THE LUCID STARS.—J. E. Gore
The term “lucid” has been applied to the stars visible to the naked eye, without optical aid of any kind.[4] Many people think that the number of stars visible in this way is very large. But in reality the number visible to the naked eye is comparatively small. Some persons are, of course, gifted with very keen eyesight—“miraculous vision” it is sometimes called—and can see more stars than others; but to average eyesight the number visible in this way, and which can be individually counted, is very limited. The famous Hipparchus formed a catalogue of stars in the year 127 B. C. This presumably contained all the most conspicuous stars he could see in his latitude, and it includes only 1,025 stars. Al-Sûfi, the Persian astronomer, in his Description of the Fixed Stars, written in the Tenth Century, describes the positions of only 1,018 stars, although he refers to a number of other faint stars, of which he does not record the exact places. Pliny thought that about 1,600 stars were visible in the sky of Europe.
In modern times, however, a considerable number of fainter stars have been recorded as visible to the naked eye. The famous German astronomer, Heis, who had keen eyesight, records the positions of 3,903 stars north of the Equator, and 1,040 between the Equator and 20 degrees south declination, or a total of 4,943 stars between the North Pole and 20 degrees south of the Equator. This would, I find, give a total of about 7,366 stars for both hemispheres if the stars were equally distributed. Behrmann, in his Atlas of Southern Stars, between 20 degrees south declination and the South Pole, shows 2,344 stars as visible to the naked eye. This would give a total of 7,124 for both hemispheres. The actual number seen by Heis and Behrmann in both hemispheres is 4,943 + 2,344, or 7,287 stars. The Belgian astronomer, Houzeau, published a catalogue and atlas of the stars in both hemispheres, made from his own observations in Jamaica and South America, and finds a total of 5,719 stars in the whole sky. As all these observers had good eyesight, we may take a mean of the above results as the total number visible to the naked eye in the whole star sphere. This gives 6,874 stars, or in round numbers we may say that there are about 7,000 stars visible to average eyesight in both hemispheres. This gives, of course, about 3,500 stars to one observer at the same time at any point on the earth’s surface.
As the whole star sphere contains an area of 41,253 square degrees, we have an average of one star to six square degrees. In other words there is, on an average, one lucid star in a space equal to about thirty times the area covered by the full moon! This result may seem rather surprising considering the apparently large number of stars visible to the naked eye on a clear night, but the fact can not be denied. The stars are not, of course, equally distributed over the surface of the sky, but are gathered together in some places, and sparsely scattered in others, and this may perhaps help to give the impression of a greater number than there really are.
That the stars are of various degrees of brightness was recognized by the ancient astronomers. Ptolemy divided them into six classes, the brightest being called first magnitude, those considerably fainter the second, those much fainter still the third, down to the sixth magnitude, which were supposed to be the faintest just visible to the naked eye on a clear moonless night. Ptolemy only recorded whole magnitudes, but Al-Sûfi, in the Tenth Century, divided these magnitudes, for the first time, into thirds. Thus a star slightly less than an average star of the second magnitude he called 2—3, that is nearer in brightness to 2 than to 3; one a little brighter than the third he recorded as 3—2, or nearer to 3 than to 2, and so on. This method has been followed by Argelander, Behrmann, Heis, and Houzeau, but in the photometric catalogues of Harvard, Oxford, and Potsdam the magnitudes are measured in decimals of a degree. This has been found necessary for greater accuracy, as the heavens contain stars of all degrees of brightness.
The term “magnitude” means the ratio between the light of a star of a given magnitude and that of another exactly one magnitude fainter. This ratio has been variously estimated by different astronomers, and ranges from 2.155, found by Johnson in 1851, to 3.06, assumed by Pierce in 1878. The value now universally adopted by astronomers is 2.512 (of which the logarithm is 0.4). This number is nearly a mean of all the estimates made, and agrees with the value found by Pogson in 1854 by means of an oil flame, and by Rosen with a Zöllner photometer in 1870. It simply means that an average star of the first magnitude is 2.512 times the brightness of a star of the second magnitude; a star of the second, 2.512 times brighter than one of the third, and so on. This makes a star of the first magnitude just 100 times brighter than one of the sixth.
There are several stars brighter than an average star of the first magnitude, such as Aldebaran. These are Sirius, which is nearly 11 times brighter than Aldebaran (according to the revised measures at Harvard); Canopus, the second brightest star in the heavens, and about two magnitudes brighter than Aldebaran; Arcturus, Capella, Vega, Alpha Centauri, Rigel, Procyon, Alpha Eridani, Beta Centauri, and Alpha Orionis. Al-Sûfi rated 13 stars of the first magnitude, visible at his station in Persia, and Halley enumerates 16 in the whole sky. According to the Harvard photometric measures, there are 13 stars in both hemispheres brighter than Aldebaran, which is rated 1.07.
