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 const.i.tution, has been worked out with consummate skill by Clerk Maxwell; who finds that the only possible const.i.tution for Saturn's a.s.semblage of rings is a mult.i.tude 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 const.i.tuted 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 const.i.tuent 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 acc.u.mulation 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 circ.u.mstances of the motion of such an a.s.semblage 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 lat.i.tudes, 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.

LECTURE XIV

BESSEL--THE DISTANCES OF THE STARS, AND THE DISCOVERY OF STELLAR PLANETS

We will now leave the solar system for a time, and hastily sketch the history of stellar astronomy from the time of Sir William Herschel.

You remember how greatly Herschel had changed the aspect of the heavens for man,--how he had found that none of the stars were really fixed, but were moving in all manner of ways: some of this motion only apparent, much of it real. Nevertheless, so enormously distant are they, that if we could be transported back to the days of the old Chaldaean astronomers, or to the days of Noah, we should still see the heavens with precisely the same aspect as they wear now. Only by refined apparatus could any change be discoverable in all those centuries. For all practical purposes, therefore, the stars may still be well called fixed.

Another thing one may notice, as showing their enormous distances, is that from every planet of the solar system the aspect of the heavens will be precisely the same. Inhabitants of Mars, or Jupiter, or Saturn, or Ura.n.u.s, will see exactly the same constellations as we do. The whole dimensions of the solar system shrink up into a speck when so contemplated. And from the stars none of the planetary orbs of our system are visible at all; nothing but the sun is visible, and that merely as a twinkling star, brighter than some, but fainter than many others.

The sun and the stars are one. Try to realize this distinctly, and keep it in mind. I find it often difficult to drive this idea home. After some talk on the subject a friendly auditor will report, "the lecturer then described the stars, including that greatest and most magnificent of all stars, the sun." It would be difficult more completely to misapprehend the entire statement. When I say the sun is one of the stars, I mean one among the others; we are a long way from them, they are a long way from each other. They need be no more closely packed among each other than we are closely packed among them; except that some of them are double or multiple, and we are not double.

It is highly desirable to acquire an intimate knowledge of the constellations and a nodding acquaintance with their princ.i.p.al stars. A description of their peculiarities is dull and uninteresting unless they are at least familiar by name. A little _viva voce_ help to begin with, supplemented by patient night scrutiny with a celestial globe or star maps under a tent or shed, is perhaps the easiest way: a very convenient instrument for the purpose of learning the constellations is the form of map called a "planisphere," because it can be made to show all the constellations visible at a given time at a given date, and no others. The Greek alphabet also is a thing that should be learnt by everybody. The increased difficulty in teaching science owing to the modern ignorance of even a smattering of Greek is becoming grotesque. The stars are named from their ancient grouping into constellations, and by the prefix of a Greek letter to the larger ones, and of numerals to the smaller ones. The biggest of all have special Arabic names as well. The brightest stars are called of "the first magnitude," the next are of "the second magnitude," and so on. But this arrangement into magnitudes has become technical and precise, and intermediate or fractional magnitudes are inserted. Those brighter than the ordinary first magnitude are therefore now spoken of as of magnitude 1/2, for instance, or 6, which is rather confusing. Small telescopic stars are often only named by their numbers in some specified catalogue--a dull but sufficient method.

Here is a list of the stars visible from these lat.i.tudes, which are popularly considered as of the first magnitude. All of them should be familiarly recognized in the heavens, whenever seen.

Star. Constellation.

Sirius Canis major Procyon Canis minor Rigel Orion Betelgeux Orion Castor Gemini Pollux Gemini Aldebaran Taurus Arcturus Bootes Vega Lyra Capella Auriga Regulus Leo Altair Aquila Fomalhaut Southern Fish Spica Virgo

[alpha] Cygni is a little below the first magnitude. So, perhaps, is Castor. In the southern heavens, Canopus and [alpha]

Centauri rank next after Sirius in brightness.

