Astronomical Curiosities: Facts and Fallacies

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.389

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 θ Eridani, β Leonis, ζ 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 3⅓, or 3·33 magnitude in modern measures; “large fourth,” 3⅔ 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.”390

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, Cœlam 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 β Ursæ Minoris (Ptolemy’s No. 6 of that constellation) is of the 2nd magnitude, while in the case of γ Ursæ Minoris (Ptolemy’s No. 7), Ptolemy called it 2nd, and Argelander rated it 3rd; Argelander thus making γ one magnitude fainter than Ptolemy’s estimate. Now, Al-Sufi, observing over 900 years ago, rated γ 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 β 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 Anva391 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 71½ 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” (α and β 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 (ε, δ, and ρ 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 (λ 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 (α 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 β, η, γ, δ, and ε Virginis, which form with Spica (α 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 (α 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.392

CHAPTER XIX

The Constellations393

Curious to say, Al-Sufi rated the Pole Star as 3rd magnitude; for it is now only slightly less than the 2nd. At present it is about the same brightness as β of the same constellation (Ursa Minor) which Al-Sufi rated 2nd magnitude. It was, however, also rated 3rd magnitude by Ptolemy (or Hipparchus), and it may possibly have varied in brightness since ancient times. Admiral Smyth says that in his time (1830) it was “not even a very bright third size” (!)394 Spectroscopic measures show that it is approaching the earth at the rate of 16 miles a second; but this would have no perceptible effect on its brightness in historical times. This may seem difficult to understand, and to some perhaps incredible; but the simple explanation is that its distance from the earth is so great that a journey of even 2000 years with the above velocity would make no appreciable difference in its distance! This is undoubtedly true, as a simple calculation will show, and the fact will give some idea of the vast distance of the stars. The well-known 9th magnitude companion to the Pole Star was seen by day in the Dorpat telescope by Struve and Wrangel; and “on one occasion by Encke and Argelander.”395

The star β Ursæ Minoris was called by the Arabians Kaukab al-shamáli, the North Star, as it was – owing to the precession of the Equinoxes – nearer to the Pole in ancient times than our present Pole Star was then.

The “Plough” (or Great Bear) is supposed to represent a waggon and horses. “Charles’ Wain” is a corruption of “churl’s wain,” or peasant’s cart. The Arabians thought that the four stars in the quadrilateral represented a bier, and the three in the “tail” the children of the deceased following as mourners! In the Greek mythology, Ursa Major represented the nymph Callisto, a daughter of Lycaon, who was loved by Jupiter, and turned into a bear by the jealous Juno. Among the old Hindoos the seven stars represented the seven Rishis. It is the Otawa of the great Finnish epic, the “Kalevala.” It was also called “David’s Chariot,” and in America it is known as “The Dipper.”

Closely north of the star θ in Ursa Major is a small star known as Flamsteed 26. This is not mentioned by Al-Sufi, but is now, I find from personal observation, very visible, and indeed conspicuous, to the naked eye. I find, however, that owing to the large “proper motion” of the bright star (1″·1 per annum) the two stars were much closer together in Al-Sufi’s time than they are at present, and this probably accounts for Al-Sufi’s omission. This is an interesting and curious fact, and shows the small changes which occur in the heavens during the course of ages.

Close to the star ζ, the middle star of the “tail” of Ursa Major (or handle of the “Plough”), is a small star known as Alcor, which is easily visible to good eyesight without optical aid. It is mentioned by Al-Sufi, who says the Arabians called it al-suha, “the little unnoticed one.” He says that “Ptolemy does not mention it, and it is a star which seems to test the powers of the eyesight.” He adds, however, an Arabian proverb, “I show him al-suha, and he shows me the moon,” which seems to suggest that to some eyes, at least, it was no test of sight at all. It has, however, been suspected of variation in light. It was rated 5th magnitude by Argelander, Heis, and Houzeau, but was measured 4·02 at Harvard Observatory. It has recently been found to be a spectroscopic binary.

The constellation of the Dragon (Draco) is probably referred to in Job (chap. xxvi. v. 13), where it is called “the crooked serpent.” In the Greek mythology it is supposed to represent the dragon which guarded the golden apples in the Garden of the Hesperides. Some have suggested that it represented the serpent which tempted Eve. Dryden says, in his translation of Virgil —

“Around our Pole the spiry Dragon glides,And like a wand’ring stream the Bears divides.”

The fact that the constellation Boötis rises quickly and sets slowly, owing to its lying horizontally when rising and vertically when setting, was noted by Aratus, who says —

“The Bearward now, past seen,But more obscured, near the horizon lies;For with the four Signs the Ploughman, as he sinks,The deep receives; and when tired of dayAt even lingers more than half the night,When with the sinking sun he likewise setsThese nights from his late setting bear their name.”396

The cosmical setting of Boötis – that is, when he sets at sunset – is stated by Ovid to occur on March 5 of each year.