First Part — The Story of Astronomy From Primitive — Times Until th… — Dante and the Early Astronomers by M. A. Orr

First Part. — The Story of Astronomy From Primitive — Times Until the Age of Dante

I — Apparent Movements of the Heavenly Bodies as Seen From Earth

The stars appear to us like points of light, differing greatly in brightness, and scattered very irregularly over the dome above us. All are moving, some much more quickly than others, yet a little attention shows that they do not change their relative positions, and therefore that all must share in one connected movement. If, for instance, any one group be singled out, and looked for again some hours later, it will be evident that it has moved considerably as a whole, yet the stars composing it have kept the same places with regard to one another.

Careful and prolonged observations prove that to observers in the northern hemisphere one star has hardly any perceptible movement, that those nearest to it sweep round it in small circles, and those further away in larger and larger circles, parts of which are hidden below the horizon. All these circlings are performed in the same time, and therefore the stars near the stationary point move more slowly in their small circles than those further away.

All this is precisely what we should see if the sky were a great hollow sphere, turning about the earth on an axis which runs close to the almost stationary star—known therefore as the Pole Star. The direction is from east to west, and a complete revolution is made in a day and night.

We can plot the stars on a globe, and draw an equator on it, which will everywhere be at an equal distance from the poles, and we may add other circles, as on a terrestrial globe: then the position of each star can be referred to these circles as towns on earth are found by latitude and longitude, and the path of any moving body, such as a comet, may be traced.

The stars fade out when the sun rises, but he too sweeps across the sky as though carried round by the same sphere, and he sets like them, in the west. Has he a fixed place on the sphere, keeping always the same position relatively to the stars? No, for in the place where he has just set we do not always see the same stars. Night after night those which were clear in the western sky as soon as it was dark enough to see them, grow closer to him, till at last they are lost in his twilight beams. Thus the sun, though sharing in the daily east to west movement, has a slow movement of his own on the sky-sphere, slipping back from west to east, until in a year he has accomplished the whole round, and sets again among the same stars.

Moreover, this peculiar movement of the sun is not a mere lagging behind the stars, for his west to east motion is combined with a north and south motion. If we note the star-groups which are just behind him when he sets (or just before him when he rises), we shall find that they form a great circle round the globe, half of which lies north and half south of the celestial equator. The Greeks named this circle the Zodiac, or “Path of the Animals,” because the star-groups forming it were mostly called by the names of animals (the Ram, Lion, Fishes, etc.). When the sun is in the most northerly part of the zodiac it is summer in the northern hemisphere; when he is in the most southerly, it is summer in the south. (See Map).

This north and south motion of the sun may be noted more directly in another way. Seen from any given place on the earth, each star rises and sets at the same points of the horizon always, and has the same course in the sky; but the rising and setting points of the sun, which on about the 21st of March are due east and west, travel daily further north, and the sun mounts daily higher in northern skies until about the 20th of June; then he returns towards the south, passing the east and west points again about September 23, and reaches his furthest point south about December 21. (The dates vary slightly owing to Leap Year). The dates on which the sun reaches his furthest north and furthest south points in this yearly journey are called the “solstices,” because his motion seems to be checked, and he pauses or “stands” before reversing his direction; the dates on which he passes the midway point are the “equinoxes,” because at those points he is on the equator, and makes day and night equal all over the earth.

The time taken by the sun to pass from one vernal (spring) equinox to another is 365 days, 5 hours, 48 minutes, 45 seconds. Since this slow motion along the zodiac is from west to east, contrary to the rapid east to west motion which he shares with all the stars, he takes a little longer to complete a daily revolution than they do; and if we reckon a solar day as consisting of 24 hours, a “sidereal” (or star) day is equal to 23 hours, 56 minutes, 4 seconds.

These are very elementary facts, but they are the fundamental facts of astronomy, and without recollecting and holding them clearly in mind we cannot understand Dante’s allusions, nor see the fitness of any astronomical system, ancient or modern. To those who have only read about astronomy in books, and have not watched the skies, they may be puzzling, and I would beg these readers to make a few simple observations for themselves, as this will help them more than any written explanation can ever do to see the heavens with Dante’s eyes. To appreciate the connected movement of the whole sky, some bright stars near the Pole should first be watched, such as the Great Bear and Cassiopeia, or for those in the southern hemisphere the Southern Cross, Canopus, Achernar. Their motions should be compared with those of bright stars near the equator, such as Orion, Virgo, or Aquila. The constellations of the zodiac should be studied, and notes made of the seasons at which each disappears in the rays of the sun.

The sun’s north and south movements can be easily recognized by noting at what points of the horizon he rises or sets at different times of the year; and the different heights to which he rises in the sky are most simply observed by marking the length of the shadow of some tree or pole at midday. Or if some rough kind of gnomon 2 be made, even a flat piece of wood, laid on a sunny window-sill, with a long nail driven vertically into it, the movement and varying length of the shadow, from hour to hour, and from day to day, will make one realize vividly the diurnal and the seasonal movement of the sun. This device, in one form or another, was probably the first astronomical instrument invented, and by its means ancient astronomers in many lands solved important problems.

It is not necessary to explain that the daily apparent movements are caused in reality by the earth’s rotation on her axis, and the yearly apparent movements by her revolution round the sun. These are the book-learned facts which for the most part obscure our perception of the very things on which they are based. I would ask the reader to do his best, for the moment, to forget them.

The movements of the moon among the stars are much more easily observed than those of the sun, since we can see the stars at the same time, and her revolution is much more rapid. She also is apparently carried round with the daily east to west movement, and she also has a west to east motion of her own, but so fast that it takes her round the star sphere in one month, instead of one year. This revolution also takes place in the zodiac. She is first visible as a fine crescent, just following the sun, in the west, after he has set; next night she is markedly further from the sun, on her eastward course, and is a larger crescent; she continues increasing her distance from the sun and the size of her disc, until, as full moon, she is rising in the east when the sun sets opposite her in the west, and setting when the sun rises. After this, she begins to wane, and, still travelling in the same direction, rises later and later at night, and sets in the day; she draws gradually nearer to the sun on the western side, till at last, as a fine crescent with the horns turned in the other direction (i.e. always away from the sun), she appears just before the rising sun in the east. Then for a short time she is lost in his rays, till she emerges as a new moon on the sunset side again.

The moon completes a revolution among the stars in 27 days, 8 hours; but it takes her a little longer to come up with the sun again, since he has meanwhile been moving in the same direction along his yearly path; and the ‘synodic’ month, or period from one new moon to the next, is 29 days, 13 hours.

As well as the moving sun and the moving moon, there are five other bodies, visible to the naked eye, which move among the stars. They look like stars, but their movements would lead us rather to class them with sun and moon. They also are in the zodiac, and they also, while carried round with the universal movement from east to west, revolve slowly, each in its own period, from west to east. But their motions are more complicated than those of sun and moon. Two, which we call Venus and Mercury, are never seen very far from the sun, and they oscillate from side to side, sometimes appearing before him near sunrise, and sometimes after him at sunset. Mercury keeps closest to the sun, and is not so bright, and therefore less easy to see; but Venus is a brilliant object when she gradually swings out further from the sun, remaining longer each evening after sunset in the western sky. Then she gradually draws back, closer to the sun, is lost in his rays, and a few days after begins to appear on his other side, as a Morning Star, visible in the east before sunrise. Here she swings out again, like a pendulum, to her furthest distance west, and then draws in again, just as she did on the sunset side of the sun.

In this way, swinging slowly from side to side of the sun, Mercury and Venus make with him the circuit of the zodiac, completing a revolution from west to east in about a year. The average period of Mercury’s oscillation, counting, for instance, from one Greatest Western Elongation (i.e. furthest distance from the sun on the west) to the next, is 116 days; that of Venus is 584 days.

The other three “wandering stars”—or “planets,”3 as they were named by the ancient Greeks—Mars, Jupiter and Saturn, are also often seen as morning or evening stars near the sun, but they do not always accompany him, like Venus and Mercury. They may be seen at any distance from him, even exactly opposite, so that they rise as he sets. They keep as strictly to the zodiac, however, and travel in it from west to east, in periods of approximately two, twelve, and thirty years respectively; and their paths are also complicated by oscillations. Periodically they slacken speed, stop, and go back a little distance among the stars, then they slacken, stop, and advance again. These changes are technically called direct motion, stations or stationary points, and retrograde motion.

It must have originally taken many years of patient watching to discover and distinguish all these planets. In these days, by means of an almanac and some knowledge of the constellations, they may easily be found and traced. Mars and Venus move quickly during part of the time they are visible, and if sketches be made of their positions among the stars, and their paths marked for a few weeks, a very good idea may be gained of the motions of planets as seen in the skies.

Once again, it is not necessary to explain here that these movements of the planets are due partly to their revolution round the sun, and partly to the Earth’s motion. Nor need we, for our present purpose, consider them in any detail: all that is important to realize is the general character of the movements, and their likeness to those of sun and moon.

