Historical
The grouping of the stars into constellations is of great antiquity. The
exact date of their formation is not exactly known, but an approximate
result may be arrived at from the following considerations. On the
celestial spheres, or "globes," used by the ancient astronomers, a portion
of the southern heavens of a roughly circular form surrounding the South
Pole was left blank. This space presumably contained the stars in the
southern hemisphere which they could not see from their northern stations.
Now, the centre of this circular blank space most probably coincided with
the South Pole of the heavens at the time when the constellations were
first formed. Owing to the "Precession of the Equinoxes" this centre has
now moved away from the South Pole to a considerable distance. It can be
easily computed at what period this centre coincided with the South Pole,
and calculations show that this was the case about 2700 B.C. The position
of this circle also indicates that the constellations were formed at a
place between 36° and 40° north latitude, and therefore probably somewhere
in Asia Minor north of Mesopotamia. Again, the most ancient observations
refer to Taurus as the equinoxial constellation. Virgil says--
"Candidus auratis aperit cum cornibus annum Taurus."[382]
This would indicate a date about 3000 B.C. There is no tradition, however,
that the constellation Gemini was ever _seen_ to occupy this position, so
that 3000 B.C. seems to be the earliest date admissible.[383]
Prof. Sayce thinks that the "signs of the Zodiac" had their origin in the
plains of Mesopotamia in the twentieth or twenty-third century B.C., and
Brown gives the probable date as 2084 B.C.[384]
According to Seneca, the study of astronomy among the Greeks dates back to
about 1400 B.C.; and the ancient constellations were already classical in
the time of Eudoxus in the fourth century B.C. Eudoxus (408-355 B.C.)
observed the positions of forty-seven stars visible in Greece, thus
forming the most ancient star catalogue which has been preserved. He was a
son of Eschinus, and a pupil of Archytas and probably Plato.
The work of Eudoxus was put into verse by the poet Aratus (third century
B.C.). This poem describes all the old constellations now known, except
Libra, the Balance, which was at that time included in the Claws of the
Scorpion. About B.C. 50, the Romans changed the Claws, or Chelæ, into
Libra. Curious to say, Aratus states that the constellation Lyra contained
no bright star![385] Whereas its principal star, Vega, is now one of the
brightest stars in the heavens!
With reference to the origin of the constellations, Aratus says--
"Some men of yore
A nomenclature thought of and devised
And forms sufficient found."
This shows that even in the time of Aratus the constellations were of
great antiquity.
Brown says--
"Writers have often told us, speaking only from the depths of their
ignorance, how 'Chaldean' shepherds were wont to gaze at the brilliant
nocturnal sky, and to _imagine_ that such and such stars resemble this
or that figure. But all this is merely the old effort to make capital
out of nescience, and the stars are before our eyes to prove the
contrary. Having already certain fixed ideas and figures in his mind,
the constellation-former, when he came to his task, applied his
figures to the stars and the stars to his figures as harmoniously as
possible."[386] "Thus _e.g._ he arranged the stars of _Andromeda_ into
the representation of a chained lady, not because they naturally
reminded him (or anybody else) of such a figure, but because he
desired to express that idea."
A coin of Manius Aquillus, B.C. 94, shows four stars in Aquila, and seems
to be the oldest representation extant of a star group. On a coin of B.C.
43, Dr. Vencontre found five stars, one of which was much larger than the
others, and concludes that it represents the Hyades (in Taurus). He
attributes the coin to P. Clodius Turrinus, who probably used the
constellation Taurus or Taurinus as a phonetic reference to his surname. A
coin struck by L. Lucretius Trio in 74 B.C., shows the seven stars of the
Plough, or as the ancients called them Septem Triones. Here we have an
allusion to the name of the magistrate Trio.[387]
In a work published in Berne in 1760, Schmidt contends that the ancient
Egyptians gave to the constellations of the Zodiac the names of their
divinities, and expressed them by the signs which were used in their
hieroglyphics.[388]
Hesiod mentions Orion, the Pleiades, Sirius, Aldebaran, and Arcturus; and
Homer refers to Orion, Arcturus, the Pleiades, the Hyades, the Great Bear
(under the name of Amaxa, the Chariot), and the tail of the Little Bear,
or "Cynosura."
