Later on Professor Seeliger of Munich made an investigation of the relation of more than 135,000 stars down to the ninth magnitude to the Milky Way, by dividing the whole of the heavens into nine regions, one and nine being circles of 20 wide (equal to 40 diameter) at the two poles of the Galaxy; the middle region, five, is a zone 20 wide including the Milky Way itself, and the other six intermediate zones are each 20 wide. The following table shows the results as given by Professor Newcomb, who has made some alterations in the last column of 'Density of Stars' in order to correct differences in the estimate of magnitudes by the different authorities.

Regions. Area in Degree. Number of Stars. Density.

I. 1,398.7 4,277 2.78 II. 3,146.9 10,185 3.03 III. 5,126.6 19,488 3.54 IV. 4,589.8 24,492 5.32 V. 4,519.5 33,267 8.17 VI. 3,971.5 23,580 6.07 VII. 2,954.4 11,790 3.71 VIII. 1,796.6 6,375 3.21 IX. 468.2 1,644 3.14

_N.B._--The inequality of the N. and S. areas is because the enumeration of the stars only went as far as 24 S. Decl., and therefore included only a part of Regions VII., VIII., and IX.

[Ill.u.s.tration: DIAGRAM OF STAR-DENSITY From Herschel's Gauges (as given by Professor Newcomb, p. 251).]

Upon this table of densities Professor Newcomb remarks as follows:--'The star-density in the several regions increases continuously from each pole (regions I. and IX.) to the Galaxy itself (region V.). IF THE LATTER WERE A SIMPLE RING OF STARS SURROUNDING A SPHERICAL SYSTEM OF STARS, THE STAR-DENSITY WOULD BE ABOUT THE SAME IN REGIONS I., II., and III., and also in VII., VIII., and IX., but would suddenly increase in IV. and VI. as the boundary of the ring was approached. Instead of such being the case, the numbers 2.78, 3.03, and 3.54 in the north, and 3.14, 3.21, and 3.71 in the south, show a progressive increase from the galactic pole to the Galaxy itself. The conclusion to be drawn is a fundamental one. The universe, or at least the denser portion of it, is really flattened between the galactic poles, as supposed by Herschel and Struve.'

But looking at the series of figures in the table, and again as quoted by Professor Newcomb, they seem to me to show in some measure what he says they do not show. I therefore drew out the above diagram from the figures in the table, and it certainly shows that the density in regions I., II., and III., and in regions VII., VIII., and IX., may be said to be 'about the same,' that is, they increase very slowly, and that they _do_ 'suddenly increase' in IV. and VI. as the boundary of the Galaxy is approached. This may be explained either by a flattening towards the poles of the Galaxy, or by the thinning out of stars in that direction.

In order to show the enormous difference of star-density in the Galaxy and at the galactic poles, Professor Newcomb gives the following table of the Herschelian gauges, on which he only remarks that they show an enormously increased density in the galactic region due to the Herschels having counted so many more stars there than any other observers.

+-----------+----+----+----+----+-----+-----+-----+-----+-----+

Region, .

I.

II.

III.

IV.

V.

VI.

VII.

VIII.

IX.

Density, .

107

154

281

560

2,019

672

261

154

111

+-----------+----+----+----+----+-----+-----+-----+-----+-----+

[Ill.u.s.tration: DIAGRAM OF STAR-DENSITY From a table in _The Stars_ (p.

249).]

But an important characteristic of these figures is, that the Herschels alone surveyed the whole of the heavens from the north to the south pole, that they did this with instruments of the same size and quality, and that from almost life-long experience in this particular work they were unrivalled in their power of counting rapidly and accurately the stars that pa.s.sed over each field of view of their telescopes. Their results, therefore, must be held to have a comparative value far above those of any other observer or combination of observers. I have therefore thought it advisable to draw a diagram from their figures, and it will be seen how strikingly it agrees with the former diagram in the very slow increase of star-richness in the first three regions north and south, the sudden increase in regions IV. and VI. as we approach the Galaxy, while the only marked difference is in the enormously greater richness of the Galaxy itself, which is an undoubtedly real phenomenon, and is brought out here by the unrivalled observing power of the two greatest astronomers in this special department that have ever lived.