The distances, and therefore the sizes, of all the heavenly bodies are completely beyond measurement, except with instruments and refined methods; their physical nature could only be guessed at before the discoveries of universal gravitation and spectrum analysis, in the 17th and 19th centuries of our era. All that can be observed by naked eye astronomy is difference of brightness and colour; as for instance the contrast between ruddy Mars and white Jupiter; the steadier light of all the planets as compared with stars; and the interesting fact that the moon shines by reflected sunlight, which is made evident by the connection between her phases and her position with regard to the sun. Her surface, too, is clearly seen to be diversified by dark markings of definite shape, but on no other body in all the sky can we make out the least detail without a telescope.

The movements of the heavenly bodies, therefore, which still form one of the most important parts of astronomy, were almost all that could be studied by ancient astronomers, and gave them the only key they had to the problems of the universe.

To sum up:—The chief apparent movements of the heavens, visible to the naked eye, are eight, viz:—

The daily revolution of the entire heavens, carrying with it every visible celestial body, in a little less than 24 hours; the revolutions of sun, moon, and five naked eye planets, in seven different periods.

The first of these is from east to west, and is by far the most rapid. The axis of revolution passes through two points which we call the celestial poles, and the motion is parallel to the celestial equator.

All the others are in the main from west to east, though the progress of the planets is complicated by periodical retrograde movements. All take place in the zodiac, which is a series of constellations forming a great band round the heavens. The path of the sun is a great circle through this, called the Ecliptic (because eclipses can only happen when the moon is also on it); and the paths of moon and planets are slightly and variously inclined to it.

Thus the daily path of a star is affected only by the simple uniform movement of the entire heaven (in reality the rotation of the Earth) but the daily path of a planet, or of the sun or moon, results from a combination of this general movement with its own peculiar movement, which is generally in the opposite direction.

If it is difficult to conceive a body moving simultaneously in two different directions, an earthly analogy will make it easy. On a great moving platform, such as that which encircled the Paris Exhibition in 1900, there are fixed posts etc. which revolve exactly as the whole platform revolves and do not move about amongst themselves. These are like the fixed stars on the (apparently) revolving sphere. But human beings are free to add their own movements to that given them by the platform on which they stand. One man turns his back and walks steadily and very slowly in the opposite direction, and so he neutralizes part of the platform movement and is not carried onward quite so quickly as the stationary posts: he is the sun. A woman walks as he does, but much more quickly, so that she rapidly passes many posts, although all the time she is being carried backwards with them: she is the moon. Children run backwards and forwards: they are the planets. Finally, if all these people are also constantly crossing the platform slowly from right to left and back again, their movements will be oblique to the platform movement and will imitate the north and south movements of sun, moon, and planets.

It is in this fashion that the movements of the skies present themselves to careful observers on this seemingly stationary earth; and in the youth of the world these apparent movements were believed to be real. The ancients thought that the sky was actually revolving round a steadfast earth, while the sun and moon and certain other “wandering stars” had in addition various motions peculiar to themselves.

The table of periods which follows (see pp. 22-23) will be found useful for occasional reference. Some of the terms used will be explained later.

REVOLUTIONS OF SUN, MOON, AND PLANETS
AS SEEN FROM THE EARTH.

	Days.	Hrs.	Mins.	Secs.
Tropical Solar Year: period from one vernal equinox to another, or from one summer solstice to the next, &c. (Our civil year is based on this).	365	5	48	45·5
Sidereal Year: period between two successive returns of the sun to any star on his path	365	6	9	8·9
The difference between these two kinds of year is due to Precession of the Equinoxes, vide infra, p. 23.
	Days.	Hrs.	Mins.	Secs.
Solar Day: period between two successive passages of the sun across the meridian (noon)	—	24	0	0
Sidereal Day: period between two successive passages of a star across the meridian	—	23	56	4
The difference between these two kinds of day is due to lag of the sun behind the stars, his daily motion westward being slightly retarded by his slow yearly motion eastward.
	Days.	Hrs.	Mins.	Secs.
Mean Synodic Month: period between two full moons	29	12	44	2·8
Mean Sidereal Month: period between two successive returns of moon to any star on her path	27	7	43	11·5
The difference between these two kinds of months is due to the fact that while the moon is making her revolution among the stars, the sun is also moving slowly on in the same direction.
	Days.	Hrs.	Mins.	Secs.
Mean Anomalistic Month: period between perigee and perigee (vide infra)	27	13	18	37·4

Planets:—Mean Synodic Revolution: period between two successive conjunctions with the sun, and mean zodiacal revolution: period of revolution round the zodiac.

	Mean Synodic Revolution.		Mean Zodiacal Revolution.
Mercury	116	Days 4	1·0	Years
Venus	584	″	1·0	″
Mars	780	″	1·88	″
Jupiter	399	″	11·86	″
Saturn	348	″	29·46	″

Precession of Equinoxes: 50·25 seconds of arc in one year; that is, 360 degrees (a revolution among the stars of the zodiac) in 25,800 years nearly.

II — The Beginnings of Astronomy

Note.

As these pages are passing through the press, a letter from Mr. Maunder appears in The Observatory for August 1913 on “The Origin of the Constellations,” and this should be consulted by anyone interested in the subject. Mr. Maunder points out that Ptolemy gives us much more precise information than Aratus regarding the southern limits of the ancient constellations, and that the changes which he says he ventured to make in their traditional forms are extremely insignificant.

Mr. Maunder further observes that the celestial equator of Aratus cannot give any clue to the origin of the constellations (as R. Brown suggested), but only to the date of the work from which Aratus copied, when some astronomer had drawn the equator through the constellations. A slight alteration of the text, Mr. Maunder says, would give a correct equator for the date b.c. 1000.

See also Mr. and Mrs. Maunder’s article in Monthly Notices of the Royal Astronomical Society for March 1904.

Proctor’s “Origin of the Constellation Figures” is in his book Myths and Marvels of Astronomy.

The sky appears to us like an arch, embracing all our lives, Dante says.5 From the dawn of intelligence man must have recognized his dependence upon the all-embracing heavens, especially the sun, without which life would be impossible. The consciousness expressed itself in many ways: in adoration of the sky, the sun, moon, and hosts of heaven; in superstitious fear which regarded events on earth as directly controlled by the heavenly bodies; in careful watching and recording of their movements for useful purposes. Thus, long before astronomy became an exact science, and was studied simply for its own sake, patient observers had laid the foundations, and were familiar with many of the movements we have been describing.

These are of great importance to primitive man. Sun, moon, and stars are invaluable as guides, especially at sea, and we know that the ancient Greek mariners used to steer their ships by observations of the Great Bear, while the Phoenicians preferred to use the Little Bear for this purpose. But the strongest and most universal incentive to careful and prolonged study of the skies is our complete dependence upon them for the measurement of time.

In the earliest period of their history, the Jews, the Greeks, and probably every other nation, divided the day simply into morning, noon, and evening, according as the sun was rising, or apparently stationary, or sinking, with regard to the horizon; and the passage of some bright stars indicated the time at night. But at a very early period the first of all astronomical instruments was invented, by which the sun’s varying height can be measured: hence the time of noon, the dates of equinoxes and solstices, and the length of the solar year can be determined. The gnomon in its simplest form is a pole set up vertically on a smooth level surface, on which its shadow as cast by the sun can be observed. The moment of shortest shadow marks the middle of the day, the shortest midday shadow marks the summer solstice, the longest the winter solstice, the equinoxes falling between. The instrument also indicates the points of the compass, for the sun is always due south in northern latitudes at midday: hence the Latin word meridies (French midi) means south as well as midday, and the Meridian in astronomy is a line which passes through the north and south points and the zenith, and is crossed by the sun at midday.

The gnomon was said to have been introduced into Greece by Anaximander about 600 b.c., and the Babylonians claimed to be the inventors, but it was probably invented independently by several races. The Chinese certainly observed the length of the shadow more than two thousand years b.c., and the very interesting fact has recently come to light that a tribe in a hitherto unexplored part of Borneo use such an instrument, invented by themselves. They set up a post about 6 ft. high, and throw over the top a piece of string weighted at each end to show when it is vertical; the length of the shadow cast by the post is measured with a notched stick. By this means they tell the time of day; and they also observe the sun (presumably with the gnomon) to know the right season for planting their rice.6

However rough the first gnomon may have been, its importance can scarcely be overrated, for it introduced measurement and calculation into observation of the sun’s movements, and it is the ancestor of our modern sextants, transit telescopes, and other instruments of precision.

It was also the beginning of the sundial. The course followed by the moving end of the shadow was traced on the ground, and divided into equal parts: hence arose the custom which the Greeks adopted from the Babylonians of counting twelve hours in every day, from sunrise to sunset, and twelve hours in every night, from sunset to sunrise, regardless of the varying lengths of day and night at different seasons. This is known as the system of “temporary hours.” If we used it in England, the twelve hours of a midsummer day would take twice as long to pass as the twelve fleeting hours of a midsummer night; but in Greece the inequality is much less, and in the latitudes of Babylonia it is never striking. The skill and knowledge of the Greeks enabled them, later on, to construct dials of different kinds, which marked “equal hours,” such as we use now; but the system of “temporary hours” did not altogether die out till after the invention of pendulum clocks in the 17th century of our era.

