And, finally, concerning the nebulae. These mysterious objects exercised a strong fascination for Herschel, and many are the speculations he indulges in concerning them. At one time he regards them all as cl.u.s.ters of stars, and the Milky Way as our cl.u.s.ter; the others he regards as other universes almost infinitely distant; and he proceeds to gauge and estimate the shape of our own universe or galaxy of suns, the Milky Way.

Later on, however, he pictures to himself the nebulae as nascent suns: solar systems before they are formed. Some he thinks have begun to aggregate, while some are still glowing gas.

[Ill.u.s.tration: FIG. 88.--Old drawing of the Andromeda nebula.]

He likens the heavens to a garden in which there are plants growing in all manner of different stages: some shooting, some in leaf, some in flower, some bearing seed, some decaying; and thus at one inspection we have before us the whole life-history of the plant.

Just so he thinks the heavens contain worlds, some old, some dead, some young and vigorous, and some in the act of being formed. The nebulae are these latter, and the nebulous stars are a further stage in the condensation towards a sun.

And thus, by simple observation, he is led towards something very like the nebular hypothesis of Laplace; and his position, whether it be true or false, is substantially the same as is held to-day.

[Ill.u.s.tration: FIG. 89.--The great nebula in Orion.]

We _know_ now that many of the nebulae consist of innumerable isolated particles and may be spoken of as gas. We know that some are in a state of whirling motion. We know also that such gas left to itself will slowly as it cools condense and shrink, so as to form a central solid nucleus; and also, if it were in whirling motion, that it would send off rings from itself, and that these rings could break up into planets. In two familiar cases the ring has not yet thus aggregated into planet or satellite--the zone of asteroids, and Saturn's ring.

The whole of this could not have been a.s.serted in Herschel's time: for further information the world had to wait.

These are the problems of modern astronomy--these and many others, which are the growth of this century, aye, and the growth of the last thirty or forty, and indeed of the last ten years. Even as I write, new and very confirmatory discoveries are being announced. The Milky Way _does_ seem to have some affinity with our sun. And the chief stars of the constellation of Orion const.i.tute another family, and are enveloped in the great nebula, now by photography perceived to be far greater than had ever been imagined.

What is to be the outcome of it all I know not; but sure I am of this, that the largest views of the universe that we are able to frame, and the grandest manner of its construction that we can conceive, are certain to pale and shrink and become inadequate when confronted with the truth.

NOTES TO LECTURE XIII

BODE'S LAW.--Write down the series 0, 3, 6, 12, 24, 48, &c.; add 4 to each, and divide by 10; you get the series:

4 7 10 16 28 52 100 196 388 Mercury Venus Earth Mars ---- Jupiter Saturn Ura.n.u.s ----

numbers which very fairly represent the distances of the then known planets from the sun in the order specified.

Ceres was discovered on the 1st of January, 1801, by Piazzi; Pallas in March, 1802, by Olbers; Juno in 1804, by Harding; and Vesta in 1807, by Olbers. No more asteroids were discovered till 1845, but there are now several hundreds known. Their diameters range from 500 to 20 miles.

Neptune was discovered from the perturbations of Ura.n.u.s by sheer calculation, carried on simultaneously and independently by Leverrier in Paris, and Adams in Cambridge. It was first knowingly seen by Galle, of Berlin, on the 23rd of September, 1846.

LECTURE XIII

THE DISCOVERY OF THE ASTEROIDS

Up to the time of Herschel, astronomical interest centred on the solar system. Since that time it has been divided, and a great part of our attention has been given to the more distant celestial bodies. The solar system has by no means lost its interest--it has indeed gained in interest continually, as we gain in knowledge concerning it; but in order to follow the course of science it will be necessary for us to oscillate to and fro, sometimes attending to the solar system--the planets and their satellites--sometimes extending our vision to the enormously more distant stellar s.p.a.ces.

Those who have read the third lecture in Part I. will remember the speculation in which Kepler indulged respecting the arrangements of the planets, the order in which they succeeded one another in s.p.a.ce, and the law of their respective distances from the sun; and his fanciful guess about the five regular solids inscribed and circ.u.mscribed about their orbits.

The rude coincidences were, however, accidental, and he failed to discover any true law. No thoroughly satisfactory law is known at the present day. And yet, if the nebular hypothesis or anything like it be true, there must be some law to be discovered hereafter, though it may be a very complicated one.

An empirical relation is, however, known: it was suggested by Tatius, and published by Bode, of Berlin, in 1772. It is always known as Bode's law.

Bode's law a.s.serts that the distance of each planet is approximately double the distance of the inner adjacent planet from the sun, but that the rate of increase is distinctly slower than this for the inner ones; consequently a better approximation will be obtained by adding a constant to each term of an appropriate geometrical progression. Thus, form a doubling series like this, 1-1/2, 3, 6, 12, 24, &c. doubling each time; then add 4 to each, and you get a series which expresses very fairly the relative distances of the successive planets from the sun, except that the number for Mercury is rather erroneous, and we now know that at the other extreme the number for Neptune is erroneous too.

I have stated it in the notes above in a form calculated to give the law every chance, and a form that was probably fashionable after the discovery of Ura.n.u.s; but to call the first term of the doubling series 0 is evidently not quite fair, though it puts Mercury's distance right. Neptune's distance, however, turns out to be more nearly 30 times the earth's distance than 388. The others are very nearly right: compare column D of the table preceding Lecture III. on p. 57, with the numbers in the notes on p. 294.

The discovery of Ura.n.u.s a few years afterwards, in 1781, at 192 times the earth's distance from the sun, lent great _eclat_ 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.

[Ill.u.s.tration: FIG. 90.--Planetary orbits to scale; showing the Asteroidal region between Jupiter and Mars. (The orbits of satellites are exaggerated.)]

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,[27] but if they are taken with insufficient interval between them it is extremely difficult to construct the whole circ.u.mstances 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 G.o.ddess of Sicily.

Its distance from the sun as determined by Gauss was 2767 times the earth's distance. Bode's law made it 28. 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...o...b..t 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 267, 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...o...b..rs 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 sh.e.l.l 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 sh.e.l.l before explosion, and would complete its...o...b..t 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 pa.s.sed, they could be unhesitatingly a.s.serted 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 sh.e.l.l 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 ma.s.s 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 const.i.tuted 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 mult.i.tude 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.