a.d. 750 TO 1250.

Once more the scene changes. While European science is at low ebb, if we look to the banks of the Tigris, not many miles from the ruins of ancient Babylon, we find the centre of a new and famous school of astronomy.

From the deserts of Arabia an immense empire had arisen, which in less than a century spread eastwards as far as India, and westwards to Morocco and Spain. Its first capital was Damascus, but in 755, after the defeat of the Omeyyad dynasty, the new Caliph fixed his capital at Baghdad, the wondrous city of the Thousand and one Nights. This Caliph was the renowned Al Mansur. To his court there came one day a scholar from India, who was skilled in the knowledge of the stars, and he laid before the Caliph a book which treated of things celestial and showed how to foretell eclipses. Al Mansur was profoundly interested, and ordered a translation of the book to be made into Arabic. The astronomical system of the Hindus was at that time very similar to the Greek, and there can be no doubt that Greek astronomy had found its way to India several centuries before this.

Shortly after this the writings of Greek philosophers and astronomers were brought to the court at Baghdad. They had been carefully preserved, copied, and translated into Syriac, by Nestorian monks in some of the many monasteries which were founded in Persia and other countries of the East when these heretic Christians were driven out of Europe in the fifth century; and many of the Court physicians of Baghdad came from a Nestorian school of medicine. Haroun al Raschid, son of Al Mansur, gave orders for Ptolemy’s Syntax to be translated into Arabic, and it now received its name of Almagest: several other translations were made later, and Aristotle was eagerly studied. This Caliph sent an embassy to Charlemagne, and among the presents sent by the East to the West were an elephant and a clepsydra.

Al Mamun, son and successor of Haroun Al Raschid, is said to have learned astronomy under a Persian teacher. He also added to his father’s library, and one of the terms of a treaty he made with Michael, the Greek emperor, was that a collection of Greek writings should be made throughout the empire, and forwarded (originals or copies) to Baghdad. Moreover, he was not content with merely reading astronomy, Greek, Persian, or Hindu: he ordered Ptolemy’s estimate of the size of the earth to be tested, by measuring an arc of a meridian in his own country, and he founded a splendid observatory in the province of Baghdad. The instruments were of the same kinds as the Alexandrian, but they were larger, and better made, and the circles were more accurately divided. The Arab astronomers were good observers, and among them for the first time we hear of astronomers winning fame by skill in instrument making. Their dials were superior to those of any other race, and they made some important improvements in mathematics, which were immensely useful to astronomers. One great service was the introduction of the decimal notation, which they learned from the Hindus.

Astrology is forbidden by the Koran, but it was practised eagerly, nevertheless, by the Arabs, who constructed tables for this purpose, and made improvements in the methods used.

Traces of Arab contributions to astronomy survive in our words “zenith” and “nadir,” and “almanac”; our word for a “cipher” is the Arabic “zifra,” and indicates the main advantage of the decimal notation in arithmetic; while “sine” is the Latin translation of an Arabic word, and reminds us of the great improvements made in trigonometry.[64]

Among the many names of Ptolemy’s successors at Baghdad, strange and uncouth to our ears, the three most famous are Mohammed ebn Ketir of Fargana, Mohammed ben Geber Albatani, and Mohammed Abul Wefa al Buzjani, which became known to the West under the shortened forms of Alfraganus, Albategnius, and Abul Wefa.

Egypt too had her Arab school of astronomy, as she had had her Greek. A little later than Abul Wefa, Ebn Jounis drew up the famous Hakemite Tables of the sun, moon, and planets, under the patronage of the Caliph Hakem of Cairo.

At the western end of the Arab dominions there were centres of intellectual activity in Morocco and southern Spain. Cordova, the city of the marvellous mosque, had also, in the tenth century, an Academy, and a library which rivalled that of Baghdad; and here, in the midst of almost ceaseless public strife and agitation, in a strangely mingled atmosphere of cultured refinement unknown to the rest of Europe, and of ferocious barbarism, of tyranny and tolerance, heroic deeds of chivalry and treacherous intrigues, there lived and dreamed and worked men of science and philosophers, poets, and artists.

The best known of the Spanish Arabs whose names are connected with astronomy are Arzachel, who drew up the Tables of Toledo; Averroës, the great philosopher, author of De Substantia Orbis, and a commentary on Aristotle’s Metaphysics, who saw “a black spot on the sun” on the day he had predicted a transit of Mercury; and Al Betrugi (or Alpetragius) who wrote on the Spheres. There was also a certain Abul Hazan, a renowned geographer, who travelled across North Africa, and made a catalogue of 240 stars, including some not given by Ptolemy.