Clepsydras, or water-clocks, were also used in Egypt and Babylonia, and ancient Greece; and there is still a large one in Canton, where a reservoir is placed in a tower, and the water falling, drop by drop, into a receiver whose depth is marked in figures on the wall, indicates the passing of time just as sand does in running through an hour-glass. These clocks cannot have kept very good time, however, or they would have been more used by the Babylonian and Greek astronomers who took pains to ascertain the exact positions of the stars. Owing to the diurnal revolution of the skies, the time at which any celestial body rises or crosses the meridian after another is an index of their distance apart, east and west on the sphere, and this is how it is reckoned by modern astronomers. But the ancients seem to have been never able to trust their clepsydras sufficiently to use this method, and only referred to them for approximate time.

The gnomon, valuable as it is for marking the sun’s daily course, and the north and south part of his yearly motion, is a limited instrument. It cannot show his westerly motion on the sphere, nor is it of any use for the planets. To trace these motions, and the monthly journey of the moon, the first step is to distinguish the stars, by grouping and naming them, especially those which lie in the path of sun, moon, and planets. The invention of some kind of zodiac is probably older even than the invention of the gnomon, and also originated independently among different races. The germ of the idea may be found to-day among races low in the scale of civilization. The Australian aborigines are familiar with that unique star-cluster which we call the Pleiades, and know that its appearances and disappearances are periodical and coincide with the seasons. A Queensland tribe, for instance, has a legend in which the stars figure as six sisters who have been transported to the skies, and it is said that they sometimes appear before the sun in order to throw down icicles, an evident allusion to the fact that the Pleiades begin to appear just before sunrise in May, the Australian winter. The natives of Tahiti divide their year into “Matarii i nia” and “Matarii i raro,” which means Pleiades Above and Pleiades Below (i.e. the horizon at the beginning of night). Sir Norman Lockyer has shown that the mysterious alignments of stones found at Stonehenge, Carnac, and other places, may have been so arranged in order to show the direction, some of the sun at his rising on certain dates, notably the morning of the summer solstice, and some of the Pleiades or other striking stars, whose rising just before the sun would enable ancient astronomers to fix the dates of important festivals.

Such observations as these, of which many instances might be drawn from many parts of the world, are first steps towards studying the whole path of the sun through the stars, and of forming a calendar with a name or number for every day in the year. Until the stars are known, and a calendar fixed, the motions of sun and moon cannot be learned in detail, the planets can scarcely be distinguished from the stars and from one another, and there are no settled dates from which to calculate their periods.

The first zodiac of which we have written record is a lunar one of 28 constellations, which is referred to in the “Canon of the Emperor Yaou,” a Chinese emperor who began to reign in b.c. 2356. “Yaou commanded He and Ho, in reverend accordance with their observation of the wide heavens, to calculate and delineate the movements and appearances of the sun, the moon, the stars, and the zodiacal spaces, and so to deliver respectfully the seasons to the people.” That these astronomers studied “the movements and appearances” of the sun by means of the gnomon as well as observations of the stars is plain from what follows, where directions are given for determining the solstices. One astronomer was commanded by the Emperor to “reside at Nankeaou and arrange the transformations of the summer, and respectfully to observe the extreme limit of the shadow. The day, he said, is at its longest, and the star is Ho: you may thus exactly determine midsummer.” Ho (= fire) is the fiery red Antares in Scorpio. The star of the winter solstice, when “the day is at its shortest” was Maou, which is the Pleiades. Directions are also given for observing the spring and autumn equinoxes, when day and night are of medium length, and certain other stars are to be observed.7

The Hindus had also a lunar Zodiac, but with only 27 constellations, and the Arabs had their 28 “Mansions of the Moon.” These 27 or 28 asterisms were evidently suggested by the moon’s sidereal period of 27¼ days. But her synodical period, i.e. her revolution with regard to the sun, in which she runs through her phases, is much more convenient for marking a period of time for general uses, and this month of about 30 days has been almost universally adopted by primitive peoples, the first day being counted when the crescent new moon begins to be seen after sunset. From this custom arose another, that of counting the beginning of the day from sunset, but in various times and places other starting-points have been chosen—sunrise, midday, or midnight.

Twelve of these synodical lunar months are nearly equal to one solar year, and this doubtless suggested the solar zodiac of twelve constellations, each constellation marking the portion of sky passed over by the sun in a month. The Chinese “Yellow Path of the Sun” contained twelve animals, the Mouse, Cow, Tiger, Rabbit, Dragon, Serpent, Horse, Ram, Ape, Hen, Dog, and Pig. These animals were widely adopted by other nations—the Koreans and the Japanese, the Mongols of Tibet, the Tartars, and the Turks.

Another zodiac, however, was destined to have an even wider popularity, spreading, in the course of centuries, from Greece to Arabia, Persia, India, and China, where it finally superseded the native constellations; it crossed the Mediterranean into Africa, conquered the whole of Europe, and is used to-day over the whole civilised world.

The names of these twelve zodiacal constellations are familiar to us all:—

English Names.	Latin Names.
Ram	Aries
Bull	Taurus
Twins	Gemini
Crab	Cancer
Lion	Leo
Virgin	Virgo
Scales	Libra
Scorpion	Scorpio
Archer	Sagittarius
Capricorn	Capricornus
Water-Bearer	Aquarius
Fishes	Pisces.

Strange to say, we cannot tell with any certainty where, when, or by whom, this ancient series of constellations was devised and named. The earliest full description which we possess is by a Greek poet of the 4th century b.c., Aratus. A line from the prologue to his “Phenomena” was quoted by St. Paul in his address to the Athenians on Mars’ Hill.

“From Zeus we lead the strain, he whom mankind
Ne’er leave unhymned; of Zeus all public ways,
All haunts of men are full, and full the sea
And harbours; and of Zeus all stand in need.
We are his offspring;8 and he, mild to man,
Gives favouring signs and rouses us to toil,
Calling to mind life’s wants; when clods are best
For plough and mattock, when the time is ripe
For planting vines and sowing seeds he tells.
Since he himself hath fixed in heaven these signs,
The stars dividing; and throughout the year
Stars he provides to indicate to men
The seasons’ course, that all things duly grow.”9

But Aratus did not know who had invented the names of the star-groups which he describes. “Some man of yore,” he supposes,

“A nomenclature thought of and devised,
And forms sufficient found. For men could not
Or tell or learn the separate names of all,
Since everywhere are many, size and tint
Of multitudes the same, but all are drawn around.
So thought he good to make the stellar groups,
That each by other lying orderly,
They might display their forms. And thus the stars
At once took names and rise familiar now.”10

It is, to say the least, exceedingly doubtful, whether the naming of star-groups was so promptly carried out by one individual, especially as Aratus’ poem includes, besides the twelve zodiacal constellations, thirty-six others, which contain all the bright stars of the sky except those too far south to be seen in the temperate regions of our northern hemisphere. The spaces thus left blank were afterwards filled up, chiefly in the 17th and 18th centuries of our era, and the regions round the South Pole are now crowded with a mixture of birds and scientific instruments; but the names and the figures of the traditional forty-eight constellations still find undisputed places on our globes and star-maps.

Some of these figures are very strange and suggestive. We have a maiden with wings, a centaur shooting arrows, a flying horse, a water-snake with a crow and a cup on its back, a charioteer with a goat on his shoulder, a man strangling a serpent, another pouring water into the mouth of a fish, and a strange beast like a goat with a fish’s tail. All had their meaning, doubtless, to their originators, but to us they are cryptic characters, hard to decipher. Among the zodiacal constellations only one is obvious, Libra the Scales, the sign in which the sun is when days and nights are perfectly balanced in length; but this is comparatively recent, for Aratus and his contemporaries give in its place the Claws of the Scorpion, the latter being an enormous monster extending over the space of two asterisms. The figures may have been religious symbols, or an illustration of some myth concerning the sun’s yearly course, or each of the twelve may have indicated the weather or the occupation suitable to the month it represented. The ear of corn in the hand of the Virgin, and the juxtaposition of three watery figures in Capricornus, Aquarius, and Pisces, suggest the latter explanation. Many different ideas probably played a part in the origin of these mysterious constellation-forms. The Greeks, and after them the Romans, when adopting the old constellations, sometimes adopted also the old myths which still clung about them; sometimes they ascribed legends to them from their own mythology. Thus, the kneeling figure with his foot upon a dragon, became and remains the hero Hercules, although Aratus only describes him as a man toiling at some unknown task, and says he is called simply the Kneeler. Successive generations of astronomers altered some of the figures, but probably only to a slight extent.11

The poem of Aratus enjoyed an immense popularity in classical times and throughout the Middle Ages, and no doubt helped to stereotype the forms whose origin was already forgotten when he wrote. He was not an astronomer, however, and the poem is only a popular paraphrase of a lost work by Eudoxus. This Greek astronomer had lived a hundred years earlier, and it is thought that he himself copied from an older source. The attempt to discover this source has been the object of many ingenious conjectures, and much research among ancient monuments and writings. Some of the old constellations are met with in Isaiah and Job, in Homer, on tablets found at Nineveh, and an immense antiquity is sometimes claimed for them. Dupuis, writing at the end of the eighteenth century, thought he had conclusively proved that the figures of the zodiac were designed in Egypt 15,000 years ago!12 Miss Plunkett, in her “Ancient Calendars and Constellations” assigns them to the seventh millenium before Christ.