Hipparchus called the constellations Asterisms ([Greek: asterismos]),
Aristotle and Hyginus [Greek: Somata] (bodies), and Ptolemy [Greek:
Schêmata] (figures). By some they were called [Greek: Morphôseis]
(configurations), and by others [Greek: Meteôre]. Proclus called those
near the ecliptic [Greek: Zôdia] (animals). Hence our modern name Zodiac.
Hipparchus, Ptolemy, and Al-Sufi referred the positions of the stars to
the ecliptic. They are now referred to the equator. Aboul Hassan in the
thirteenth century (1282) was the first to use Right Ascensions and
Declinations instead of Longitudes and Latitudes. The ancient writers
described the stars by their positions in the ancient figures. Thus they
spoke of "the star in the head of Hercules," "the bright star in the left
foot of Orion" (Rigel); but Bayer in 1603 introduced the Greek letters to
designate the brighter stars, and these are now universally used by
astronomers. These letters being sometimes insufficient, Hevelius added
numbers, but the numbers in _Flamsteed's Catalogue_ are now generally
used.
Ptolemy and all the ancient writers described the constellation figures as
they are seen on globes, that is from the outside. Bayer in his Atlas,
published in 1603, reversed the figures to show them as they would be seen
from the _interior_ of a hollow globe and as, of course, they are seen in
the sky. Hevelius again reversed Bayer's figures to make them correspond
with those of Ptolemy. According to Bayer's arrangement, Betelgeuse
([Greek: a] Orionis) would be on the left shoulder of Orion, instead of
the right shoulder according to Ptolemy and Al-Sufi, and Rigel ([Greek: b]
Orionis) on the right foot (Bayer) instead of the left foot (Ptolemy).
This change of position has led to some confusion; but at present the
positions of the stars are indicated by their Right Ascensions and
Declinations, without any reference to their positions in the ancient
figures.
The classical constellations of Hipparchus and Ptolemy number forty-eight,
and this is the number described by Al-Sufi in his "Description of the
Fixed Stars" written in the tenth century A.D.
Firminicus gives the names of several constellations not mentioned by
Ptolemy. M. Fréret thought that these were derived from the Egyptian
sphere of Petosiris. Of these a Fox was placed north of the Scorpion; a
constellation called Cynocephalus near the southern constellation of the
Altar (Ara); and to the north of Pisces was placed a Stag. But all these
have long since been discarded. Curious to say neither the Dragon nor
Cepheus appears on the old Egyptian sphere.[389]
Other small constellations have also been formed by various astronomers
from time to time, but these have disappeared from our modern star maps.
The total number of constellations now recognized in both hemispheres
amounts to eighty-four.
The first catalogue formed was nominally that of Eudoxus in the fourth
century B.C. (about 370 B.C.). But this can hardly be dignified by the
name of catalogue, as it contained only forty-seven stars, and it omits
several of the brighter stars, notably Sirius! The first complete (or
nearly complete) catalogue of stars visible to the naked eye was that of
Hipparchus about 129 B.C. Ptolemy informs us that it was the sudden
appearance of a bright new or "temporary star" in the year 134 B.C. in the
constellation Scorpio which led Hipparchus to form his catalogue, and
there seems to be no reason to doubt the accuracy of this statement, as
the appearance of this star is recorded in the Chinese Annals. The
Catalogue of Hipparchus contains only 1080 stars; but as many more are
visible to the naked eye, Hipparchus must have omitted those which are not
immediately connected with the old constellation figures of men and
animals.
Hipparchus' Catalogue was revised by Ptolemy in his famous work the
_Almagest_. Ptolemy reduced the positions of the stars given by Hipparchus
to the year 137 A.D.; but used a wrong value of the precession which only
corresponded to about 50 A.D.; and he probably adopted the star magnitudes
of Hipparchus without any revision. Indeed, it seems somewhat doubtful
whether Ptolemy made any observations of the brightness of the stars
himself. Ptolemy's catalogue contains 1022 stars.
Prof. De Morgan speaks of Ptolemy as "a splendid mathematician and an
indifferent observer"; and from my own examination of Al-Sufi's work on
the Fixed Stars, which was based on Ptolemy's work, I think that De
Morgan's criticism is quite justified.
Al-Sufi's _Description of the Fixed Stars_ was written in the tenth
century and contains 1018 stars. He seems to have adopted the _positions_
of the stars given by Ptolemy, merely correcting them for the effects of
precession; but he made a very careful revision of the star magnitudes of
Ptolemy (or Hipparchus) from his own observations, and this renders his
work the most valuable, from this point of view, of all the ancient
catalogues.