Of all the astronomical writings of the Arabs, one of those which became earliest and best known in Europe was the Elements of Astronomy and Chronology of Alfraganus. This was actually used by Dante as his favourite text-book, and he mentions it in the Convivio. I shall therefore give a short account of its contents, following the edition of Golius, printed in Arabic and Latin at Amsterdam in 1669.

In the first chapter Alfraganus gives an account of the calendars used by different nations—Arabs and Berbers, Syrians, Romans, Persians, and Egyptians. After this he plunges at once into a description of the Universe, as portrayed by Ptolemy, and follows his master so closely that his book is almost a much-abridged and simplified Almagest, with a few additions, and with all the mathematics left out.

It is accepted almost without dispute among learned men, says Alfraganus, that the sky is spherical, and rotates on two fixed poles, one north, one south. This is proved by the observed movements of the stars. Equally undisputed among the learned is the fact that Earth and water together form a globe, which is surrounded by air. The spherical form of Earth is proved by the fact that phenomena such as lunar eclipses and shooting stars are seen at a later hour by observers in the East, and by the changing height of stars above the horizon as one travels north or south. Earth is at the centre of the universe, and is but a point compared with the heavens.

There are two principal celestial motions: (1) the “prime motion” which causes the whole sky to revolve with every celestial body, and produces day and night; (2) the proper motions of the sun and other stars in the opposite direction and round other poles. The great circle of the first motion Alfraganus calls the Equator of the Day; that of the second, the Star-bearing Circle, i.e. the zodiac, or more precisely, the ecliptic.

The twelve zodiacal signs are then described, with the division of each into degrees and minutes, the positions of the equinoxes at the beginning of Aries and Libra, and of the solstices at the beginning of Cancer and Capricorn. The Colure is described as a great circle cutting the zodiac (i.e. ecliptic) and equator at the points where they are furthest apart (i.e. at the solstices). This greatest difference was found by Ptolemy to be 23° 51′ but according to the measurement ordered to be made by Al Mamun of pious memory, which was carried out by a number of experts, it is 23° 35′. This value is adopted and quoted subsequently throughout the book of Alfraganus.

Alfraganus then proceeds to explain very clearly how the movements of sun and stars appear from different latitudes on Earth—on the equator, at stations further north, and finally at the pole. He shows how it happens that on the equator day and night are always of equal length, and the sun passes exactly overhead twice a year; whereas day and night vary more and more in length, according to season, as one travels further north, and the sun is lower; until at last at the pole the year consists of one long day and one equally long night, the celestial pole is in the zenith and the celestial equator on the horizon, so that the sky revolves like a mill-stone (i.e. the stars do not rise and set, but trace out horizontal circles, like a wheel which is not upright but flat on the ground).

The circumference of Earth, as determined by Al Mamun of glorious memory, is 20,400 miles, and the diameter, therefore, is nearly 6500.[65] Alfraganus deduces from this the area of the whole Earth and also of the habitable portion of Earth. The latter extends only from the equator to 66° 25′ North, and its longitude at the equator is equal to 180° or 10,200 miles, at the northern limit to 4080 miles. This is divided into seven “Climates,“ as in Ptolemy’s Geography, the first lying a little north of the equator. Alfraganus gives for each the length of the longest day, the height of the pole above the horizon, the extent of territory, and the principal regions and towns comprised. He admits that south of the first climate as far as 0° is some land, surrounded by sea, and sparsely inhabited, and north of the seventh climate are a few towns, but these are of no account.

Our author treats next of the risings and settings of the zodiacal signs, and of the division of the day into 24 equal or 24 “temporary” hours (see p. 26).

After this, the unanimous opinion of wise and learned men concerning the spheres is duly set forth in seven chapters; how there are eight great Orbs, the smaller enclosed within the greater, the star sphere being the outermost and largest of all; how epicycles are fixed in these; how only the star sphere has its centre exactly in Earth, the others being slightly eccentric; what are the positions of the poles and centres of the great spheres and the small epicycles, their relative sizes, and their different velocities as they turn; finally, how well the system represents the movements of sun, moon, stars, and planets. The moon’s mean daily motion, resulting from a wonderful combination of five circular motions, amounts to about 13° 11′; the sun’s is 59′, and he completes a revolution in 365¼ days “less an insignificant fraction.” (This being a popular treatise Alfraganus apparently thinks it unnecessary to state the length of the year more precisely). The sluggish motion (“motus tardissimus”) of the star sphere, which is communicated to all the rest in addition to their own motions, is 1° in a century, according to Ptolemy, so that it completes a revolution in 36,000 years.