An ingenious theory, suggested independently by Schwartz and Proctor, and developed by Mr. E. W. Maunder,13 is founded on an examination of the space round the South Pole which was left blank by the ancient constellation designers. From its extent, Proctor concluded that they cannot have seen further south than about 40° from the South Pole, and therefore that they must have lived in a latitude of about 40° north of the equator (say, central Asia or Asia Minor); from the position of its centre, which must have been the Pole, he concluded that the date was about b.c. 2200. For the centre of the circular patch seems to lie near the star Delta Hydri, which was the South Pole star at that time. (This movement of the Pole among the stars, due to “precession,” will be explained later). This date does not differ much from that found by Robert Brown, from the position of the celestial equator among the stars, as described by Aratus; he says b.c. 2084.14 Schwartz gave b.c. 1400; Mr. Maunder, from additional considerations of the positions of various constellation figures, says that they must all have been originally designed about b.c. 2800.

Unfortunately the descriptions of Aratus are neither very precise nor consistent with one another, and he is our oldest and our main authority for the forms and positions of the ancient constellations.15 It may, however, be taken as practically certain that they had been designed many centuries before he wrote, and that the Greeks received them from the Babylonians. Orion and the Pleiades, the Great Bear and Arcturus, and perhaps many others, were familiarly known in the Levant as early as the tenth century before Christ; and we find traces of our zodiac, or its beginnings, in Babylonia at least as early as the eleventh. It is always to Egyptians and Babylonians that the Greeks referred as their predecessors and teachers in astronomy, but the native constellations of Egypt seem to have been different, and so far as we know at present the Babylonians began earlier and made greater progress in star-lore than any other nation before Greece. The latest results of expert investigation of astronomical tablets discovered in the ancient clay libraries of Babylonia and Assyria, tend to show that astronomy was of native growth there, and developed very slowly.16 Star-worship and the need for a calendar led their inhabitants to observe the skies thousands of years ago; but their early work was naturally vague and rude.

This star-worship and star-study seems to have been learned by the Semitic Babylonians, and their descendants and rivals the Assyrians, from a race with whom they met and mingled in the grey dawn of history, but whose existence was unknown to us before the middle of last century.

This people, who belonged to a totally distinct family of nations, and are known to us now as Sumerians, had settled near the mouth of the Persian Gulf, when it ran further inland than it does now, and more than five thousand years ago used a kind of writing on soft stones (later, on bricks) which had obviously arisen from some form of picture writing, and ultimately developed into cuneiform. Their reverence for the heavenly bodies is shown by the fact that the familiar star sign, which appears on very early Sumerian inscriptions, denotes their word for god or lord, and on the monuments of Babylonia and Assyria we meet constantly the triple sign This, we learn from the inscriptions, stood for three great deities, the Moon-god, the Sun-god, and the goddess of the planet Venus. Our illustration shows an inscription in early Babylonian script, and a scene which represents the vassal of a king of Ur (Abraham’s “Ur of the Chaldees”) being led into the presence of the Moon-god.17 It is believed to date from about b.c. 2400. The Babylonians were an intensely superstitious people, and a large part of their omens were drawn from observations of the skies. Every city from this period onward had its ziggurat or great tower formed of several superimposed cubes, usually seven in number, diminishing in size and probably crowned by the shrine of the local deity. It is not certain what purposes were served by these towers, but the successive platforms may well have been the observatories from which the Babylonian priests, gazing through the clear air and over the level plains, watched, year after year, and century after century, eclipses of sun and moon, risings and settings of stars and planets, and all the changing pageant of the skies, which to them were eloquent of peace and prosperity, or of war and misfortunes in their land.

Although this illusory art chiefly occupied the early Babylonian astronomers, they made some observations of real value, and gradually acquired true knowledge concerning the movements of the heavenly bodies.

Tablets a few centuries older than the Chinese Canon of Yaou containing lists of the Sumerian names of twelve months, show that this people had established a luni-solar year. Fortunately for the progress of astronomy the year does not contain an exact number of months, or even of days: at the end of twelve lunar months, a few more days and hours must elapse before the sun has returned to his original place among the stars, and before the round of the seasons is completed. Therefore the first rough approximation had to be constantly corrected if calendar festivals were to recur at the same seasons; and thus the priests, who in early times were usually the calendar makers and keepers, became gradually better and better acquainted with the movements of sun and moon, and the appearance of star-groups. It is interesting to compare the different ways in which various races have solved the problem of calendar-formation.

The Chinese had a year of twelve months, and added an intercalary month occasionally, in such a way that the average length of the year was brought up to 366 days. The written character for “intercalary” in both Chinese and Japanese is a compound of the characters for “gate” and “Emperor,” because in ancient days the Emperor used to perform the ceremonies proper to each of the twelve months in the special room of his palace dedicated to that month, but in the intercalary month he performed them in the doorway of the palace.

The Egyptians and the Arabs seem to have given up the attempt to harmonize the two periods, though both of these nations reckoned twelve months in their years. The Egyptians counted thirty days to each month, and added five days more at the end of the twelfth, so that the months can have had no connection with the moon: the year had, in fact, been calculated from the position of the sun among the stars, beginning with the morning on which Sirius rose just before it. This “heliacal rising” of Sirius heralded the great event of their year, the overflow of the Nile. The Arab year, on the contrary, was purely lunar, for it consisted of twelve months which were alternately of twenty-nine and thirty days: they therefore corresponded pretty closely with the moon’s phases, but had no connection with the sun or the seasons. The Mahomedans still use this lunar year.

The new moon festivals of the Hebrews prove that the moon was important to their calendar, but the three chief feasts of First-fruits, of Ingathering, and of the Passover, were so closely connected with the seasons that their year must have been luni-solar. It consisted of twelve months, one of which was sometimes doubled, but how they decided when this was necessary is nowhere described in the Old Testament. Some think, that as an offering of first-fruits was to be made on a certain day of a certain month, the month preceding it was doubled in every year in which it was evident that the crops would not be far enough advanced for the first-fruits to be gathered so soon: in this way no direct observations had to be made of the sun’s movements, but the year was accommodated to them by observations of the seasons.18

The Babylonian calendar is the most interesting of all, for it was the most intimately connected with star-observation. At first an extra month seems to have been added to the usual twelve, in an irregular way, whenever found necessary, judging by a tablet of the great king Hammurabi, who united all the cities of southern Babylonia under one rule, and gave them the famous Code of Laws, communicated to him by the Sun-god. The tablet runs as follows:—

“Thus saith Hammurabi: the year having gone wrong, let the coming month be registered by the name of Ululu the second. And instead of the payment of taxes being made on the 25th day of Tasritsu, let it be made on the 25th day of Ululu the second.”

Hammurabi reigned about b.c. 2200. A thousand years or more after this, we find that royal decrees for correcting the calendar were never necessary, for the astronomers had invented more than one system for keeping the year right. One of these was to observe, like the Egyptians, the heliacal rising of certain stars. The little group of three stars in the head of the Ram, which we call Alpha, Beta, and Gamma Arietis, was found very convenient for this purpose. When it rose just before the sun in the month Nisan, the observers knew that all the twelve months would fall in their right seasons, but when it remained invisible (hidden in the morning twilight) until the following month, the calendar was evidently running ahead of the sun, and that year was lengthened by adding a thirteenth month. This is the meaning of the directions given on a tablet now in the British Museum:—

“The asterism Dilgan 19 rises heliacally in the month of Nisan. Whenever this asterism remains invisible, let its month be forgotten,”

that is, let it be taken over again, as if it had not already been counted. Similar directions are given for some other asterisms and their corresponding months. But a second method, which was peculiar, so far as we know, to the Babylonians, was that of using the moon as a pointer to indicate the place of the sun. Whereas the sun’s place among the stars can only be inferred, the moon’s can be plainly seen, and her phase indicates her distance from the sun at any time. A tablet of unknown date, belonging to the last millenium before our era, or a little earlier, gives the following directions:—

“When on the first day of the month of Nisan the asterism Mulmul (the Pleiades)20 and the Moon are seen together, the year will be normal. When on the third day of Nisan the asterism Mulmul and the Moon are together, the year will be full” (that is, will contain 13 months).