Very little is known about Al-Sufi's life, and the few details we have are
chiefly derived from the works of the historians Abu'-l-faradji and
Casiri, and the Oriental writers Hyde, Caussin, Sedillot, etc. Al-Sufi's
complete name was Abd-al-Rahmän Bin Umar Bin Muhammad Bin Sahl
Abu'l-husaïn al-Sufi al-Razi. The name Sufi indicates that he belonged to
the sect of Sufis (Dervishes), and the name Razi that he lived in the town
of Raï in Persia, to the east of Teheran. He was born on December 7, 903
A.D., and died on May 25, 986, so that, like many other astronomers, he
lived to a good old age. According to ancient authorities, Al-Sufi--as he
is usually called--was a very learned man, who lived at the courts of
Schiraz and Baghdad under Adhad-al-Davlat--of the dynasty of the
Buïdes--who was then the ruler of Persia. Al-Sufi was held in high esteem
and great favour by this prince, who said of him, "Abd-al-Rahmän al-Sufi
taught me to know the names and positions of the fixed stars, Scharif Ibn
al-Aalam the use of astronomical tables, and Abu Ali al-Farisi instructed
me in the principles of grammar." Prince Adhad-al-Davlat died on March 26,
983. According to Caussin, Al-Sufi also wrote a book on astrology, and a
work entitled _Al-Ardjouze_, which seems to have been written in verse,
but its subject is unknown. He also seems to have determined the exact
length of the year, and to have undertaken geodetic measurements. The
al-Aalam mentioned above was also an able astronomer, and in addition to
numerous observations made at Baghdad, he determined with great care the
precession of the equinoxes. He found the annual constant of precession to
be 51"·4, a value which differs but little from modern results.
In the year 1874, the late M. Schjellerup, the eminent Danish astronomer,
published a French translation of two Arabic manuscripts written by
Al-Sufi and entitled "A Description of the Fixed Stars." One of these
manuscripts is preserved in the Royal Library at Copenhagen, and the other
in the Imperial Library at St. Petersburgh.[390]
Al-Sufi seems to have been a most careful and accurate observer, and
although, as a rule, his estimates of the relative brightness of stars are
in fairly good agreement with modern estimates and photometric measures,
there are many remarkable and interesting differences. Al-Sufi's
observations have an important bearing on the supposed "secular variation"
of the stars; that is, the slow variation in light which may have occurred
in the course of ages in certain stars, apart from the periodical
variation which is known to occur in the so-called variable stars. More
than 900 years have now elapsed since the date of Al-Sufi's observations
(about A.D. 964) and over 2000 years in the case of Hipparchus, and
although these periods are of course very short in the life-history of any
star, still _some_ changes may possibly have taken place in the brightness
of some of them. There are several cases in which a star seems to have
diminished in light since Al-Sufi's time. This change seems to have
certainly occurred in the case of [Greek: th] Eridani, [Greek: b] Leonis,
[Greek: z] Piscis Australis, and some others. On the other hand, some
stars seem to have certainly increased in brightness, and the bearing of
these changes on the question of "stellar evolution" will be obvious.
In most cases Al-Sufi merely mentions the magnitude which he estimated a
star to be; such as "third magnitude," "fourth," "small third magnitude,"
"large fourth," etc. In some cases, however, he directly states that a
certain star is a little brighter than another star near it. Such
cases--unfortunately not numerous--are very valuable for comparison with
modern estimates and measures, when variation is suspected in the light of
a star. The estimates of Argelander, Heis, and Houzeau are based on the
same scale as that used by Ptolemy and Al-Sufi. Al-Sufi's estimates are
given in thirds of a magnitude. Thus, "small third magnitude" means 3-1/3,
or 3·33 magnitude in modern measures; "large fourth," 3-2/3 or 3·66
magnitude. These correspond with the estimates of magnitude given by
Argelander, Heis, and Houzeau in their catalogues of stars visible to the
naked eye, and so the estimates can be directly compared.