We shall find later on that Professor Newcomb himself, as the result of a quite different inquiry arrives at a result in accordance with these diagrams which will then be again referred to. As this is a very interesting subject, it will be well to give another diagram from two tables of star-density in Sir John Herschel's volume already quoted. The tables are as follows:--

Zones of Galactic Average number of Star North Polar Distance. per Field of 15'.

0 to 15 4.32 15 to 30 5.42 30 to 45 8.21 45 to 60 13.61 60 to 75 24.09 75 to 90 53.43

Zones of Galactic Average number of Stars South Polar Distance. per Field of 15'.

0 to 15 6.05 15 to 30 6.62 30 to 45 9.08 45 to 60 13.49 60 to 75 26.29 75 to 90 59.06

In these tables the Milky Way itself is taken as occupying two zones of 15 each, instead of one of 20 as in Professor Newcomb's tables, so that the excess in the number of stars over the other zones is not so large. They show also a slight preponderance in all the zones of the southern hemisphere, but this is not great, and may probably be due to the clearer atmosphere of the Cape of Good Hope as compared with that of England.

[Ill.u.s.tration: DIAGRAM OF STAR-DENSITY. From Table in Sir J. Herschel's _Outlines of Astronomy_ (10th ed., pp. 577-578).]

It need only be noted here that this diagram shows the same general features as those already given, of a continuous increase of star-density from the poles of the Galaxy, but more rapidly as the Galaxy itself is more nearly approached. This fact must, therefore, be accepted as indisputable.

Cl.u.s.tERS AND NEBULae IN RELATION TO THE GALAXY

An important factor in the structure of the heavens is afforded by the distribution of the two cla.s.ses of objects known as cl.u.s.ters and nebulae.

Although we can form an almost continuous series from double stars which revolve round their common centre of gravity, through triple and quadruple stars, to groups and aggregations of indefinite extent--of which the Pleiades form a good example, since the six stars visible to the naked eye are increased to hundreds by high telescopic powers, while photographs with three hours' exposure show more than 2000 stars--yet none of these correspond to the large cla.s.s known as cl.u.s.ters, whether globular or irregular, which are very numerous, about 600 having been recorded by Sir John Herschel more than fifty years ago. Many of these are among the most beautiful and striking objects in the heavens even with a very small telescope or good opera-gla.s.s. Such is the luminous spot called Praesepe, or the Beehive in the constellation Cancer, and another in the sword handle of Perseus.

In the southern hemisphere there is a hazy star of about the fourth magnitude, Omega Centauri, which with a good telescope is seen to be really a magnificent cl.u.s.ter nearly two-thirds the diameter of the moon, and described by Sir John Herschel as very gradually increasing in brightness to the centre, and composed of innumerable stars of the thirteenth and fifteenth magnitudes, forming the richest and largest object of the kind in the heavens. He describes it as having rings like lace-work formed of the larger stars. By actual count, on a good photograph, there are more than 6000 stars, while other observers consider that there are at least 10,000.

In the northern hemisphere one of the finest is that in the constellation Hercules, known as 13 Messier. It is just visible to the naked eye or with an opera gla.s.s as a hazy star of the sixth magnitude, but a good telescope shows it to be a globular cl.u.s.ter, and the great Lick telescope resolves even the densest central portion into distinct stars, of which Sir John Herschel considered there were many thousands. These two fine cl.u.s.ters are figured in many of the modern popular works on astronomy, and they afford an excellent idea of these beautiful and remarkable objects, which, when more thoroughly studied, will probably aid in elucidating some of the obscure problems connected with the const.i.tution and development of the stellar universe.

