Lecture Iii. on P. 57, With the Numbers in the Notes on P. 294.

The discovery of Uranus a few years afterwards, in 1781, at 19·2 times the earth's distance from the sun, lent great éclât to the law, and seemed to establish its right to be regarded as at least a close approximation to the truth.

The gap between Mars and Jupiter, which had often been noticed, and which Kepler filled with a hypothetical planet too small to see, comes into great prominence by this law of Bode. So much so, that towards the end of last century an enthusiastic German, von Zach, after some search himself for the expected planet, arranged a committee of observing astronomers, or, as he termed it, a body of astronomical detective police, to begin a systematic search for this missing subject of the sun.

In 1800 the preliminaries were settled: the heavens near the zodiac were divided into twenty-four regions, each of which was intrusted to one observer to be swept. Meanwhile, however, quite independently of these arrangements in Germany, and entirely unknown to this committee, a quiet astronomer in Sicily, Piazzi, was engaged in making a catalogue of the stars. His attention was directed to a certain region in Taurus by an error in a previous catalogue, which contained a star really non-existent.

In the course of his scrutiny, on the 1st of January, 1801, he noticed a small star which next evening appeared to have shifted. He watched it anxiously for successive evenings, and by the 24th of January he was quite sure he had got hold of some moving body, not a star: probably, he thought, a comet. It was very small, only of the eighth magnitude; and he wrote to two astronomers (one of them Bode himself) saying what he had observed. He continued to observe till the 11th of February, when he was attacked by illness and compelled to cease.

His letters did not reach their destination till the end of March. Directly Bode opened his letter he jumped to the conclusion that this must be the missing planet. But unfortunately he was unable to verify the guess, for the object, whatever it was, had now got too near the sun to be seen. It would not be likely to be out again before September, and by that time it would be hopelessly lost again, and have just as much to be rediscovered as if it had never been seen.

Mathematical astronomers tried to calculate a possible orbit for the body from the observations of Piazzi, but the observed places were so desperately few and close together. It was like having to determine a curve from three points close together. Three observations ought to serve, but if they are taken with insufficient interval between them it is extremely difficult to construct the whole circumstances of the orbit from them. All the calculations gave different results, and none were of the slightest use.

The difficulty as it turned out was most fortunate. It resulted in the discovery of one of the greatest mathematicians, perhaps the greatest, that Germany has ever produced--Gauss. He was then a young man of twenty-five, eking out a living by tuition. He had invented but not published several powerful mathematical methods (one of them now known as "the method of least squares"), and he applied them to Piazzi's observations. He was thus able to calculate an orbit, and to predict a place where, by the end of the year, the planet should be visible. On the 31st of December of that same year, very near the place predicted by Gauss, von Zach rediscovered it, and Olbers discovered it also the next evening. Piazzi called it Ceres, after the tutelary goddess of Sicily.

Its distance from the sun as determined by Gauss was 2·767 times the earth's distance. Bode's law made it 2·8. It was undoubtedly the missing planet. But it was only one hundred and fifty or two hundred miles in diameter--the smallest heavenly body known at the time of its discovery. It revolves the same way as other planets, but the plane of its orbit is tilted 10° to the plane of the ecliptic, which was an exceptionally large amount.

Very soon, a more surprising discovery followed. Olbers, while searching for Ceres, had carefully mapped the part of the heavens where it was expected; and in March, 1802, he saw in this place a star he had not previously noticed. In two hours he detected its motion, and in a month he sent his observations to Gauss, who returned as answer the calculated orbit. It was distant 2·67, like Ceres, and was a little smaller, but it had a very excentric orbit: its plane being tilted 34-1/2°, an extraordinary inclination. This was called Pallas.

Olbers at once surmised that these two planets were fragments of a larger one, and kept an eager look out for other fragments.

In two years another was seen, in the course of charting the region of the heavens traversed by Ceres and Pallas. It was smaller than either, and was called Juno.

In 1807 the persevering search of Olbers resulted in the discovery of another, with a very oblique orbit, which Gauss named Vesta. Vesta is bigger than any of the others, being five hundred miles in diameter, and shines like a star of the sixth magnitude. Gauss by this time had become so practised in the difficult computations that he worked out the complete orbit of Vesta within ten hours of receiving the observational data from Olbers.

For many weary years Olbers kept up a patient and unremitting search for more of these small bodies, or fragments of the large planet as he thought them; but his patience went unrewarded, and he died in 1840 without seeing or knowing of any more. In 1845 another was found, however, in Germany, and a few weeks later two others by Mr. Hind in England. Since then there seems no end to them; numbers have been discovered in America, where Professors Peters and Watson have made a specialty of them, and have themselves found something like a hundred.

Vesta is the largest--its area being about the same as that of Central Europe, without Russia or Spain--and the smallest known is about twenty miles in diameter, or with a surface about the size of Kent. The whole of them together do not nearly equal the earth in bulk.

The main interest of these bodies to us lies in the question, What is their history? Can they have been once a single planet broken up? or are they rather an abortive attempt at a planet never yet formed into one?

The question is not entirely settled, but I can tell you which way opinion strongly tends at the present time.