I have made an independent identification of all the stars mentioned by
Al-Sufi. In the majority of cases my identifications concur with those of
Schjellerup; but in some cases I cannot agree with him. In a few cases I
have found that Al-Sufi himself, although accurately describing the
position of the stars observed by _him_, has apparently misidentified the
star observed by Hipparchus and Ptolemy. This becomes evident when we plot
Ptolemy's positions (as given by Al-Sufi) and compare them with Al-Sufi's
descriptions of the stars observed by him. This I have done in all cases
where there seemed to be any doubt; and in this way I have arrived at some
interesting results which have escaped the notice of Schjellerup. This
examination shows clearly, I think, that Al-Sufi did not himself measure
the _positions_ of the stars he observed, but merely adopted those of
Ptolemy, corrected for the effect of precession. The great value of his
work, however, consists in his estimates of star magnitudes, which seem to
have been most carefully made, and from this point of view, his work is
invaluable. Prof. Pierce says, "The work which the learning of M.
Schjellerup has brought to light is so important that the smallest errors
of detail become interesting."[391]
Although Al-Sufi's work is mentioned by the writers referred to above, no
complete translation of his manuscript was made until the task was
undertaken by Schjellerup, and even now Al-Sufi's name is not mentioned
in some popular works on astronomy! But he was certainly the best of all
the old observers, and his work is deserving of the most careful
consideration.
Al-Sufi's descriptions of the stars were, it is true, based on Ptolemy's
catalogue, but his work is not a mere translation of that of his
predecessor. It is, on the contrary, a careful and independent survey of
the heavens, made from his own personal observations, each of Ptolemy's
stars having been carefully examined as to its position and magnitude, and
Ptolemy's mistakes corrected. In examining his descriptions, Schjellerup
says, "We soon see the vast extent of his labours, his perseverance, and
the minute accuracy and almost modern criticism with which he executed his
work." In fact, Al-Sufi has given us a careful description of the starry
sky as it appeared in his time, and one which deserves the greatest
confidence. It far surpasses the work of Ptolemy, which had been without a
rival for eight centuries previously, and it has only been equalled in
modern times by the surveys of Argelander, Gould, Heis, and Houzeau. Plato
remarked with reference to the catalogue of Hipparchus, _Coelam posteris
in hereditatem relictum_, and the same may be said of Al-Sufi's work. In
addition to his own estimates of star magnitudes, Al-Sufi adds the
magnitudes given by Ptolemy whenever Ptolemy's estimate differs from his
own; and this makes his work still more valuable, as Ptolemy's magnitudes
given in all the editions of the _Almagest_ now extant are quite
untrustworthy.
In the preface to his translation of Al-Sufi's work, Schjellerup mentions
some remarkable discrepancies between the magnitudes assigned to certain
stars by Ptolemy and Argelander. This comparison is worthy of confidence
as it is known that both Al-Sufi and Argelander adopted Ptolemy's (or
Hipparchus') scale of magnitudes. For example, all these observers agree
that [Greek: b] Ursæ Minoris (Ptolemy's No. 6 of that constellation) is of
the 2nd magnitude, while in the case of [Greek: g] Ursæ Minoris (Ptolemy's
No. 7), Ptolemy called it 2nd, and Argelander rated it 3rd; Argelander
thus making [Greek: g] one magnitude fainter than Ptolemy's estimate. Now,
Al-Sufi, observing over 900 years ago, rated [Greek: g] of the 3rd
magnitude, thus correcting Ptolemy and agreeing with Argelander. Modern
photometric measures confirm the estimates of Al-Sufi and Argelander. But
it is, of course, possible that one or both stars may be variable in
light, and [Greek: b] has actually been suspected of variation. Almost all
the constellations afford examples of this sort. In the majority of cases,
however, Al-Sufi agrees well with Argelander and Heis, but there are in
some cases differences which suggest a change in relative brightness.
Among other remarkable things contained in Al-Sufi's most interesting work
may be mentioned the great nebula in Andromeda, which was first noticed in
Europe as visible to the naked eye by Simon Marius in 1612. Al-Sufi,
however, speaks of it as a familiar object in his time.
Schjellerup says--
"For a long time many of the stars in Ptolemy's catalogue could not be
identified in the sky. Most of these discordances were certainly due
to mistakes in copying, either in longitude or latitude. Many of these
differences were, however, corrected by the help of new manuscripts.