[Ill.u.s.tration: FIG. 91.--Diagram ill.u.s.trating Parallax.]

The distances of the fixed stars had, we know, been a perennial problem, and many had been the attempts to solve it. All the methods of any precision have depended on the Copernican fact that the earth in June was 184 million miles away from its position in December, and that accordingly the grouping and aspect of the heavens should be somewhat different when seen from so different a point of view. An apparent change of this sort is called generally parallax; _the_ parallax of a star being technically defined as the angle subtended at the star by the radius of the earth's...o...b..t: that is to say, the angle E[sigma]S; where E is the earth, S the sun, and [sigma] a star (Fig. 91).

Plainly, the further off [sigma] is, the more nearly parallel will the two lines to it become. And the difficulty of determining the parallax was just this, that the more accurately the observations were made, the more nearly parallel did those lines become. The angle was, in fact, just as likely to turn out negative as positive--an absurd result, of course, to be attributed to unavoidable very minute inaccuracies.

For a long time absolute methods of determining parallax were attempted; for instance, by observing the position of the star with respect to the zenith at different seasons of the year. And many of these determinations appeared to result in success. Hooke fancied he had measured a parallax for Vega in this way, amounting to 30" of arc.

Flamsteed obtained 40" for [gamma] Draconis. Roemer made a serious attempt by comparing observations of Vega and Sirius, stars almost the antipodes of each other in the celestial vault; hoping to detect some effect due to the size of the earth's...o...b..t, which should apparently displace them with the season of the year. All these fancied results however, were shown to be spurious, and their real cause a.s.signed, by the great discovery of the aberration of light by Bradley.

After this discovery it was possible to watch for still outstanding very minute discrepancies; and so the problem of stellar parallax was attacked with fresh vigour by Piazzi, by Brinkley, and by Struve. But when results were obtained, they were traced after long discussion to age and gradual wear of the instrument, or to some other minute inaccuracy. The more carefully the observation was made, the more nearly zero became the parallax--the more nearly infinite the distance of the stars. The brightest stars were the ones commonly chosen for the investigation, and Vega was a favourite, because, going near the zenith, it was far removed from the fluctuating and tiresome disturbances of atmospheric refraction. The reason bright stars were chosen was because they were presumably nearer than the others; and indeed a rough guess at their probable distance was made by supposing them to be of the same size as the sun, and estimating their light in comparison with sunlight.

By this confessedly unsatisfactory method it had been estimated that Sirius must be 140,000 times further away than the sun is, if he be equally big. We now know that Sirius is much further off than this; and accordingly that he is much brighter, perhaps sixty times as bright, though not necessarily sixty times as big, as our sun. But even supposing him of the same light-giving power as the sun, his parallax was estimated as 1"8, a quant.i.ty very difficult to be sure of in any absolute determination.

Relative methods were, however, also employed, and the advantages of one of these (which seems to have been suggested by Galileo) so impressed themselves upon William Herschel that he made a serious attempt to compa.s.s the problem by its means. The method was to take two stars in the same telescopic field and carefully to estimate their apparent angular distance from each other at different seasons of the year. All such disturbances as precession, aberration, nutation, refraction, and the like, would affect them both equally, and could thus be eliminated.

If they were at the same distance from the solar system, relative parallax would, indeed, also be eliminated; but if, as was probable, they were at different distances, then they would apparently shift relatively to one another, and the amount of shift, if it could be observed, would measure, not indeed the distance of either from the earth, but their distance from each other. And this at any rate would be a step. It might be completed by similarly treating other stars in the same field, taking them in pairs together. A bright and a faint star would naturally be suitable, because their distances were likely to be unequal; and so Herschel fixed upon a number of doublets which he knew of, containing one bright and one faint component. For up to that time it had been supposed that such grouping in occasional pairs or triplets was chance coincidence, the two being optically foreshortened together, but having no real connection or proximity. Herschel failed in what he was looking for, but instead of that he discovered the real connection of a number of these doublets, for he found that they were slowly revolving round each other. There are a certain number of merely optical or accidental doublets, but the majority of them are real pairs of suns revolving round each other.

