over the sky makes us disposed to believe that they are innumerable,
and to be counted, if not by millions, at all events by hundreds of
thousands. This is, nevertheless, an illusion. All observers who have
taken the trouble to make an exact enumeration of the stars visible
to the naked eye have arrived at a maximum of 3,000 as the mean
number which can be observed in every part of the heavens, visible at
the same time, at the same place; this, of course, is but half of the
entire heavens.
Argelander has published an exact catalogue of the stars visible on
the horizon of Berlin during the course of the year. This catalogue
comprises 3,256 stars. According to Humboldt, there are 4,146 visible
on the horizon of Paris in the whole course of the year; and as this
number increases in proportion as we approach the Equator, that is to
say, in proportion as the double movement of the earth unfolds to us
during a year a more extensive portion of the heavens, 4,638 stars
are already visible to the naked eye on the horizon of Alexandria.
We repeat, the maximum number is comprised between 5,000 and 6,000
stars for the entire heavens, including those seen by the most
piercing and most accustomed eyes in the best nights for observation.
When the atmosphere is lit up by the moon, or by twilight, or, as
happens in the great centres of population, by the illumination
of the houses and streets, the lowest magnitude stars are effaced
altogether, and the number of those visible is consequently much more
limited. We may add in conclusion, that the more the scintillation,
the more easy it is to distinguish very faint stars.
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.
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.
FOOTNOTES:
[4] Except concave spectacles used by short-sighted persons.
[5] This custom has since prevailed. The following are the letters
and their names:
α Alpha η Eta ν Nu τ Tau
β Beta θ Theta ξ Xi υ Upsilon
γ Gamma ι Iota ο Omicron φ Phi
δ Delta κ Kappa π Pi χ Chi
ε Epsilon λ Lambda ρ Rho ψ Psi
ζ Zeta μ Mu σ Sigma ω Omega
THE CONSTELLATIONS.—CAMILLE FLAMMARION
The earth is forgotten, with its small and ephemeral history. The
sun himself, with all his immense system, has sunk in the infinite
night. On the wings of inter-sidereal comets we have taken our flight
toward the stars, the suns of space. Have we exactly measured, have
we worthily realized the road passed over by our thoughts? The
nearest star to us reigns at a distance of 275,000 times 37 millions
of leagues—that is to say, at ten trillions[6] of leagues (about
twenty-five billions of miles); out to that star an immense desert
surrounds us, the most profound, the darkest, and the most silent of
solitudes.
The solar system seems to us very vast, the abyss which separates our
world from Mars, Jupiter, Saturn, and Neptune appears to us immense;
relatively to the fixed stars, however, our whole system represents
but an isolated family immediately surrounding us: a sphere as vast
as the whole solar system would be reduced to the size of a simple
point if it were transported to the distance of the nearest star. The
space which extends between the solar system and the stars, and which
separates the stars from each other, appears to be entirely void of
visible matter, with the exception of nebulous fragments, cometary
or meteoric, which circulate here and there in the immense voids.
Nine thousand two hundred and fifty systems like ours (bounded by
Neptune), would be contained in the space which isolates us from the
nearest star!
If a terrible explosion occurred in this star, and if the sound could
traverse the void which separates it from us, this sound would take
more than three millions of years to reach us.
It is marvelous that we can perceive the stars at such a distance.
What an admirable transparency in these immense spaces to permit the
light to pass, without being wasted, to thousands of billions of
miles! Around us, in the thick air which envelops us, the mountains
are already darkened and difficult to see at seventy miles; the least
fog hides from us objects on the horizon. What must be the tenuity,
the rarefaction, the extreme transparency of the ethereal medium
which fills the celestial spaces!
Let us suppose ourselves, then, on the sun nearest to ours. From
there our dazzling furnace is already lost like a little star, hardly
recognizable among the constellations: earth, planets, comets sail in
the invisible. We are in a new system. If we thus approach each star
we find a sun, while all the other suns of space are reduced to the
rank of stars. Strange reality!—the normal state of the universe is
night. What we call day only exists for us because we are near a star.
The immense distance which isolates us from all the stars reduces
them to the state of motionless lights apparently fixed on the vault
of the firmament. All human eyes, since humanity freed its wings
from the animal chrysalis, all minds since the minds have been, have
contemplated these distant stars lost in the ethereal depths; our
ancestors of Central Asia, the Chaldeans of Babylon, the Egyptians
of the Pyramids, the Argonauts of the Golden Fleece, the Hebrews
sung by Job, the Greeks sung by Homer, the Romans sung by Virgil—all
these earthly eyes, for so long dull and closed, have been fixed
from age to age on these eyes of the sky, always open, animated, and
living. Terrestrial generations, nations and their glories, thrones
and altars have vanished: the sky of Homer is always there. Is it
astonishing that the heavens were contemplated, loved, venerated,
questioned, and admired even before anything was known of their true
beauties and their unfathomable grandeur?