A word now on the number of stars that can be seen with the help of the telescope. Here we shall find the numbers which our imagination had erroneously led us to believe are visible to the naked eye.
According to the illustrious director of the Observatory of Bonn—Argelander—the seventh magnitude comprises nearly 13,000 stars; the eighth, 40,000; and, lastly, the ninth, 142,000. The calculations of Struve give the total number of stars visible in the entire heavens by the aid of Sir William Herschel’s 20-foot reflector as more than 20,000,000. But, without doubt, these approximate numbers are much below the real ones. It will be seen, besides, that the richness of the heavens in stars is very unequal. The bright zone known under the name of the Milky Way alone contains, according to Herschel, 18,000,000.
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.