This relative method of mapping micrometrically a field of neighbouring stars, and comparing their configuration now and six months hence, was, however, the method ultimately destined to succeed; and it is, I believe, the only method which has succeeded down to the present day.

Certainly it is the method regularly employed, at Dunsink, at the Cape of Good Hope, and everywhere else where stellar parallax is part of the work.

Between 1830 and 1840 the question was ripe for settlement, and, as frequently happens with a long-matured difficulty, it gave way in three places at once. Bessel, Henderson, and Struve almost simultaneously announced a stellar parallax which could reasonably be accepted. Bessel was a little the earliest, and by far the most accurate. His, indeed, was the result which commanded confidence, and to him the palm must be awarded.

He was largely a self-taught student, having begun life in a counting-house, and having abandoned business for astronomy. But notwithstanding these disadvantages, he became a highly competent mathematician as well as a skilful practical astronomer. He was appointed to superintend the construction of Germany's first great astronomical observatory, that of Konigsberg, which, by his system, zeal, and genius, he rapidly made a place of the first importance.

Struve at Dorpat, Bessel at Konigsberg, and Henderson at the Cape of Good Hope--all of them at newly-equipped observatories--were severally engaged at the same problem.

But the Russian and German observers had the advantage of the work of one of the most brilliant opticians--I suppose the most brilliant--that has yet appeared: Fraunhofer, of Munich. An orphan lad, apprenticed to a maker of looking-gla.s.ses, and subject to hard struggles and privations in early life, he struggled upwards, and ultimately became head of the optical department of a Munich firm of telescope-makers. Here he constructed the famous "Dorpat refractor" for Struve, which is still at work; and designed the "Konigsberg heliometer" for Bessel. He also made a long and most skilful research into the solar spectrum, which has immortalized his name. But his health was broken by early trials, and he died at the age of thirty-nine, while planning new and still more important optical achievements.

A heliometer is the most accurate astronomical instrument for relative measurements of position, as a transit circle is the most accurate for absolute determinations. It consists of an equatorial telescope with object-gla.s.s cut right across, and each half movable by a sliding movement one past the other, the amount by which the two halves are dislocated being read off by a refined method, and the whole instrument having a mult.i.tude of appendages conducive to convenience and accuracy.

Its use is to act as a micrometer or measurer of small distances.[28]

Each half of the object-gla.s.s gives a distinct image, which may be allowed to coincide or may be separated as occasion requires. If it be the components of a double star that are being examined, each component will in general be seen double, so that four images will be seen altogether; but by careful adjustment it will be possible to arrange that one image of each pair shall be superposed on or coincide with each other, in which case only three images are visible; the amount of dislocation of the halves of the object-gla.s.s necessary to accomplish this is what is read off. The adjustment is one that can be performed with extreme accuracy, and by performing it again and again with all possible modifications, an extremely accurate determination of the angular distance between the two components is obtained.

[Ill.u.s.tration: FIG. 92.--Heliometer.]

Bessel determined to apply this beautiful instrument to the problem of stellar parallax; and he began by considering carefully the kind of star for which success was most likely. Hitherto the brightest had been most attended to, but Bessel thought that quickness of proper motion would be a still better test of nearness. Not that either criterion is conclusive as to distance, but there was a presumption in favour of either a very bright or an obviously moving star being nearer than a faint or a stationary one; and as the "bright" criterion had already been often applied without result, he decided to try the other. He had already called attention to a record by Piazzi in 1792 of a double star in Cygnus whose proper motion was five seconds of arc every year--a motion which caused this telescopic object, 61 Cygni, to be known as "the flying star." Its motion is not really very perceptible, for it will only have traversed one-third of a lunar diameter in the course of a century; still it was the quickest moving star then known. The position of this interesting double he compared with two other stars which were seen simultaneously in the field of the heliometer, by the method I have described, throughout the whole year 1838; and in the last month of that year he was able to announce with confidence a distinct though very small parallax; substantiating it with a ma.s.s of detailed evidence which commanded the a.s.sent of astronomers. The amount of it he gave as one-third of a second. We know now that he was very nearly right, though modern research makes it more like half a second.[29]