Imagine a shell travelling in an elliptic orbit round the earth to suddenly explode: the centre of gravity of all its fragments would continue moving along precisely the same path as had been traversed by the centre of the shell before explosion, and would complete its orbit quite undisturbed. Each fragment would describe an orbit of its own, because it would be affected by a different initial velocity; but every orbit would be a simple ellipse, and consequently every piece would in time return through its starting-point--viz. the place at which the explosion occurred. If the zone of asteroids had a common point through which they all successively passed, they could be unhesitatingly asserted to be the remains of an exploded planet. But they have nothing of the kind; their orbits are scattered within a certain broad zone--a zone everywhere as broad as the earth's distance from the sun, 92,000,000 miles--with no sort of law indicating an origin of this kind.

It must be admitted, however, that the fragments of our supposed shell might in the course of ages, if left to themselves, mutually perturb each other into a different arrangement of orbits from that with which they began. But their perturbations would be very minute, and moreover, on Laplace's theory, would only result in periodic changes, provided each mass were rigid. It is probable that the asteroids were at one time not rigid, and hence it is difficult to say what may have happened to them; but there is not the least reason to believe that their present arrangement is derivable in any way from an explosion, and it is certain that an enormous time must have elapsed since such an event if it ever occurred.

It is far more probable that they never constituted one body at all, but are the remains of a cloudy ring thrown off by the solar system in shrinking past that point: a small ring after the immense effort which produced Jupiter and his satellites: a ring which has aggregated into a multitude of little lumps instead of a few big ones. Such an event is not unique in the solar system; there is a similar ring round Saturn. At first sight, and to ordinary careful inspection, this differs from the zone of asteroids in being a solid lump of matter, like a quoit. But it is easy to show from the theory of gravitation, that a solid ring could not possibly be stable, but would before long get precipitated excentrically upon the body of the planet. Devices have been invented, such as artfully distributed irregularities calculated to act as satellites and maintain stability; but none of these things really work. Nor will it do to imagine the rings fluid; they too would destroy each other. The mechanical behaviour of a system of rings, on different hypotheses as to their constitution, has been worked out with consummate skill by Clerk Maxwell; who finds that the only possible constitution for Saturn's assemblage of rings is a multitude of discrete particles each pursuing its independent orbit. Saturn's ring is, in fact, a very concentrated zone of minor asteroids, and there is every reason to conclude that the origin of the solar asteroids cannot be very unlike the origin of the Saturnian ones. The nebular hypothesis lends itself readily to both.

The interlockings and motions of the particles in Saturn's rings are most beautiful, and have been worked out and stated by Maxwell with marvellous completeness. His paper constituted what is called "The Adams Prize Essay" for 1856. Sir George Airy, one of the adjudicators (recently Astronomer-Royal), characterized it as "one of the most remarkable applications of mathematics to physics that I have ever seen."

There are several distinct constituent rings in the entire Saturnian zone, and each perturbs the other, with the result that they ripple and pulse in concord. The waves thus formed absorb the effect of the mutual perturbations, and prevent an accumulation which would be dangerous to the persistence of the whole.

The only effect of gravitational perturbation and of collisions is gradually to broaden out the whole ring, enlarging its outer and diminishing its inner diameter. But if there were any frictional resistance in the medium through which the rings spin, then other effects would slowly occur, which ought to be looked for with interest. So complete and intimate is the way Maxwell works out and describes the whole circumstances of the motion of such an assemblage of particles, and so cogent his argument as to the necessity that they must move precisely so, and no otherwise, else the rings would not be stable, that it was a Cambridge joke concerning him that he paid a visit to Saturn one evening, and made his observations on the spot.

NOTES TO LECTURE XIV

The total number of stars in the heavens visible to a good eye is about 5,000. The total number at present seen by telescope is about 50,000,000. The number able to impress a photographic plate has not yet been estimated; but it is enormously greater still. Of those which we can see in these latitudes, about 14 are of the first magnitude, 48 of the second, 152 of the third, 313 of the fourth, 854 of the fifth, and 2,010 of the sixth; total, 3,391.

The quickest-moving stars known are a double star of the sixth magnitude, called 61 Cygni, and one of the seventh magnitude, called Groombridge 1830. The velocity of the latter is 200 miles a second. The nearest known stars are 61 Cygni and [alpha] Centauri. The distance of these from us is about 400,000 times the distance of the sun. Their parallax is accordingly half a second of arc. Sirius is more than a million times further from us than our sun is, and twenty times as big; many of the brightest stars are at more than double this distance. The distance of Arcturus is too great to measure even now. Stellar parallax was first securely detected in 1838, by Bessel, for 61 Cygni. Bessel was born in 1784, and died in 1846, shortly before the discovery of Neptune.

The stars are suns, and are most likely surrounded by planets. One planet belonging to Sirius has been discovered. It was predicted by Bessel, its position calculated by Peters, and seen by Alvan Clark in 1862. Another predicted one, belonging to Procyon, has not yet been seen.

A velocity of 5 miles a second could carry a projectile right round the earth. A velocity of 7 miles a second would carry it away from the earth, and round the sun. A velocity of 27 miles a second would carry a projectile right out of the solar system never to return.