Coming now to the fixed stars, their number, and brightness, Alfraganus does not copy Ptolemy’s great catalogue, but informs us that learned men (“sapientes”) did number all the fixed stars as far south as they could see in the 3rd climate, and divided them according to magnitude into six classes. “To the first class they assigned the bright and shining stars such as Canis (Sirius) and Procyon, Vultur Cadens (Vega) and Cor Leonis (Regulus). Stars a little less bright they called second magnitude: such are Alfarcatein and Benet Naax,” Arab constellations which the Latin version describes as the two bright stars of Ursa Minor, and those brilliant ones in the tail of Ursa Major. Thus they proceeded with the other magnitudes, the smallest measured being of the sixth magnitude. The number of stars in each class is given, and the total of 1022;[66] then a list of the 15 first-magnitude stars, which are the same as Ptolemy’s (See p. 155). This is followed by a list of the Arab “Mansions of the moon.”

So far (with the exception of the mansions of the moon) the Arab writer has followed the Greek, but we have now reached a point where he diverges. Ptolemy, he says, only tells us the distances and sizes of the sun and moon, and said nothing about the other heavenly bodies; but if we suppose the greatest distance of the moon to be the same as the least distance of Mercury, and from this calculate his greatest distance (for the ratio is known), and if we proceed in the same way with Mercury and Venus, we shall find that the greatest distance of Venus equals the least distance of the sun as given by Ptolemy. Ptolemy’s least distance for the sun, which was totally wrong, was 1160 Earth-radii: the greatest distance of Venus, calculated in this way from Ptolemy’s figures, was 1150. Alfraganus takes this unlucky coincidence as an indication that there is only just sufficient space between each sphere and the next to allow their respective epicycles to pass one another, and upon this entirely erroneous assumption he proceeds to lay down the distances of each planet from the earth, and finally of the stars, which are all supposed to be at the same distance, equal to the greatest distance of Saturn.

Who first suggested this method of estimating distances we do not know: the first mention of it occurs in Europe in the fifth century a.d. The following table shows the distances obtained in this way:—

GREATEST DISTANCE.

In this, the moon’s distance is approximately correct, but the sun’s is not much more than one-twentieth of its true value. To set the stars at a distance of only twenty thousand times Earth’s semi-diameter seems to us to bring them very close,[67] but they would still be beyond measurement by naked eye methods, so it is no contradiction to Alfraganus’ earlier statement that Earth is a point compared with the heavens.

The Arabs also believed that they had succeeded in measuring the apparent diameters of the planets and even of the points of light which are all we can see of stars, so Alfraganus gives the accepted sizes of all. I give them below in descending order of size. The modern values in the third column show how false were the results obtained by this mistaken method.

DIAMETER: EARTH = 1.

In the above table the size of the moon (whose parallax had been found by the Greeks) is the only one which is nearly right. The sun is far too small, and so are the stars. We cannot yet know with certainty the diameter of any star, but they are all comparable with the sun, and many are enormously larger.[68] As their distances are all different, some of the brightest may be comparatively small, and some of the faintest the largest of all.

The Arabs took a backward step in adopting these imaginary measurements, for Hipparchus had recognized that only the moon was near enough to measure, and although Ptolemy accepted Aristarchus’ value for the sun, he distinctly stated that the planets had no parallaxes and he could not tell their distances.

The next four chapters describe briefly the risings, settings, and meridian transits of stars as seen from different latitudes on Earth; the heliacal risings and settings and the conjunctions with the sun of planets, stars, and moon: the phases of the moon and the direction of her horns at different times of the year. Parallax is then clearly defined and discussed.

A description follows of the earth’s shadow, thrown by the sun into space—its tapering form, its position, always pointing away from the sun, its width at the distance of the moon, and its length according to Ptolemy. This is stated to be 268 times Earth’s semi-diameter, which is nearly correct,[69] for although Alfraganus believed (from Ptolemy’s erroneous parallax) that the sun, was much nearer than it really is, it followed from this—since the size was deduced from the distance—that he also thought it much smaller, and the length of a shadow thrown by any dark body is longer the nearer it is to the light-source, but shorter, the smaller is the light-source.