Each Babylonian month began when the new moon was first visible after sunset; if at this moment she was seen with the Pleiades, it is clear that the sun, which had just set, was not far west of the cluster; if however, it was not till the moon was three days old that she was seen with the Pleiades, she would then be some distance above the horizon at sunset: consequently the sun was some distance west of the Pleiades. In this case he would also be west of Dilgan, the Ram’s Head, so those stars would rise after him in the morning, and be hidden in his light: therefore, both the morning and the evening observation combined to show that his course was not completed, and that the year must be lengthened by the addition of an extra month.

Several lists of stars and star-groups indicating the months in this way have been found, the early lists containing only a few, the later twelve. If our zodiac originated with the Babylonians, there is little doubt the idea took its rise from these monthly stars, but it is not possible, with our present knowledge, to say when these old astronomers first linked the isolated stars into a continuous series of twelve star-groups and connected the idea of the month with the invisible group among which the sun was known to be shining, instead of with the stars seen east or west of him, or in conjunction with the crescent moon.21

A Scorpion with immense claws, and a Goat with fishes’ scales appear several times on monuments at least as old as 1000 b.c. and it is very probable, although this fact alone would not prove it, that they were then used as constellation figures. It has been definitely proved from inscriptions that before 600 b.c. the name of Scorpion was applied to some stars of our present Scorpion, that there was a Lion corresponding with ours, and the principal star in that asterism, which was called “The King” by Greeks and Romans (Basiliskos and Regulus), bore a name with the same meaning in Babylonia; the Celestial Bull seems to have been the group of the Hyades, and the Great Twins were the two stars Castor and Pollux. The last two identifications seem to show how the single stars or small groups of the monthly lists were expanded into the large zodiacal constellations, for the Hyades cluster is in our present Bull, and Castor and Pollux are in our Twins.

Under the great Assyrian kings who in the 8th and 7th centuries b.c. made Nineveh the capital of their empire, Babylonian astronomy flourished exceedingly, and it made much progress through all the political changes which followed, until the beginning of our era. The motions, phases, and eclipses of the moon were carefully studied and could be accurately predicted, the positions of many stars were determined; the zodiac was divided into twelve equal spaces, which afterwards became 36 by sub-division (the constellations being too unequal in size for convenience); and finally the whole circle was marked out in 360 degrees. The movements of all the naked eye planets were well understood, their positions being constantly compared with those of a number of standard stars, mostly in the zodiac; and after watching and recording these for a number of years the astronomers were able to calculate where each planet would be found at future dates. Tables have been found on clay tablets of the 2nd century b.c. predicting the heliacal risings and settings, and the stations and retrogressions etc., with considerable accuracy.

When astronomy had reached this stage of accurate prediction, it was no longer in its infancy, but was fairly on its way to become a true science.22

Nevertheless, the astronomy of the Babylonians, advanced as it was, seems never to have progressed beyond the empirical stage. With them, there seems to have been no desire to group the facts they so patiently and skilfully collected into a system, and form a theory to explain them.

And this must be said of other ancient nations also. The Egyptians made careful observations, especially of the heliacal risings of different stars, by means of which they determined the length of the year, as we have already mentioned, and oriented their temples and pyramids. They worshipped the sun in all his aspects, and their astrology so much resembles the Babylonian that it is believed to have been derived from it. The Babylonians seem to have been more interested in the planets than any other nation of antiquity, but they were known also in other countries. The Chinese recorded comets, and all races were greatly interested in eclipses, which they were able to predict with some accuracy, having discovered that they occur in cycles. Yet we find no more rational attempt to explain these phenomena than the Hindu legend of a great dragon that attacks the sun, or the Egyptian story of a sow that swallows the moon; and their cosmogonies can only be regarded as poetical descriptions or survivals of early childlike notions of the universe.

The Hindu world resting on the back of an elephant, and that on a tortoise, is no doubt but an allegory. The Egyptians pictured the earth as a great parallelogram, long from north to south but narrow from east to west, like their own land, with the sky over it, upheld by huge pillars or lofty mountains. The stars were set in this domed lid of the world, but sun, moon, and planets were floating each in its own boat on a great celestial river which ran just below the summits of the mountains, and whose course was hidden towards the north. The bark of the sun came nearer to Egypt in the summer, because at that time the celestial river overflowed its usual bank, like the Nile. The red Doshiri was said to sail backwards, referring no doubt to the retrograde movement of Mars.

In Eridu, one of the oldest cities of southern Babylonia, on the Persian Gulf, the great abyss of the ocean was looked upon as the origin of all things, and it was believed that it encircled the earth like a great river. Later on, we find the world described as a great mountain, resting on the watery deep, and under the mountain is the abode of the dead. It is entered from the west, which surely was suggested by the setting of the heavenly bodies in the west. The vaulted sky above the earth has divisions: the rim of the lowest part rests upon the supporting watery deep; above it are the upper waters (the source of rain); and above this again is the dwelling-place of the celestials. The sun issues forth each morning from a door in the upper heaven, or from the mount of sunrise, and enters another heavenly door, or the sunset mountain, at night.

The similarity to these Babylonian ideas of the Hebrew “firmament,” the “waters above the firmament,” and the “of the great deep,” in the book of Genesis,23 and Ezekiel’s “Sheol” in “the nether parts of the earth,”24 has often been noted.

The Boat of the Sun travelling over the sky.
From an ancient Egyptian papyrus.

The recumbent figure covered with leaves symbolizes the earth; the figure leaning over Earth, covered with stars, is the sky; the boat of the rising sun and of the setting sun floats over it. The central figure represents Maon, the Divine Intelligence which preserves the order of the universe.

(Reproduced from Flammarion’s ‘Astronomical Myths,’ by permission of Messrs. Macmillan & Co.)

To sum up:—

If we include as astronomy any observation of the heavenly bodies which leads to a recognition of order and periodicity in their movements and a power of forecasting their positions, then every race and age has had its astronomers, rough though their methods may be at first. With growing civilization more refined methods are used; the gnomon is invented for studying the movements of the sun; the changing positions of moon and planets are noted by means of certain stars; finally, all the visible stars are grouped into constellations, and it is recognized that a great band of star-groups crosses the sky, which forms the pathway alike of sun, moon, and planets; the length of the month and of the year are determined more or less accurately, and when an unvarying calendar has been formed, the celestial cycles can be better recorded and studied. But in all this there is as yet no scientific motive properly so called, no curiosity regarding the phenomena for the simple pleasure of knowing and understanding them, no attempt to group them into a system or to explain their underlying causes. The primitive idea that the heavenly bodies exist for the convenience of earth-dwellers is illustrated by the Egyptian hieroglyph for night, which consists of the sign for sky combined with a star suspended like a lamp; the other idea that they are mysterious divinities is shown by the Babylonian star-sign for a god or king,. The ancients found that the stars were of great use, especially for measuring periods of time; they recognised also in them a marvellous order and regularity, of which they dreamed that they found an echo on earth, and endeavoured to divine the future by watching the skies. Can we doubt that they were also attracted by the beauty that calls all men through all ages to lift their eyes and look upward?

HYMN TO THE SETTING SUN.

Sung by the Priests of Babylon.

Sun-god, in the midst of heaven,
At thy setting
May the latch of the glorious heavens
Speak thee peace.
May heaven’s door to thee be gracious,
May the Director, thy beloved messenger, direct thee.

Lord of E-bara, may the road of thy path be prosperous,
Sun-god, cause thy highway to prosper,
Going the everlasting road to thy rest.
Sun-god, thou art he who is judge of the land,
Causing her decisions to be prosperous.

From a lecture by T. G. Pinches.
(Nature, Dec. 31, 1891).

III — Greek Astronomy

First Period. b.c. 900 to b.c. 350.

“Great men! elevated above the common standard of human nature by discovering the laws which celestial occurrences obey, and by freeing the wretched mind of man from the fears which eclipses inspired! Hail to you and to your genius, interpreters of heaven, worthy recipients of the laws of the universe, authors of the principles which connect gods and men!”

Pliny
(Apostrophe to Thales and Hipparchus.)

1. Homeric Greece

To turn from the astronomy of Egypt and Assyria to the astronomy of the Greeks is like coming to a sudden bend in a river which has flowed through level country for many miles in a slow majestic course, and finding beyond the bend a series of rapids and waterfalls. Instead of patient age-long accumulation of observations, instead of a mystical adoration of stars, supposed to be beyond man’s power to understand, we find that the Greek’s first instinct is to inquire into the meaning and the origin of what he saw, even before he had taken time to investigate. Behind the varied splendours of earth and skies which fascinated his bodily eyes, his intellect divined laws and forces which held the whole together in a wonderful harmony. Then, as fresh facts, or a fresh point of view, thrust itself upon him, a new explanation must be attempted, and thus many complete systems of the universe were evolved. Not the name only, the idea of Cosmos was Greek.

Homer c. 900 b.c.

Hesiod c. 800 b.c.