But for the purpose of the present work the most interesting fact connected with star-cl.u.s.ters is their remarkable distribution in the heavens. Their special abundance in and near the Milky Way had often been noted, but the full importance of the fact could not be appreciated till Mr. Proctor and, later, Mr. Sidney Waters marked down, on maps of the two hemispheres, all the star-cl.u.s.ters and nebulae in the best catalogues. The result is most interesting. The cl.u.s.ters are seen to be thickly strewn over the entire course of the Milky Way, and along its margins, while in every other part of the heavens they are thinly scattered at very distant intervals, with the one exception of the Magellanic clouds of the southern hemisphere where they are again densely grouped; and if anything were needed to prove the physical connection of these cl.u.s.ters with the Galaxy it would be their occurrence in these extensive nebulous patches which seem like outlying portions of the Milky Way itself. With these two exceptions probably not one-twentieth part of the whole number of star-cl.u.s.ters are found in any part of the heavens remote from the Milky Way.

Nebulae were for a long time confounded with star-cl.u.s.ters, because it was thought that with sufficient telescopic power they could all be resolvable into stars as in the case of the Milky Way itself. But when the spectroscope showed that many of the nebulae consisted wholly or mainly of glowing gases, while neither the highest powers of the best telescopes nor the still greater powers of the photographic plate gave any indications of resolvability, although a few stars were often found to be, as it were, entangled in them, and evidently forming part of them, it was seen that they const.i.tuted a distinct stellar phenomenon, a view which was enforced and rendered certain by their quite unique mode of distribution. A few of the larger and irregular type, as in the case of the grand Orion nebula visible to the naked eye, the great spiral nebula in Andromeda, and the wonderful Keyhole nebula round Eta Args, are situated in or near the Milky Way; but with these and a few other exceptions the overwhelming majority of the smaller irresolvable nebulae appear to avoid it, there being a s.p.a.ce almost wholly free from nebulae along its borders, both in the northern and southern hemispheres; while the great majority are spread over the sky, far away from it in the southern hemisphere, and in the north cl.u.s.tering in a very marked degree around the galactic pole. The distribution of nebulae is thus seen to be the exact opposite to that of the star-cl.u.s.ters, while both are so distinctly related to the position of the Milky Way--the ground-plane of the sidereal system, as Sir John Herschel termed it--that we are compelled to include them all as connected portions of one grand and, to some extent, symmetrical universe, whose remarkable and opposite mode of distribution over the heavens may probably afford a clue to the mode of development of that universe and to the changes that are even now taking place within it. The maps referred to above are of such great importance, and are so essential to a clear comprehension of the nature and const.i.tution of the vast sidereal system which surrounds us, that I have, with the permission of the Royal Astronomical Society, reproduced them here. (See end of volume.)

A careful examination of them will give a clearer idea of the very remarkable facts of distribution of star-cl.u.s.ters and nebulae than can be afforded by any amount of description or of numerical statements.

The forms of many of the nebulae are very curious. Some are quite irregular, as the Orion nebula, the Keyhole nebula in the southern hemisphere, and many others. Some show a decidedly spiral form, as those in Andromeda and Canes Venatici; others again are annular or ring-shaped, as those in Lyra and Cygnus, while a considerable number are termed planetary nebulae, from their exhibiting a faint circular disc like that of a planet. Many have stars or groups of stars evidently forming parts of them, and this is especially the case with those of the largest size. But all these are comparatively few in number and more or less exceptional in type, the great majority being minute cloudy specks only visible with good telescopes, and so faint as to leave much doubt as to their exact shape and nature. Sir John Herschel catalogued 5000 in 1864, and more than 8000 were discovered up to 1890; while the application of the camera has so increased the numbers that it is thought there may really be many hundreds of thousands of them.

The spectroscope shows the larger irregular nebulae to be gaseous, as are the annular and planetary nebulae as well as many very brilliant white stars; and all these objects are most frequent in or near the Milky Way.

Their spectra show a green line not produced by any terrestrial element.

With the great Lick telescope several of the planetary nebulae have been found to be irregular and sometimes to be formed of compressed or looped rings and other curious forms.

Many of the smaller nebulae are double or triple, but whether they really form revolving systems is not yet known. The great ma.s.s of the small nebulae that occupy large tracts of the heavens remote from the Galaxy are often termed irresolvable nebulae, because the highest powers of the largest telescopes show no indication of their being star-cl.u.s.ters, while they are too faint to give any definite indications of structure in the spectroscope. But many of them resemble comets in their forms, and it is thought not impossible that they may be not very dissimilar in const.i.tution.