The two last chapters are devoted to eclipses, lunar and solar, and Alfraganus points out that, unlike lunar eclipses, eclipses of the sun vary in duration and magnitude according to the place on Earth from which they are viewed.

The book concludes: “Enough having now been said concerning the eclipses of sun and moon, by the goodness of God we have been enabled to bring this writing to an end; and for this Deo Laus et Gloria.”

The time at which Alfraganus lived is not precisely known, but it seems to have been in the first half of the 9th century, since from internal evidence he wrote after, but probably not much after, the death of Al Mamun. His name indicates that he was a native of the beautiful and fertile country, shut in by lofty mountains, which lies on either side of the ancient river Jaxartes. He was surnamed the Calculator, and wrote on sun dials and the astrolabe, but we do not know of any observational work of his.

Later Arab writers although they all continued to base their work on that of Ptolemy, improved on some of his estimates. Albategnius began his book “On the Number and Motions of the Stars” by saying that having studied Ptolemy’s Syntax and mastered the Greek methods, and having noticed some errors in the positions of the stars, he felt impelled to add to Ptolemy’s observations, as the latter had added to those of Abrachis (Hipparchus), for it is not given to man to attain perfection. He gives a much more accurate value for precession than Alfraganus had done, who merely copied Ptolemy, for he makes it 54½ seconds yearly, or one degree in 66 instead of in 100 years. His tropical year, too, is only two minutes shorter than the modern value, so that he improved upon Hipparchus in this respect; and he made the discovery which Ptolemy missed, the motion of the sun’s apogee. He merely notes, however, that the position found by himself differed from that given in the Almagest, so it is doubtful whether he realized his discovery, or merely thought that a large error had been made.

Although some of Ptolemy’s values were thus corrected by the Baghdad astronomers, no change was made in his theory of epicycles and eccentrics, which all accepted as having a concrete existence, partly because at first they did not distinguish between these and the spheres discussed by Aristotle, which he had described as formed of the same material as the planets. As Ptolemy does not explicitly state that his circles were only symbols, this is not surprising. They are formed, say the Arabs, of the fifth essence al-acir (the æther); and they conceived the epicycle as gliding over the outer surface of the deferent, like a small soap-bubble on the back of a big one. This notion, coupled with Ptolemy’s erroneous distance of the sun, misled them, as we have seen, into their imaginary discovery of planetary distances.

It was also partly due to Ptolemy’s unfortunate habit of adopting the doubtful or merely provisional results of his predecessors, and representing them as well established and confirmed by himself, that they fell into another error. Tabit ben Korra, noting the discrepancy between the Greek and the Arab value of precession, investigated the question, and put forward a theory that the motion varies both in amount and direction. In his book “On the Motion of the Eighth Sphere” he describes an elaborate apparatus which he had invented to account for this variation, but he is very modest about it, and after narrating the results obtained by others, and how they had left them to be judged by posterity, he adds “And this is what we have done, with God’s blessing.” Then follow his figures and tables. This imaginary discovery was accepted by some of the Arab school, and it appears in many mediæval tables, instead of precession, under the name of the “trepidation.”

The belief in the material reality of the spheres caused the Arabs to add a ninth sphere to the eighth of Ptolemy and Alfraganus, for they thought it was enough to demand of the eighth that it should carry all the stars and give them their slow movement of precession (or trepidation). This ninth sphere, therefore, enveloped the whole universe: upon it were fixed no epicycles, no stars, no planets, but it originated the “prime motion” by turning once in a day and night, and communicating this revolution to all the inner spheres. It became known in mediæval astronomy as the Primum Mobile or first moving.

The Baghdad school of astronomy came to an end with Abul Wefa in 998, and the Spanish schools died out when Seville and Cordova were captured by the Christians in the thirteenth century; but the impetus given to the study of Greek astronomy and astronomical observation was carried on by other nations. In Persia a fine observatory was founded by Nasir-ed-din; in Spain the Christian king, Alfonso X, ordered tables to be drawn up to replace those of Arzachel, and the Libros de Saber to be compiled. The movement in Persia was short-lived, but in Europe the revival of astronomy had begun.