The first ideas of astronomy among the Greeks were as primitive as those of any other race in its early stages. They evidently had no conception of the sky as a sphere, or of the revolution of the stars as a whole, round fixed poles, though they watched the motions of certain bright star-groups, and called them by the names that we use now (however these names may have reached them), as we see in Homer and Hesiod. Ulysses, guiding his raft cunningly by night, keeps on his left the Bear, also called the Wain, which turns round in her place and keeps watch on Orion, and never bathes in ocean; he watches also the Pleiades and the “slow-setting Ploughman” (Boötes)—an apt description, as anyone may see who watches Arcturus, the brightest star of Boötes, when low on the western horizon. Being a northern star, its motion seems very slow, and makes so small an angle with the horizon that for a long time Arcturus glides above it before finally dropping below; whereas the Pleiades, or any other stars near the equator, move very quickly and almost at right angles to the horizon, and so drop below it quite suddenly. It is Ulysses also who warns his companion, when they are setting out to spy upon the Trojan camp, that two watches of the night are already past, “for the stars have gone forward.” The stars also announced the seasons, for Hesiod says that the time of harvest is indicated by the heliacal rising of the Pleiades, and when Orion with Sirius stands in mid-heaven, and Arcturus rises in morning twilight, it is time for the vintage.

Homer and Hesiod both mention Venus, as a morning star “the brightest of all the stars, which comes to herald the light of dawn,” and also as an evening star, apparently without recognizing that it was the same star; as they do not mention any other planet we do not know if the others were known to the ancient Greeks.

The first appearance of the new moon’s slender crescent was watched for from hill-tops, and celebrated by sacrifices, and this—as with other ancient nations—fixed the first day of their month.

Mimnermus c. 580 b.c.

Day seems to have been divided into three parts, morning, midday, and evening, according as the sun was rising, or nearly stationary, or sinking. The sun was thought to rest upon and slide over the solid dome of the sky, otherwise perhaps it would have fallen to the ground; and at night it was supposed to go behind Mount Atlas, and then to travel behind high northern mountains to its rising place in the east. This primitive explanation of its movements is so poetically described by an early poet, Mimnermus, that I cannot resist a quotation, though the lines can hardly be regarded as an astronomical fragment. They may be freely rendered thus:—

Endlessly toiling Helios speeds.
No rest for him or for his steeds
  When Dawn has climbed the height.
Soon as he lays his weary head
Upon the golden wingèd bed
  Made by Hephaestos’ might,
It bears him sleeping o’er the seas,
Far from the fair Hesperides,
  Through realms of darkest night;
Till in the Ethiopian land
He sees his horses ready stand;
  And when the child of light,
The rosy-fingered, early-born,
Has ushered in another morn,
  He mounts his chariot bright.

The earth, as pictured on the shield of Achilles, was flat and round, just as it appears from a height, and of course Greece was the centre, just as Egypt was the centre of the Egyptian, and Babylon the centre of the Babylonian cosmogonies. It was a small earth: a few countries lay round the Middle Sea, and further to the south was the land of the Ethiopians where the Sun passes overhead and burns the inhabitants black; there was another sea to the north, over which the Argonauts sailed, and in the extreme east was the Lake of the Sun, out of which he rose every morning. This was a great gulf of the River Oceanus which encircled the whole earth. Its sources were in the furthest west, just beyond the Pillars of Hercules, and thence it flowed north, east, and south, finally returning into itself. A branch from near the source, called the Styx, flowed down into the underground world of Hades, the abode of the dead, and beneath this again was Tartarus, where were imprisoned the Titans who had fought against Jove.

Above the flat earth the blue dome of heaven was spread like a tent, and across it travelled

“The never-wearied Sun, the Moon exactly round,
And all those stars with which the ample brows of
heaven are crowned.”

What a compact little universe, and how important a part of it was man! But as thought developed, the universe expanded.

2. Thales and Anaximander b.c. 585.

Thales c. 600 b.c.

In the sixth year of the war of the Lydians against Cyaxares, king of the Medes, just when a battle was about to begin, day was suddenly changed into night by an eclipse of the sun, and Herodotus adds: Thales had told the Ionians of this before, and in what year it would happen. This does not necessarily imply any accurate understanding of eclipses on the part of the Ionian philosopher. He had visited Egypt, and may have learned from the priest-astronomers there that eclipses recur in cycles and so can be predicted. But Thales was not content with cycles. He wanted to know, not only that eclipses would happen at such and such times, but how they happened. Perhaps from reports of Babylonian observations, perhaps from questions put to Egyptian astronomers, he learned that solar eclipses only happen when the moon is new and in the ecliptic, that is, in the same part of the sky as the sun, and that the black body then seen on the sun has always a rounded edge. These no doubt were the arguments on which he founded his assertion that solar eclipses are caused by the moon passing in front of the sun; and he further added that this shows the moon to be of an “earthy” nature, that is, not made of fire or any substance either luminous or transparent, but of opaque matter, probably having weight and substance, and not altogether unlike what we know on earth. He is said to have stated also that the moon receives her light from the sun, a conclusion which would follow from a little attention and thought bestowed on her phases.

Besides his speculations regarding the moon, Thales took pains to note the sun’s movements as accurately as possible, by means of gnomons, with a view to discover the exact length of the solar year, and it was he who advised the Greeks to adopt the Phoenician method of directing their course at sea by the Little Bear instead of the Great Bear, which appears to have been the constellation used in Homeric times.

Thales imagined that Ocean did not merely encircle Earth, but that the whole Earth, which was a thin flat disc, floated upon the Ocean.

This zealous observer must have had something of the absent-mindedness of his great successor, Newton; for it is told of him that while star-gazing he fell into a well!

b.c. 611-545. Anaximander

It is evident that the moon’s passing in front of the sun implies a lesser distance from us, and it must have been this which suggested her place in the scheme of Anaximander. This scheme is rather difficult to understand, from the allusions and quotations of later writers, for we have no original writing by Anaximander; but we can gather enough to show that already in the sixth century b.c. the Greek philosophers were asking themselves what was the explanation of the movements and appearances of the heavenly bodies, how they were supported in the sky, what force moved them, how large and how distant they were, and what they were made of. Anaximander asserted boldly that sun and moon were larger than the whole earth: he thought the sun might be 27 and the moon 19 times as large. How he reached this conclusion it is impossible to say. The Egyptians had already tried to measure the apparent size of the sun as compared with the circumference of the sky, by noting how long it took to set from the moment the lower rim touched the horizon to the moment when the whole disc disappeared: this, divided by the 24 hours taken by the sun to traverse the 360 degrees of the sky, gave the sun’s size in degrees (it is about half a degree), and had they been able to find the actual distance of the sun from the earth, they could have deduced its actual size, but this they had no means of determining.

There are two possible ways of seeing that the moon is smaller than the sun, although they usually appear to us the same size. Anaximander may have seen or heard of an “annular” eclipse, in which the moon is rather more distant from us than at a total eclipse, and therefore her dark body just fails to cover the whole sun, and a bright ring of light surrounds her. More probably he realized what was implied in Thales’ explanation of solar eclipses, and concluded that the moon must be smaller than the sun, because she looks no larger although she is nearer to us.

His scheme is the first of which we have any knowledge in which the movements of the heavenly bodies are explained by supposing them not all in one sky together, but placed in a series of heavens, one above the other: hence it is of peculiar interest to the Dante student, for in it we trace the first attempt towards the theory of the Revolving Spheres. It is true that the Babylonians and Hebrews divided their heaven into three parts, one above the other, but this was only to divide the place of atmospheric phenomena from the dwelling-place of the gods, and sun, moon, planets and stars all moved in the same heaven. Here, in the universe of Anaximander, we find one heaven, the lowest, for air, rain, etc., another for all the stars, a higher heaven for the moon, a yet higher for the sun, and above all the region of fire, the brightest, lightest element, whose nature it was to ascend and which therefore is outside all, as it was the nature of earth to descend and therefore to be at the bottom. Probably either in or above the heaven of celestial fire was the heaven of the gods, for, as Aristotle remarks, all our ancestors, indeed all who believe in gods at all, whether Greek or of any other race, place the dwelling-place of the gods above in high heaven, as the unchanging, unmoving region of eternity.25

Unfortunately we do not know what would be of great interest, whether Anaximander also provided separate heavens for the planets, or found a home for them in the heaven of the stars. Perhaps he hardly knew of their existence, or said with Aratus who wrote nearly 800 years later:—

“Of these I dare not speak with certainty,
As of the fixed stars’ orbits.”