As average stars of the different magnitudes the following may be taken as examples, derived from the Harvard measures: First magnitude, Aldebaran and Spica; second magnitude, β Aurigæ and β Canis Majoris; third magnitude, ι Aurigæ and β Ophiuchi; fourth magnitude, θ Herculis and ε Draconis; and fifth magnitude, ρ Ursæ Majoris and ω Sagittarii. Stars of about the sixth magnitude are, of course, numerous, and lie near the limit of naked-eye vision for average eyesight, although on clear moonless nights still fainter stars may be “glimpsed” by keen-eyed observers.
The stars have been divided into groups and constellations, now chiefly used for the purpose of reference, but in ancient times they were associated with the imaginary figures of men and animals, etc. The origin of these constellation figures is doubtful, but they are certainly of great antiquity. Ptolemy’s constellations were 48 in number, but different writers from the First Century B. C. give different numbers, ranging from 43 to 62. Bayer’s Uranometria, published in 1603, contains 60, 12 new constellations in the Southern Hemisphere having been added by Theodorus to Ptolemy’s original 48.
The figures representing the constellations were originally drawn on spheres, or celestial globes, as they are now called. The ancient astronomers attributed the invention of the sphere to Atlas. It seems certain that a celestial sphere was constructed by Eudoxus in the Fourth Century B. C. Strabo speaks of one made by Krates about the year 130 B. C., and according to Ovid, Archimedes had constructed one at a considerably earlier period. None of these ancient spheres has been preserved. There is, however, in the Vatican a fragment in marble of a Græco-Egyptian planisphere, and a globe in the museum of Arolsen, but these are of much later date. Our knowledge of the original constellation figures is derived from the accounts given by Ptolemy and his successors, and from a few globes which only date back to the Arabian period of astronomy. Among the Arabian globes still existing the most famous is one made of copper, and preserved in the Borgia Museum at Velletri in Italy. It is supposed to have been made by a person called Caisar, who was executed by the Sultan of Egypt in A. D. 1225. The most ancient of all is one discovered some years ago at Florence. It is supposed to date back to A. D. 1081, and to have been made by Meucci. There is also one in the Farnese Museum at Naples, made in A. D. 1225. Of modern celestial globes the oldest is one made by Jansson Blaeu in 1603. This gives all the constellations of the Southern Hemisphere as well as the Northern.
Ptolemy’s figures of the constellations were restored by the famous painter Albert Dürer of Nuremberg in 1515. The figures on modern globes and maps have been copied from this restoration. Dürer’s maps are now very rare.
In 1603, an atlas was published by Bayer. This was the first atlas to show the southern sky, and the first to designate the brightest stars by the letters of the Greek alphabet.[5] Flamsteed published an atlas in 1729. Maps and catalogues of the lucid stars have been published in recent times by Argelander, Behrmann, Heis, Houzeau, Proctor, and others. Of these Heis’s is, perhaps, the most reliable, at least so far as accurate star magnitudes are concerned. Houzeau shows both hemispheres, all the stars had been observed by himself in Jamaica and South America. Behrmann’s maps are confined to the Southern Hemisphere, between the South Pole and 20 degrees south of the Equator. The maps of the Uranometria Argentina, made at Cordoba in the Argentine Republic, show all the southern stars to the seventh magnitude, but many of these are beyond the reach of ordinary eyesight.
It is a well-known fact that the planets Venus and Jupiter are bright enough to form shadows of objects on a white background. It has also been found that the brightest stars, especially Sirius, are sufficiently brilliant to cast shadows. Kepler stated that a shadow was formed by even Spica, but I am not aware that this has been confirmed by modern observations.
There are some remarkable collections or clusters of stars visible to the naked eye, of these the Pleiades are probably the best known. To ordinary eyesight 6 stars are visible, but Möstlin, Kepler’s tutor, is said to have seen 14 with the naked eye, and some observers in modern times have seen 11 or 12. Other naked-eye clusters are the Hyades in Taurus, called Palilicium by Halley, and the Præsepe, or Bee-Hive in Cancer. Of larger groups, the Plow or Great Bear, Cassiopeia’s Chair, and Orion are probably known to most people.
Many of the lucid stars are double, that is, consist of two components, but most of these are only visible in powerful telescopes. There are, however, a few objects visible to the naked eye as double, and these have been called “naked-eye doubles,” although not strictly double in the correct sense of the term.
