The Brilliancy And Distances Of The Stars

( Originally Published Early 1900's )

THE stars are not all equally bright, and custom has divided them into certain classes known as " magnitudes." The largest and brightest are said to be stars of the 1st magnitude ; next come stars of the 2nd magnitude, and so on by a descending scale. Stars of about the 6th magnitude are reputed to be the smallest visible to the naked eye, but by the use of telescopes we can go on observing stars down to about the 15th magnitude or even smaller. It will be readily understood that this is a very loose and arbitrary phraseology, but it has become so consecrated by time and custom that it will certainly never be set aside. Whilst everybody is agreed as to what is the brightest star in the heavens, namely Sirius, and that about 20 stars are worthy to be ranked as of the 1st magnitude, though less bright than Sirius, sharp differences of opinion present themselves when we try to mark off 2nd magnitude stars from 1st magnitude stars, and still more when we have to define where the 2nd magnitude stars end and the 3rd magnitude stars begin. Lower down in the scale the difficulties of classification become infinitely greater they may, indeed, be said to be hopeless.

Considering the love of precision and exactness which characterises nineteenth-century science, it is somewhat singular that so little has been done to submit to measurement on definite principles the brilliancy of the various stars, at any rate those visible to the naked eye. Sir John Herschel made an attempt in this direction about 6o years ago. Many years afterwards some Germans, especially an observer named Seidel, nibbled at it, but Professor Pickering in America and the late Professor Pritchard of Oxford, working at Oxford and in Egypt, are the only two observers who have accomplished any results worthy of the subject on a well organised basis. Pickering's labours at Harvard College Observatory, Boston, U. S., have been published in the form of a catalogue of 4260 stars, whose magnitudes have been determined instrumentally on definite and intelligible optical principles. Pritchard's catalogue comprises fewer stars than Pickering's, but like its American rival is based upon philosophical principles, an instrument called the Wedge Photometer having been employed. Both catalogues labour under the disadvantage, that having been made in the Northern hemisphere they do not include the whole area of the heavens.

Taking the stars as we find them, a very slight amount of attention will show that not only are they of different degrees of brilliancy, but that they are of different colours. More prolonged and refined study will disclose the further facts that some of them vary both in brilliancy and in colour. These matters are of such extreme interest that it will be best to devote a special chapter to them. The brighter stars are distinguished from one another in various ways, and many of them received in bygone times quaint and curious names. At a very remote period they were grouped into constellations, most of which survive to the present time and are recognised to be of use to a certain extent.

Leaving the constellations for treatment in a separate chapter, and confining our attention for the moment to the stars as individual objects, it may be remarked that in order to distinguish one star from another the ancient astronomers often indicated a star by speaking of the position it occupied in the constellation to which it belonged. Thus Aldebaran was called Oculus Tauri, "the Eye of the Bull." This custom was followed and largely developed by the Arabians, and many of the names invented by them are still in use, corrupted or transformed. A German astronomer named Bayer was the first to attempt (about 1603) on any considerable scale to simplify, and so improve the old plan, but the Arabian names had, either in their Arabian form, or as translated into Latin, taken such deep root that many of them are even still in constant use. Bayer's plan was to attach to the prominent stars of each constellation the letters of the Greek alphabet, though the popular idea that the opening letters of the alphabet were reserved for the brightest stars and the later letters for the less conspicuous stars, is unfortunately not universally true. However the Greek letters a, B, and y, do indicate often the 3 brightest stars of a constellation. Bayer's letters are still in vogue, the name of the constellation being put after each in the genitive case. Thus the star which bears the name of Sirius is termed a Canis Majoris, Arcturus is a Bootis, and so on. The Persians are said to have considered 3000 years ago that the whole heavens were divided into 4 great districts, each watched over by a " Royal " star. The 4 stars, each very brilliant and remarkable, which occupied the important positions of "guardians" of these districts were Aldebaran in Taurus, Antares in Scorpio, Regulus in Leo, and Fomalhaut in Piscis Australis, but Arago, who mentions this tradition, can hardly be deemed accurate in his remark that the 4 stars in question divide the heavens into 4 almost equal portions.

This chapter may be conveniently brought to a close with a list in the order of brightness of the stars which are commonly ranked as of the ist magnitude

1. a Canis Majoris (Sirius).

2. a Argus (Canopus), Invisible in England and Northern United States.

3 a Centauri. Invisible in England and United States, except extreme southern points.

4. a Boötis (Arcturus).

5. a Orionis (Rigel).

6. a Aurigae (Capella).

7. a Lyrae (Vega).

8. a Canis Minoris (Procyon).

9. a Orionis (Betelguese).

10. a Eridani (Achernar). Invisible in England and United States, except southern part of Gulf States.

11. a Tauri (Aldebaran).

12. a Centauri. Invisible in England and United States, except extreme southern points.

13. a Crucis. Invisible in England and United States.

14. a Scorpii (Antares).

15. a Aquilea (Altair).

16. a Virginis (Spica).

17. a Piscis Australis (Fomalhaut).