Soon afterwards, Struve announced a quarter of a second as the parallax of Vega, but that is distinctly too great; and Henderson announced for [alpha] Centauri (then thought to be a double) a parallax of one second, which, if correct, would make it quite the nearest of all the stars, but the result is now believed to be about twice too big.

Knowing the distance of 61 Cygni, we can at once tell its real rate of travel--at least, its rate across our line of sight: it is rather over three million miles a day.

Now just consider the smallness of the half second of arc, thus triumphantly though only approximately measured. It is the angle subtended by twenty-six feet at a distance of 2,000 miles. If a telescope planted at New York could be directed to a house in England, and be then turned so as to set its cross-wire first on one end of an ordinary room and then on the other end of the same room, it would have turned through half a second, the angle of greatest stellar parallax.

Or, putting it another way. If the star were as near us as New York is, the sun, on the same scale, would be nine paces off. As twenty-six feet is to the distance of New York, so is ninety-two million miles to the distance of the nearest fixed star.

Suppose you could arrange some sort of telegraphic vehicle able to carry you from here to New York in the tenth part of a second--_i.e._ in the time required to drop two inches--such a vehicle would carry you to the moon in twelve seconds, to the sun in an hour and a quarter. Travelling thus continually, in twenty-four hours you would leave the last member of the solar system behind you, and begin your plunge into the depths of s.p.a.ce. How long would it be before you encountered another object? A month, should you guess? Twenty years you must journey with that prodigious speed before you reach the nearest star, and then another twenty years before you reach another. At these awful distances from one another the stars are scattered in s.p.a.ce, and were they not brilliantly self-luminous and glowing like our sun, they would be hopelessly invisible.

I have spoken of 61 Cygni as a flying star, but there is another which goes still quicker, a faint star, 1830 in Groombridge's Catalogue. Its distance is far greater than that of 61 Cygni, and yet it is seen to move almost as quickly. Its actual speed is about 200 miles a second--greater than the whole visible firmament of fifty million stars can control; and unless the universe is immensely larger than anything we can see with the most powerful telescopes, or unless there are crowds of invisible non-luminous stars mixed up with the others, it can only be a temporary visitor to this frame of things; it is rushing from an infinite distance to an infinite distance; it is pa.s.sing through our visible universe for the first and only time--it will never return. But so gigantic is the extent of visible s.p.a.ce, that even with its amazing speed of 200 miles every second, this star will take two or three million years to get out of sight of our present telescopes, and several thousand years before it gets perceptibly fainter than it is now.

Have we any reason for supposing that the stars we see are all there are? In other words, have we any reason for supposing all celestial objects to be sufficiently luminous to be visible? We have every ground for believing the contrary. Every body in the solar system is dull and dark except the sun, though probably Jupiter is still red-hot. Why may not some of the stars be dark too? The genius of Bessel surmised this, and consistently upheld the doctrine that the astronomy of the future would have to concern itself with dark and invisible bodies; he preached "an astronomy of the invisible." Moreover he predicted the presence of two such dark bodies--one a companion of Sirius, the other of Procyon.

He noticed certain irregularities in the motions of these stars which he a.s.serted must be caused by their revolving round other bodies in a period of half a century. He announced in 1844 that both Sirius and Procyon were double stars, but that their companions, though large, were dark, and therefore invisible.

No one accepted this view, till Peters, in America, found in 1851 that the hypothesis accurately explained the anomalous motion of Sirius, and, in fact, indicated an exact place where the companion ought to be. The obscure companion of Sirius became now a recognized celestial object, although it had never been seen, and it was held to revolve round Sirius in fifty years, and to be about half as big.