Ptolemy applied the term double to the star ν Sagittarii, which consists of two stars separated by a distance of fourteen minutes of arc, or about half the apparent diameter of the moon. According to Riccioli, Van der Hove saw two naked-eye doubles, one in Capricornus, 5 to 5½ minutes distant, and the other in the Hyades, 4½ or 5 minutes apart. The one in Capricornus was probably α, and the one in the Hyades θ Tauri. The middle star in the tail of the Great Bear, or handle of the Plow, has near it a small star, Alcor, which to many eyes is distinctly visible without optical aid. The famous Belgian astronomer, Houzeau, who seems to have had excellent sight, saw the star χ Tauri double, and 51 and 56 Tauri separated, also ι Orionis, and others.
Many of the stars are variable in their light, and several hundred of these curious and interesting objects are now known to astronomers. In a few of these the light changes may be followed with the naked eye. It is an interesting question whether any of the lucid stars have disappeared or changed in brightness since the early ages of astronomical observations. Al-Sûfi failed to find seven of Ptolemy’s stars, and Ulug Bekh, comparing his observations with the catalogues of Ptolemy and Al-Sûfi, announced twelve cases of supposed disappearance. Some of these may, however, be due to errors of observation. Montanari, writing in 1672, mentions two stars as having disappeared, namely β and γ of the constellation Argo, but these stars are now visible in the positions originally assigned to them.
In a careful examination of Al-Sûfi’s description of the stars written in the Tenth Century, and a comparison with modern estimates and measures, I have found several very interesting cases of apparent change in the brightness of the lucid stars. Al-Sûfi was an excellent and careful observer, and as a rule his estimates agree well with modern observations. We can therefore place considerable reliance on his estimates of star magnitudes. The Story of Theta Eridani has been well told by Dr. Anderson, and there seems to be no doubt that this southern star, which is now only of the third magnitude, was a bright star of the first magnitude in Al-Sûfi’s time! The following are other interesting cases of apparent change which I have met with in my examination of Al-Sûfi’s work. The Pole Star was rated third magnitude by both Ptolemy and Al-Sûfi, but it is now of the second magnitude, or a little less. The star γ Geminorum was rated third magnitude by Ptolemy and Al-Sûfi, or equal to δ Geminorum, but γ is now of the second magnitude, and its great superiority in brightness over δ is noticeable at a glance. Another interesting case is that of ζ and ο Persei, two stars which lie near each other, about seven degrees north of the Pleiades. Al-Sûfi distinctly describes these stars as both of the 3—4 magnitude; but Argelander, Heis, and the photometric measures at Harvard agree in making ζ about one magnitude brighter than ο. The stars being close are easily compared, and their present great difference in brightness is very noticeable. This is one of the most remarkable cases I have met with in Al-Sûfi’s work, and strongly suggests variation in ο, as ζ is still about the same brightness as Al-Sûfi made it. The identity of the stars is beyond all doubt, as Al-Sûfi describes their positions very clearly, and says there is no star between them and the Pleiades, a remark which is quite correct for the naked eye. The remarkable decrease in brightness of β Leonis (Denebola) since Al-Sûfi’s time has been considered in my paper on Some Suspected Variable Stars. That it was a bright star of the first magnitude is fully proved by the observations of Al-Sûfi and Tycho Brahe. These were careful and accurate observers, and they could not have been mistaken about a star of the first magnitude. β Leonis is now fainter than an average star of the second magnitude, and there can be no reasonable doubt that it has faded considerably since the Tenth Century.
There are some other discrepancies between Al-Sûfi’s observations and modern estimates, but the above are perhaps the most remarkable. With reference to lucid stars not mentioned by Al-Sûfi, he has not, I think, omitted any star brighter than the fourth magnitude in that portion of the sky visible from his station. There are, however, a number of stars between the fourth and sixth magnitudes which he does not mention. Of these the brightest seem to be ε Aquilæ, ρ and μ Cygni, and ζ Coronæ Borealis.
With reference to the distribution of the lucid stars in the sky there seems to be a well-marked tendency to congregate on the Milky Way. It is a remarkable fact that of the 15 brightest stars in the heavens, no less than 11 lie on or near the Milky Way, although the space covered by the Galaxy does not exceed one-fifth or one-sixth of the whole sky. From a careful enumeration of the stars in or near the Milky Way which I made some years ago, I found that of stars brighter than the fourth magnitude there are 118 on the Milky Way out of a total of 392, or about 30 per cent. From the Southern catalogue known as the Uranometria Argentina, Colonel Markwick, F.R.A.S., found 121 out of 228 stars to fourth magnitude, or a percentage of 53 per cent. These results seem to show some intimate relation between the lucid stars and the Galaxy.