We have now pa.s.sed in review the main features presented to us in the heavens outside the solar system, so far as regards the numbers and distribution of the lucid stars (those visible to the naked eye) as well as those brought to view by the telescope; the form and chief characteristics of the Milky Way or Galaxy; and lastly, the numbers and distribution of those interesting objects--star-cl.u.s.ters and nebulae in their special relations to the Milky Way. This examination has brought clearly before us the unity of the whole visible universe; that everything we can see, or obtain any knowledge of, with all the resources of modern gigantic telescopes, of the photographic plate, and of the even more marvellous spectroscope, forms parts of one vast system which may be shortly and appropriately termed the Stellar universe.

In our next chapter we shall carry the investigation a step further, by sketching in outline what is known of the motions and distances of the stars, and thus obtain some important information bearing upon our special subject of inquiry.

CHAPTER V

DISTANCE OF THE STARS--THE SUN'S MOTION THROUGH s.p.a.cE

In early ages, before any approximate idea was reached of the great distances of the stars from us, the simple conception of a crystal sphere to which these luminous points were attached and carried round every day on an axis near which our pole-star is situated, satisfied the demands for an explanation of the phenomena. But when Copernicus set forth the true arrangement of the heavenly bodies, earth and planets alike revolving round the sun at distances of many millions of miles, and when this scheme was enforced by the laws of Kepler and the telescopic discoveries of Galileo, a difficulty arose which astronomers were unable satisfactorily to overcome.

If, said they, the earth revolves round the sun at a distance which cannot be less (according to Kepler's measurement of the distance of Mars at opposition) than 13-1/2 millions of miles, then how is it that the nearer stars are not seen to s.h.i.+ft their apparent places when viewed from opposite sides of this enormous...o...b..t? Copernicus, and after him Kepler and Galileo, stoutly maintained that it was because the stars were at such an enormous distance from us that the earth's...o...b..t was a mere point in comparison.

But this seemed wholly incredible, even to the great observer Tycho Brahe, and hence the Copernican theory was not so generally accepted as it otherwise would have been.

Galileo always declared that the measurement would some day be made, and he even suggested the method of effecting it which is now found to be the most trustworthy. But the sun's distance had to be first measured with greater accuracy, and that was only done in the latter part of the eighteenth century by means of transits of Venus; and by later observations with more perfect instruments it is now pretty well fixed at about 92,780,000 miles, the limits of error being such that 92-3/4 millions may perhaps be quite as accurate.

With such an enormous base-line as twice this distance, which is available by making observations at intervals of about six months when the earth is at opposite points in its...o...b..t, it seemed certain that some parallax or displacement of the nearer stars could be found, and many astronomers with the best instruments devoted themselves to the work. But the difficulties were enormous, and very few really satisfactory results were obtained till the latter half of the nineteenth century. About forty stars have now been measured with tolerable certainty, though of course with a considerable margin of possible or probable error; and about thirty more, which are found to have a parallax of one-tenth of a second or less, must be considered to leave a very large margin of uncertainty.

The two nearest fixed stars are Alpha Centauri and 61 Cygni. The former is one of the brightest stars in the southern hemisphere, and is about 275,000 times as far from us as the sun. The light from this star will take 4-1/4 years to reach us, and this 'light-journey,' as it is termed, is generally used by astronomers as an easily remembered mode of recording the distances of the fixed stars, the distance in miles--in this case about 25 millions of millions--being very c.u.mbrous. The other star, 61 Cygni, is only of about the fifth magnitude, yet it is the second nearest to us, with a light-journey of about 7-1/4 years. If we had no other determinations of distance than these two, the facts would be of the highest importance. They teach us, first, that magnitude or brightness of a star is no proof of nearness to us, a fact of which there is much other evidence; and in the second place, they furnish us with a probable minimum distance of independent suns from one another, which, in proportion to their sizes, some being known to be many times larger than our sun, is not more than we might expect. This remoteness may be partly due to those which were once nearer together having coalesced under the influence of gravitation.