The successive heavens were in layers, as it were, one above the other, “like the bark enclosing a tree,” but they were transparent and invisible. The heavens themselves were not in motion, carrying the stars, sun, and moon; Anaximander had an ingenious mechanical scheme of wheels or rings to carry them inside their respective heavens, which doubtless was clear to himself, though unfortunately it is not at all clear to us. Some writers have maintained that these heavens were spheres, but for several reasons it is difficult to believe this, and probably the sky was still to Anaximander, as to the Homeric Greeks, a slightly flattened hemisphere,26 only divided into these layers, and instead of ending at the horizon it continued a little below, to allow of the passage of the heavenly bodies between setting and rising. Perhaps it was for this reason that he gave the earth a greater thickness than the disc of Thales, comparing it to a short thick pillar, three times as broad as high, the top of which only was inhabited. His Cosmos, then, would be something like the diagram, with regard to the disposition (though not the relative sizes) of Earth and the heavenly bodies.

Somewhat timidly the barriers have been thrust back. The earth goes a little deeper into the dark unknown, the sky is wider and higher, the heavenly bodies are much larger and more distant and go under Earth’s surface; but they are cautiously upheld by solid domes, and worked by wheels. Earth is still the floor of the World, and Heaven—now a series of heavens—the vaulted roof above.

3. Later Flat Earth Systems

It is interesting to see how long this timidity persisted among the Greek philosophers, especially of the Ionian school, in spite of the fact that other schools had advanced much bolder ideas, as we shall presently see. Quite a number of universes were constructed somewhat after the pattern of Anaximander’s, with Earth as floor of the world; but some placed the stars beyond moon and sun, some definitely included the planets, though they do not seem to have explained their motions; and there were various ways of supporting the flat earth, and of supporting and moving the heavenly bodies.

Anaximenes c. 550 b.c.

Empedocles c. 450 b.c.

Anaxagoras died 428 b.c.

Anaximenes, a follower of Anaximander, having doubtless pondered the fact that very heavy bodies can float in water if only they are the right shape, and that Earth itself was supposed by Thales to be floating on the Ocean, suggested that the moon is so broad a disc that she floats in the ether, “like a leaf,” and of course the same would apply to the sun. Two later philosophers, Empedocles and Anaxagoras, held that a great whirlwind swept continually round the Earth, which both kept the heavenly bodies from falling down upon it and drove them across the sky.

Equally diverse were the opinions as to the nature and composition of the heavenly bodies. Most philosophers of this age believed that they were of pure fire, or else that they were vessels containing fire, which was extinguished, or in one way or another became invisible to us, during eclipses and when they set. Others held, as we have seen with Thales, that they were of an earthy nature; and Anaxagoras, seeing a meteorite which had fallen from the sky during the daytime, thought he actually held a piece of the sun in his hands, and concluded that the sun was an enormous mass of iron, “much greater than Peloponnesus,” and shone because it was red-hot. But the popular idea still was that the sun was a god, or the chariot driven by a god across the sky, and Anaxagoras was banished from Athens for his impious words.27 The markings on the face of the moon were thought to prove that she was of mixed composition: she was made of air mingled with only a little fire, or earth mingled with fire; but according to Democritus the markings were shadows of mountains on her surface, and Anaxagoras is reported to have said that the moon was inhabited, and the markings were “plains and valleys.”

Anaxagoras suggested that the stars were fragments torn off the circumference of the earth by the encircling whirlwind, and that they glowed with the heat caused by friction, though they were too distant for us to feel this heat, being far beyond the sun. The Milky Way was a source of speculation: some said it was the former path of the sun, and still burning from his heat, but Democritus explained it as caused by the shining of innumerable stars, too faint and close together to be distinguished separately.

The doctrines of the different philosophers as to origin and first stages of the universe do not concern us here, but we must mention that of Empedocles, as his views are directly referred to by Dante.

This philosopher was the first to assert that everything consists of the four elements, earth, air, water, and fire, pure or in combination; and the combinations he supposed to be brought about by two forces, one attractive, the other repulsive, which he named Love and Discord. Of these, one alternately predominates at different ages of the world, and thus its history is divided into periods of different character.

A great step forward was taken when it was realized that the sky is not a hemisphere, ending at the horizon, or even extending a little way below, but that it surrounds Earth in every direction, like a sphere. This idea probably originated with the Pythagoreans, or it may have occurred independently to several thinkers, when the diurnal motion of the heavens was better observed, and geometrical conceptions understood and applied. Now it became no longer necessary to extinguish and rekindle the stars, nor to send the sun round swimming on River Ocean behind northern mountains, or creeping through strange underground regions, through the night. It was clearly recognized that the visible course of each heavenly body was part of a circle, the whole of which we could see if we could only travel fast enough and go to the underside of the earth.

Leucippus c. 450 b.c.

Democritus c. 430 b.c.

But this was just what never could be done, for outside the schools of the Greeks in Italy (Pythagorean and Eleatic), Earth still had an uninhabitable underside. Distinguished men like Leucippus and Democritus sought to combine the belief in an all-surrounding spherical heaven with a flat supported earth which might still give them a solid floor beneath their feet. Leucippus made the earth a hemisphere, with a hemisphere of air above, the whole surrounded by the supporting crystal sphere which held the moon. Above this came the planets, then the sun, and probably the stars were outside this. His disciple, Democritus, on the other hand, retained the disc-like earth, raised a little at the rim, to secure its contents, and made it divide the sphere of air into two parts, so that it rested upon air, and air was also in the sky above. The underside of the disc was not inhabited, no doubt because no one could stand upside down. His order of the successive heavens is not quite the same as that of Leucippus, as he puts the moon and the Morning Star together, and the rest of the planets beyond the sun.

This scheme gave the universe a beautifully symmetrical form, which must have pleased the Greeks, but now they were puzzled to know why the heavenly bodies did not circle symmetrically with regard to the central earth. Why was not the pole in their zenith and the equator on the horizon? They could only guess that it must have been so at first, and that the disc had slipped out of position, either through some irregularity in its weight, or in the density of the underlying air. Compare Milton’s—

“Some say He bid His angels turn askance
The poles of Earth twice ten degrees and more,
From the Sun’s axle; they with labour pushed
Oblique the centric globe.”
Paradise Lost, Bk. X., 563-566.

All these theories and guesses may seem to us very crude and fanciful, and we may compare them to the eager questionings of intelligent children, too impatient to consider whether the answers given are satisfactory explanations or no. But we must remember that all we know of the early cosmogonies is from allusions and descriptions by later writers, who often—like Aristotle, for instance—only quote to condemn. “If each could defend his own opinion, may be we should see that there is truth in all.” (Conv. IV. xxi. 25-7).

At least we find a keen and disinterested desire to penetrate the causes of things, and a fertile imagination, without which science can make no advance: moreover there was a progress in true knowledge. It was discovered that the (apparent) diurnal paths of sun, moon, and every star were circles, although only a part of the paths could be seen; and that, although all were seen projected on a sphere, their actual distances from earth were very varied.

It is disappointing to find no record of observations of the planets, and from the almost random way in which they were placed in the heavens it seems that but little attention had been paid to them as yet. In fact, Seneca tells us that Democritus knew neither their number nor their names. They were often classed with comets, and thought to be entirely erratic, and the Greek mind was more attracted towards those phenomena which were seen to be orderly.

4. Pythagoras and His Followers

Socrates. As the eyes are appointed to look up at the stars, so are the ears to hear harmonious motions, and these are sister sciences. That is what the Pythagoreans say, and we, Glaucon, assent to them?

Yes, he replied.

Pythagoras c. 540 b.c.

About the same time that Anaximander was inventing solid hemispheres and rings to hold and move the heavenly bodies round about a flat earth, Pythagoras was founding a school in southern Italy which gave to the world a very different scheme. One of the characteristics of his school was secrecy, its methods were oral, and his later followers were fond of attributing to their master everything which had gradually grown out of his teaching: it is difficult therefore to say with certainty what he himself taught. It has often been stated by modern writers that he anticipated Copernicus, and discovered that the earth revolves round the sun. Though this is a mistake, we may venture to believe that Pythagoras taught that the earth is a sphere, hanging freely in space.

We are so familiar with this idea from childhood, that it is difficult to imagine what a tremendous innovation it was. Pythagorean noviciates, doubtless after solemn initiation and preparation, were told: This earth, which seems to you the floor of the world, with heaven stretched over it like a tent, is a round globe, with men like you living on the other side of it, and yet they do not fall, and earth does not fall, for it is poised in the centre of the world, and has no tendency to fall in one direction rather than in another. Earth, itself a perfect sphere, is in the centre of an infinitely greater sphere, the star-set heaven; and within this seven heavenly bodies move in perfect circles, each at its proper distance and pace, all needing no support and no force to drive them, for harmony is the motive power of the Cosmos. Their distances are proportional to the intervals between musical notes, and as they circle they make heavenly music, which we should hear did we not always hear it, like one who lives beside a waterfall 28. There is no below, and no above, for above is below and below above to our antipodes: there is but the centre, where we live, and Heaven is all around.

How did Pythagoras reach this great and startling truth of the round unsupported earth?