For this purpose Al-Sufi's work is of great importance. By a direct
examination of the sky he succeeded in finding nearly all the stars
reported by Ptolemy (or Hipparchus). And even if his criticism may
sometimes seem inconclusive, his descriptions are not subject to
similar defects, his positions not depending solely on the places
given in Ptolemy's catalogue. For, in addition to the longitudes and
latitudes quoted from Ptolemy, he has described by alignment the
positions of the stars referred to. In going from the brightest and
best known stars of each constellation he indicates the others either
by describing some peculiarity in their position, or by giving their
mutual distance as so many cubits (_dzirâ_), or a span (_schibr_),
units of length which were used at that time to measure apparent
celestial distances. The term _dzirâ_ means literally the fore-arm
from the bone of the elbow to the tip of the middle finger, or an ell.
We should not, however, conclude from this that the Arabians were so
unscientific as to measure celestial distances by an ell, as this
would be quite in contradiction to their well-known knowledge of
Geometry and Trigonometry."
With reference to the arc or angular distance indicated by the "cubit,"
Al-Sufi states in his description of the constellation Auriga that the
_dzirâ_ (or cubit) is equal to 2° 20'. Three cubits, therefore, represent
7°, and 4 cubits 9° 20'.
In Al-Sufi's own preface to his work, after first giving glory to God and
blessings on "his elected messenger Muhammed and his family," he proceeds
to state that he had often "met with many persons who wished to know the
fixed stars, their positions on the celestial vault, and the
constellations, and had found that these persons may be divided into two
classes. One followed the method of astronomers and trust to spheres
designed by artists, who not knowing, the stars themselves, take only the
longitudes and latitudes which they find in the books, and thus place the
stars on the sphere, without being able to distinguish truth from error.
It then follows that those who really know the stars in the sky find on
examining these spheres that many stars are otherwise than they are in the
sky. Among these are Al-Battani, Atârid and others."
Al-Sufi seems rather hard on Al-Battani (or Albategnius as he is usually
called) for he is generally considered to have been the most
distinguished of the Arabian astronomers. His real name was Mohammed Ibn
Jaber Ibn Senan Abu Abdallah Al-Harrani. He was born about A.D. 850 at
Battan, near Harran in Mesopotamia, and died about A.D. 929. He was the
first to make use of sines instead of chords, and versed sines. The
_Alphonsine Tables_ of the moon's motions were based on his observations.
After some severe criticisms on the work of Al-Battani and Atârid, Al-Sufi
goes on to say that the other class of amateurs who desire to know the
fixed stars follow the method of the Arabians in the science of
_Anva_[392] and the mansions of the moon and the books written on this
subject. Al-Sufi found many books on the _anva_, the best being those of
Abu Hanifa al-Dînavari. This work shows that the author knew the Arabic
tradition better than any of the other writers on the subject. Al-Sufi,
however, doubts that he had a good knowledge of the stars themselves, for
if he had he would not have followed the errors of his predecessors.
According to Al-Sufi, those who know one of these methods do not know the
other. Among these is Abu-Hanifa, who states in his book that the names of
the twelve signs (of the Zodiac) did not originate from the arrangement
or configuration of the stars resembling the figure from which the name
is derived. The stars, Abu-Hanifa said, "change their places, and although
the names of the signs do not change, yet the arrangement of the stars
ceases to be the same. This shows that he was not aware of the fact that
the arrangement of the stars does not change, and their mutual distances
and their latitudes, north and south of the ecliptic, are neither
increased nor diminished." "The stars," Al-Sufi says, "do not change with
regard to their configurations, because they are carried along together by
a physical motion and by a motion round the poles of the ecliptic. This is
why they are called fixed. Abu-Hanifa supposed that they are termed fixed
because their motion is very slow in comparison with that of the planets."
"These facts," he says, "can only be known to those who follow the method
of the astronomers and are skilled in mathematics."
Al-Sufi says that the stars of the Zodiac have a certain movement
following the order of the signs, which according to Ptolemy and his
predecessors is a degree in 100 years. But according to the authors of
_al-mumtahan_ and those who have observed subsequently to Ptolemy, it is a
degree in 66 years. According to modern measures, the precession is about
50"·35 per annum, or one degree in 71-1/2 years.