As this measurement of the distance of the nearer stars should be clearly understood by every one who wishes to obtain some real comprehension of the scale of this vast universe of which we form a part, the method now adopted and found to be most effectual will be briefly explained.

Everyone who is acquainted with the rudiments of trigonometry or mensuration, knows that an inaccessible distance can be accurately determined if we can measure a base-line from both ends of which the inaccessible object can be seen, and if we have a good instrument with which to measure angles. The accuracy will mainly depend upon our base-line being not excessively short in comparison with the distance to be measured.

If it is as much as half or even a quarter as long the measurement may be as accurate as if directly performed over the ground, but if it is only one-hundredth or one-thousandth part as long, a very small error either in the length of the base or in the amount of the angles will produce a large error in the result.

In measuring the distance of the moon, the earth's diameter, or a considerable portion of it, has served as a base-line. Either two observers at great distances from each other, or the same observer after an interval of nine or ten hours, may examine the moon from positions six or seven thousand miles apart, and by accurate measurements of its angular distance from a star, or by the time of its pa.s.sage over the meridian of the place as observed with a transit instrument, the angular displacement can be found and the distance determined with very great accuracy, although that distance is more than thirty times the length of the base. The distance of the planet Mars when nearest to us has been found in the same way. His distance from us even when at his nearest point during the most favourable oppositions is about 36 million miles, or more than four thousand times the earth's diameter, so that it requires the most delicate observations many times repeated and with the finest instruments to obtain a tolerably approximate result. When this is done, by Kepler's law of the fixed proportion between the distances of planets from the sun and their times of revolution, the proportionate distance of all the other planets and that of the sun can be ascertained. This method, however, is not sufficiently accurate to satisfy astronomers, because upon the sun's distance that of every other member of the solar system depends. Fortunately there are two other methods by which this important measurement has been made with much greater approach to certainty and precision.

[Ill.u.s.tration: Diagram ill.u.s.trating the transit of Venus.]

The first of these methods is by means of the rare occasions when the planet Venus pa.s.ses across the sun's disc as seen from the earth. When this takes place, observations of the transit, as it is termed, are made at remote parts of the earth, the distance between which places can of course easily be calculated from their lat.i.tudes and longitudes. The diagram here given ill.u.s.trates the simplest mode of determining the sun's distance by this observation, and the following description from Proctor's _Old and New Astronomy_ is so clear that I copy it verbally:--'V represents Venus pa.s.sing between the Earth E and the Sun S; and we see how an observer at E will see Venus as at v', while an observer at E' will see her as at v. The measurement of the distance v v', as compared with the diameter of the sun's disc, determines the angle v V v' or E V E'; whence the distance E V can be calculated from the known length of the base-line E E'. For instance, it is known (from the known proportions of the Solar System as determined from the times of revolution by Kepler's third law) that E V bears to V v the proportion 28 to 72, or 7 to 18; whence E E' bears to v v'

the same proportion. Suppose, now, that the distance between the two stations is known to be 7000 miles, so that v v' is 18,000 miles; and that v v' is found by accurate measurement to be 1/48 part of the sun's diameter. Then the sun's diameter, as determined by this observation, is 48 times 18,000 miles, or 864,000 miles; whence from his known apparent size, which is that of a globe 107-1/3 times farther away from us than its own diameter, his distance is found to be 92,736,000 miles.'

Of course, there being two observers, the proportion of the distance v v'

to the diameter of the sun's disc cannot be measured directly, but each of them can measure the apparent angular distance of the planet from the sun's upper and lower margins as it pa.s.ses across the disc, and thus the angular distance between the two lines of transit can be obtained. The distance v v' can also be found by accurately noting the times of the upper and lower pa.s.sage of Venus, which, as the line of transit is considerably shorter in one than the other, gives by the known properties of the circle the exact proportion of the distance between them to the sun's diameter; and as this is found to be the most accurate method, it is the one generally adopted.