18. a Crucis. Invisible in England and United States, except extreme southern points.

19. a Geminorum (Pollux).

20. a Leonis (Regulus).

21. a Cygni (Deneb).

With respect to the first 13 of the above stars it may be said that there is not much difference of opinion as to their relative rank (though some authorities do make Vega and Capella change places), but as to the remaining 7 there is not the same accord, some ranking Altair and Spica before Antares, and Regulus before Fomalhaut, Pollux, and 3 Crucis. These stars are pretty evenly distributed between the Northern and Southern hemispheres, for 10 are Northern and 11 Southern.

The following are the approximate dates on which such of the foregoing stars as are visible in England and the United States come to the meridian at midnight

Procyon January 14 Deneb ... July 31
Pollux January 15 Fomalhaut September 3
Regulus February 21 Aldebaran November 28
Spica April 11 Capella December 8
Arcturus April 24 Rigel December 8
Antares May 27 Betelgueze December 18
Vega June 29 Sirius December 31 Altair July 18

Not entirely foreign to the question of the brilliancy of the stars is the question of their distance. At the first blush of the thing an uninformed reader might naturally say that to measure the distance of a star from the earth is impossible. But so far as the principle of this task is concerned the problem is an easy one. It is in the practical working out of the principle that the difficulty lies; and this again rather arises from the extreme delicacy of the measurements and necessary safeguards than from any other cause. The process merely involves the taking of certain angular measurements and applying to them certain familiar theorems of trigonometry. It differs scarcely at all from analogous operations which are carried out every day on the earth by those engaged in land surveying. What is involved will perhaps be understood by considering what happens when a person enters a large park at one end, intending to cross to the far side where there are a number of trees in an avenue, passing en route 2 or 3 trees in the open. The trees in the far-off avenue seem to be at no great distance apart, and the trunk of one of them is nearly hidden by the trunk of one in the middle of the park; but soon after the pedestrian has started (perhaps when he has got over 5o yards) he notices that the 2 last-named trees, which a minute or two ago seemed almost in contact, are evidently some distance apart, and after walking for perhaps another minute (say another 50 yards) he sees cause to infer that a space of perhaps 120 yards separates the trees which, before he got in motion, appeared almost to touch. This transformation is the effect of " parallax," and the apparent displacement of the trees is due to the real displacement of the observer, owing to his having used his legs. But supposing the 2 trees singled out as above, instead of being within the same park close at hand had been 2 miles off, an advance of 5o yards would have caused so trifling a displacement that, though a telescope provided with a micrometer would have detected it, the naked eye might not have done so. Why this ? Because in the first case the distance traversed (5o yards) was a large fraction of the distance (say 400 yards) at which the trees were situated from the starting-point (as 50 : 400 : : I : 8). But in the second supposed case the distance traversed (50 yards) was but a small fraction of the whole distance (say 4000 yards) separating the pedestrian from the trees. The proportion is now to be expressed thus :—As 50 : 4000: : 1 :80.

Let us apply these similes to the stars. An observer on January 1st is using his telescope when the earth is at a certain known point in its annual orbit round the sun. He determines the position of a certain star. He waits 6 months, and then, on July Ist, again determines the place of his selected star ; he finds it occupies the same place. He is on July Ist removed by twice the radius of the earth's orbit, or 186 millions of miles, from the place he occupied on January Ist. If, notwithstanding this enormous displacement of himself, the star seems to have undergone no displacement, our observer argues that the star must be so far off that 186 millions of miles is a fractional part of its distance, too small to be appreciable, just as the 5o yards mentioned above is only a small fractional part of 4000 yards.

The principle of all this has been applied to several hundred stars, but only about 2 dozen have yielded positive results. These results, so far as they go. seem to tell us that the nearest star of those experimented upon is a Centauri, and that the 4 next nearest are 61 Cygni, 21185 Lalande Ursa Majoris, Sirius, and µ Cassiopeiae.

Such standards as miles, or even millions of miles, are quite unmanageable in dealing with distances such as those which separate the nearest stars from the earth, so it is customary to employ as the unit of stellar distances the distance traversed by light in one year. Now light travels at the rate of about 185,000 miles in one second, or about 63,000 times the earth's distance from the sun in one year. Applying these figures to the circumstances of a Centauri, we find that as the parallax of that star is only about t of a second of arc, a ray of light from it would not reach the earth in less than 4 1/4 years. This distance ex-pressed in miles amounts to 24,750,000,000,000 ; and a Centauri is, so far as is known, the nearest star! The reader will hardly require any further explanation of the statement made above that a mile is a hopelessly ineffective and inadequate unit in which to express stellar distances. It only remains to add that it is doubtful whether any of the stellar parallaxes hitherto arrived at are accurate to within 1/50 of a second of arc. Now 1/50 of a second is the angle subtended by of an inch at a distance of io miles ! Observations of stellar parallax, therefore, need very first-class instruments and men, and it is on this ac-count that the results up to the present time are neither very numerous nor particularly consistent.