Al-Sufi says that the Arabians did not make use of the figures of the
Zodiac in their proper signification, because they divided the
circumference of the sky by the number of days which the moon took to
describe it--about 28 days--and they looked for conspicuous stars at
intervals which, to the eye, the moon appeared to describe in a day and a
night. They began with _al-scharataïn_, "the two marks" ([Greek: a] and
[Greek: b] Arietis) which were the first striking points following the
point of the spring equinox. They then sought behind these two marks
another point at a distance from them, equal to the space described by the
moon in a day and a night. In this way they found _al-butaïn_ ([Greek: e],
[Greek: d], and [Greek: r] Arietis); after that _al-tsuraija_, the
Pleiades; then _al-dabaran_, the Hyades, and thus all the "mansions" of
the moon. They paid no attention to the signs of the Zodiac, nor to the
extent of the figures which composed them. This is why they reckoned among
the "mansions" _al-haka_ ([Greek: l] Orionis) which forms no part of the
signs of the Zodiac, since it belongs to the southern constellation of the
Giant (Orion). And similarly for other stars near the Zodiac, of which
Al-Sufi gives some details. He says that Regulus ([Greek: a] Leonis) was
called by the Arabians _al-maliki_, the Royal Star, and that _al-anva_
consists of five stars situated in the two wings of the Virgin. These
stars seem to be [Greek: b], [Greek: ê], [Greek: g], [Greek: d], and
[Greek: e] Virginis, which form with Spica ([Greek: a] Virginis) a
Y-shaped figure. Spica was called _simak al-azal_, the unarmed _simak_;
the "armed _simak_" being Arcturus, _simak al-ramih_. These old Arabic
names seem very fanciful.
Al-Sufi relates that in the year 337 of the Hegira (about A.D. 948) he
went to Ispahan with Prince Abul-fadhl, who introduced him to an
inhabitant of that city, named Varvadjah, well known in that country, and
famous for his astronomical acquirements. Al-Sufi asked him the names of
the stars on an astrolabe which he had, and he named Aldebaran, the two
bright stars in the Twins (Castor and Pollux), Regulus, Sirius, and
Procyon, the two Simaks, etc. Al-Sufi also asked him in what part of the
sky _Al-fard_ ([Greek: a] Hydræ) was, but he did not know! Afterwards, in
the year 349, this same man was at the court of Prince Adhad-al-Davlat,
and in the presence of the Prince, Al-Sufi asked him the name of a bright
star--it was _al-nasr al-vaki_, the falling Vulture (Vega), and he
replied, "That is _al-aijuk_" (Capella)! thus showing that he only knew
the _names_ of the stars, but did not know them when he saw them in the
sky. Al-Sufi adds that all the women "who spin in their houses" knew this
star (Vega) by the name of _al-atsafi_, the Tripod. But this could not be
said even of "educated women" at the present day.
With reference to the number of stars which can be seen with the naked
eye, Al-Sufi says, "Many people believe that the total number of fixed
stars is 1025, but this is an evident error. The ancients only observed
this number of stars, which they divided into six classes according to
magnitude. They placed the brightest in the 1st magnitude; those which are
a little smaller in the 2nd; those which are a little smaller again in the
3rd; and so on to the 6th. As to those which are below the 6th magnitude,
they found that their number was too great to count; and this is why they
have omitted them. It is easy to convince one's self of this. If we
attentively fix our gaze on a constellation of which the stars are well
known and registered, we find in the spaces between them many other stars
which have not been counted. Take, for example, the Hen [Cygnus]; it is
composed of seventeen internal stars, the first on the beak, the brightest
on the tail, the others on the wings, the neck and the breast; and below
the left wing are two stars which do not come into the figure. Between
these different stars, if you examine with attention, you will perceive a
multitude of stars, so small and so crowded that we cannot determine their
number. It is the same with all the other constellations." These remarks
are so correct that they might have been written by a modern astronomer.
It should be added, however, that _all_ the faint stars referred to by
Al-Sufi--and thousands of others still fainter--have now been mapped down
and their positions accurately determined.
About the year 1437, Ulugh Beigh, son of Shah Rokh, and grandson of the
Mogul Emperor Tamerlane, published a catalogue of stars in which he
corrected Ptolemy's positions. But he seems to have accepted Al-Sufi's
star magnitudes without any attempt at revision. This is unfortunate, for
an _independent_ estimate of star magnitudes made in the fifteenth century
would now be very valuable for comparison with Al-Sufi's work and with
modern measures. Ulugh Beigh's catalogue contains 1018 stars, nearly the
same number as given by Ali-Sufi.[393]