitude. As in the case of Jupiter, the results so obtained correspond with those deduced from the law of the periodic times. His diameter is thus ascertained to be ten times that of the earth, and his whole bulk of course to exceed that of the earth in the propor tion of the cube of 10, or of 1000 to 1. Uranus is so distant from the earth that there is little opportunity of minute observation concerning him. He is, however, ascertained to have six satellites moving in orbits nearly circular, and with periodic times corresponding to their distances according to the usual law. Their mean distances are respectively 13.120, 17.022, 19.845, 22.752, 45.507, and 91.008 times the radius of the planet; and their periodic times, 5.8926, 8.7068, 10.9611, 13.4559, 38.0750, and 107.6944 days. There is one remarkable difference in their motions from those of the other bodies which we have considered. Their orbits are very nearly perpendicular to the ecliptic; and their motion, therefore, can hardly be considered from West to East, agreeably to the uniform rule found to obtain in all the other motions of the system. These satellites, as well as the planet which they accompany, were all discovered by Dr. Herschel; and he further suspected, from the result of his observations, that the planet The observation of the periods when was surrounded by two rings perpendithe edge of the ring is presented to the cular to each other. This fact, if estaearth, enables us to determine the direc-blished, is a remarkable and very curious one; but it cannot at present be considered as at all certain. There are no means of ascertaining his distance and actual magnitude, like those mentioned in the case of Jupiter and Saturn; the determination of these elements must, therefore, rest on the observation of his periodic time, and the law by which the distances and periodic times are connected. We have now gone through a statement of the motions of all the bodies which are commonly considered to form the solar system. There are, indeed, other bodies belonging to it which occasionally appear in the heavens, and excite much observation and curiosity when they do so, which are known by the name of comets. Their motions, however, are more complicated and difficult of ascertainment, and cannot well be explained without the aid of some theory to which we have not, up to the present period of this treatise, attained. These motions, also, are not suited to throw much light on certain very important considerations, to which we are now qualified to proceed; it will, therefore, be most convenient to postpone any consideration of them for the present, and proceed to examine the results which we have already obtained; and to deduce from them some very important modifications, or rather a complete reconstruction of a great part of our whole system of astronomy. CHAPTER V. planet, in the focus; and that the radius vector of the revolving body describes equal areas in equal times. Again, we have reason to conclude, though not with the same certainty, that all the bodies of the solar system have motions of rotation round an axis; the planets in times which do not appear to follow any particular rule; the satellites in times always equal to the periodic time of the particular satellite round its planet. We are not, indeed, able to ascertain these facts with respect to all the bodies with which we are acquainted, of either description; but we find the case to be so with respect to all which we can observe; and it is, therefore, a natural conjecture, that it is so in the others also, as they present no appearances inconsistent with the supposition. We should, therefore, be inclined to conjecture, that a new planet, if such should hereafter be discovered revolving round the sun, would have a motion of rotation round an axis; and that, if it were accompanied by any satellite, this satellite would itself revolve round an axis, and that its times of rotation on its axis, and of revolution round the planet, would be equal. All the other motions of the solar system are from West to East; we should, therefore, expect that these would be so also. Now we have already stated, that the sun's periodic time is exactly equal to what would, in the supposition of the same law obtaining at that distance, be the periodic time of a planet revolving round the sun in an orbit of which the major axis was equal to that of the sun's SECTION I.-First idea of the motion of orbit round the earth. If, therefore, for the Earth. ON comparing together all the facts which we have ascertained with respect to the planets and their satellites, we may consider certain general laws to be completely established. The proportion between the periodic times and the major axes of the orbits is found to subsist, both with respect to every planet in its revolution round the sun, and to every satellite of each particular planet in its revolution round that planet. Subsisting thus, at distances very far different from each other, it is at least a plausible conjecture that it does so generally, and, consequently, that if a new planet or satellite were discovered, its motions would follow this same law. The same remark will apply to Kepier's other laws, namely, that these revolutions take place in elliptic orbits round the sun, or the an instant we suppose that the appearances actually observed could equally well be explained on the supposition of the earth revolving round the sun at that distance at which we have hitherto considered the sun to revolve round the earth, the periodic time observed would correspond with that determined by the general law regulating the duration of such revolutions. We are always able to observe the position of the moon with respect to the earth, and the supposition we are proposing would not be fit for adoption, if it were found inconsistent with her motions. But if it be not so, and if it be also true, the moon would evidently be a body revolving round the earth, and accompanying it in its course round the sun; or it would be a satellite of the earth. We should, therefore, be led to expect, that if the earth and moon were such a planet and satellite, they would each have a motion of rotation from West to East; and that the motion of rotation of the moon would be completed in the time of its revolution round the earth. In fact, we know that it is so; and this instance of correspondence, though by itself it furnishes no proof of the truth of the supposition, leads us at least to consider it as one worth investigation. The motions of the moon, also, both of revolution and rotation, are from West to East, like those of the other planets and satellites. It would be easy at once to point out some arguments which, assuming that the supposition is not inconsistent with the appearances observed, would induce us to consider it the true one; but as no probabilities of this kind could warrant us in adopting the supposition, if it failed to correspond with these appearances, the preferable order will be first to examine whether it is capable of explaining them. If it proves so, it will then be time to consider whether it furnishes a more probable explanation of them than the supposition which we have hitherto adopted, and which observation originally leads us to, namely, that the earth is at rest, and that all the heavenly bodies revolve about it. We proceed, therefore, first to investigate the effects which might be produced by the rotation of the earth round an axis, and its revolution round the sun, supposing these to exist. We shall find that they correspond with the appearances actually presented. It is, however, a plausible objection, that these motions cannot exist, for that, if they did, we should be sensible of them. Our next object, therefore, will be to consider and remove this objection, and we shall, then, examine the probabilities which there are in favour of the supposition of the earth's motion; and, finally, point out one particular phenomenon which can only be explained on that supposition, and which, therefore, seems almost exclusively to demonstrate its truth. This is the phenomenon of the aberration of the fixed stars: it has been mentioned before, but its explanation deferred. SECTION II.-Identity of the appearances on the supposition that the Sun and Heavens are at rest, and the Earth describes an orbit round the Sun, and revolves on an axis with those actually observed. THE general principle which will lead us through all the considerations requisite to the discussion of this subject, is this: that wherever it is known that of two bodies one revolves round, or has any motion with respect to, the other, their relative motions may be equally well explained, whichever of the two we suppose to be at rest, and the other in motion. The simplest case is that of two bodies only, considered without reference to any others, and on the supposition that the motion of the moving body takes place in a plane; and a very simple diagram, and very simple considerations, will suffice to show that their relative motions, whatever they be, may be equally well explained, whichever we consider to be at rest. Of course, when two bodies only are concerned, their relative motions will be the same on different suppositions, if their distances from, and directions with respect to each other, are the same on each; we are not concerned with their actual positions in space. Let then A and B in fig. 36, reFig. 36. present any two bodies whatever, and let us first suppose B at rest, and A to move through any line A a, either curved or straight, and drawn in any direction whatsoever. Draw B E a line in any given direction whatever, as, for instance, Eastward, in the plane passing through A a B; then the relative positions of the two bodies at the beginning and end of the motion will be ascertained by the distances AB, a B, and the angles ABE, a BE, respectively. Let Bb be a curve equal and similar to A a, and situated in the same manner with respect to the line AB, that the curve Aa is with respect to the line BA; the relative position of the two bodies will be the same if A be supposed at rest, and B to move from B to b, that it was on the former supposition. To show this, let Ab be joined, and 6 E be |