His school relied more on experiment and observation than the Ionian, and the colonizing Greeks of Italy had travelled. They might have noticed the curvature of the sea, and the varying height of the Pole Star according to latitude. We know that in early days the Greeks were struck by the remarkable fact that the brilliant star Canopus (second only to Sirius in brightness), which was invisible in Greece, could just be seen close to the southern horizon in Rhodes, and was well seen in Egypt. Then the moon may have helped once more. When it was understood that lunar eclipses only happen at full moon, when we are between her and the sun, and that they may therefore be explained by the earth’s shadow falling on the moon, then, since the edge of that shadow is always a circle, it is demonstrable that the body throwing that shadow can have no form but that of a ball.

Sun and moon are obviously round: it was guessed that they also are globes rather than discs, and the spherical shape of all heavenly bodies was a doctrine of the later if not the earliest Pythagoreans.

Whatever may have been the steps which led to these two great discoveries that Earth is a sphere, and that the apparent path of every celestial body is a circle, the sphere and the circle were soon accepted as the only forms suitable for celestial bodies and their orbits. The founder of the school was a great mathematician, and it is not strange that these forms should have commended themselves to his disciples. The sphere, which has its surface everywhere similar, and its contents greater than those of any other figure with equal surface, was the “most perfect” of solids; and the circle, which has no beginning and no end, is alike in every part, and presents ideas of haunting suggestiveness to the geometer, was the “most perfect” of lines.

In the system of Pythagoras we first find the five planets distinctly enumerated, and playing as important parts as sun and moon. Number was the principle of this universe, and the planets with sun and moon made the sacred number of seven. Among the Greeks, and through the middle ages, all these bodies are spoken of as planets or “wanderers,” in distinction from the “fixed” stars which do not appear to move amongst themselves. These seven “planets” represented the seven notes of a musical scale, and the star sphere made up the octave. Pythagoras is said to have been the first to teach that Phosphor and Hesperus, the morning and the evening star, were the same. When, however, we ask what was the order of the planets in his scheme, we meet with many conflicting reports, and a serious difficulty suggests itself. If the planets had really been observed with care, it must have been seen that their motions could not be accounted for by simple circular movement. The large oscillations of Mercury and Venus on either side of the sun would strike an observer before he thought of tracing their movements among the stars, and noting that they made a circuit of the zodiac. Similarly, the other planets are most conspicuous, rising after sunset and remaining long visible through the night, at the very time of their retrograde movements, so these must have been noticed if a long enough series of observations had been made to distinguish them from one another. The only solution of the difficulty seems to be that Pythagoras, on the journeys into Egypt and Babylon which he is said to have made, learned that there exist planets to the number of five, which move in regular periods, and he may also have learned the length of their zodiacal periods at the same time, or perhaps these were only known to his school much later. If the order assigned to them was that which was finally and generally accepted by the ancient world, the periods must have been known, for this is the only possible clue to the order Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. The planet with shortest period (the moon, with a month) was naturally placed by the Greeks nearest to earth, with the smallest circle to traverse, and so on outwards.

It is very possible, however, that the early Pythagoreans, at least, did not venture to assert more than that there were five planets, without assigning to them any order, for Aristotle tells us that their universe was divided thus:—

From Earth to Moon was the Ouranos, or sky, within which exists all that is changing and corruptible.

Cosmos, the place of ordered movement, was the region of Sun, Moon, and Planets.

Olympos, the place of pure elements, held the stars; the region of Celestial Fire came beyond this, and the Apeiron, the Infinite Space, or Infinite Air, from which the world draws its breath, was outside all.

Philolaus towards end of 5th century b.c.

The diagram shows, then, the earliest form of the Pythagorean universe. But they did not remain content with this. Out of it grew a most interesting scheme (referred to by Dante), which is usually attributed to one Philolaus, of whom hardly anything is known, not even his date.

It seems to have struck Philolaus as a difficulty that the seven planets, which were circling round Earth in the same direction but at very different distances and speeds, and also the immense sphere of stars beyond, were all sweeping together at the same time in an opposite direction, and at the almost incredible pace of one revolution in a day. The brilliant idea occurred to him: Leave the stars at rest, let the seven planets revolve in their seven orbits, the nearer to the centre the faster, and let earth herself revolve fastest of all, viz. in twenty-four hours, in the same direction. If she keeps one face always turned towards the centre, like the moon, this will account quite as well for the apparent diurnal revolution of all the heavenly bodies, and the change of day and night on the earth.

Philolaus did not make Earth remain stationary and simply turn on her axis, which would have had just the same effect on the apparent motions of the heavens; for it seemed more natural that she should revolve as did the rest. The five naked eye planets are all mentioned by name in his scheme.

Was the centre, deprived of Earth, to be left empty? No, the centre was the Watch Tower of Zeus, the Hearth of the Universe, and here they placed the purest element, fire. It was invisible to us, because we live on the side of the earth-sphere turned away from the centre; and also invisible to us was another planet, Antichthon, or Counter-Earth, for this revolved within our orbit, and also in twenty-four hours. It was added to the system, because the addition of Earth as a heavenly body spoiled the sacred number of seven, but by adding Antichthon, and counting the star sphere as another, the total was brought up to ten, another sacred number.

The objection was made that, if Earth is moving in space, this must bring about a change in the apparent sizes of sun and moon, as Earth is nearer or farther from them, but the Pythagoreans were quite ready to believe that all the heavenly bodies are so distant that this journey of Earth makes no difference to their apparent size or brightness. The planets were thought to be worlds like ours, and inhabited; and it was even guessed that plants and animals on the moon must be fifteen times as strong as ours, apparently because there the average day consists of nearly fifteen of our days (of twenty-four hours), and the nights are equally long.

It was the braver of the Pythagoreans to shake the steady earth from her centre, and set her whirling in the depths of space, that they realized, as no one had done before, how large she must be; for Greece and the surrounding lands, the Middle and the other seas, instead of making the whole of the earth, were now understood to be only a portion of a great globe.

Here, then, is a conception of the Universe widely different from Homer’s. The little flat disc has become a great round ball, a planet among planets, swiftly moving through space; the crystal dome that tenderly covered it like a bell-glass over some fragile flower, has lifted, and the vast sphere is seen, infinitely distant, and studded with enormous stars. Man himself is now a tiny creature on a great earth, and his world but one among many, but if he is humiliated by his insignificance, is he not elevated by the vastness of his outlook?

Heracleides c. 370 b.c.

But not even here did the Greeks stop. It was taking a less startling step than they had already taken, to reach the truth that Earth was merely rotating on her axis once in a day, and so causing the apparent diurnal revolution of the heavens. This step was taken (it is said) by a Pythagorean called Hicetas of Syracuse, who is quoted as saying that the earth, “while it turns and twists itself with the greatest velocity round its axis, produces all the same phenomena as if the heavens were moved and the earth were standing still.” We are told also that “Heracleides of Pontus and Ecphantus the Pythagorean let the earth move, not progressively, but in a turning manner like a wheel fitted with an axis, from west to east round its own centre.”

A brilliant guess,29 which seems fully justified by facts, has recently explained the personalities of these two mysterious Pythagoreans of unknown date, Hicetas and Ecphantus, whose names have been coupled for centuries with that of Heracleides, as teaching the rotation of Earth on her axis. It seems that they resemble the Shadow in Hans Andersen’s tale, which became a man and lived apart from the man to whom it originally owed its existence, for it is now thought that they were speakers introduced by Heracleides into one of his dramatic dialogues to discuss astronomy.

Heracleides, therefore, was the sole author of this remarkable discovery.

In this way Earth was restored to her central position, but as a rotating sphere, and the later Pythagoreans apparently tried to reconcile their new scheme with the old by calling Antichthon the uninhabited hemisphere of Earth, and placing the central fire within the earth.

IV — Greek Astronomy

Second Period. b.c. 400 to a.d. 150.

“Chiamavi il cielo, e intorno vi si gira,
Mostrandovi le sue bellezze eterne.”

1. Plato

The Ionian school of philosophy died about the middle of the fifth century b.c., and the Pythagorean towards the end of the fourth. But meanwhile a new school of astronomers was growing up. The philosophers still laid down general principles, founded on abstract reasoning, which they believed must regulate the nature and movements of the heavenly bodies, but astronomy began to be regarded as a branch of mathematics, not of philosophy, and the mathematicians, leaving problems of ultimate causes to the philosophers, devoted themselves to observation and calculation. They carefully studied the peculiar motions of each planet, and their chief aim was to represent these geometrically by some scheme which should include them all, and make it possible to predict the places of the heavenly bodies in the sky for any given date.

One cause of this great progress in methods was no doubt the natural intellectual growth of the Greek race, as they discovered that their eager curiosity concerning nature could only be satisfied by patient investigation. The value of observation was taught, in the latter half of the fourth century, by the philosophy of Aristotle, and a great impetus must have been given by the campaigns of Alexander, in which the Greeks saw distant countries, new climates, strange peoples and customs.

Callisthenes c. 330 b.c.

But a potent cause of the advance in astronomy seems to have been the closer connection between Greek astronomers and those of Egypt and Babylon. The astronomer Callisthenes went with Alexander to the East, and received a letter from Aristotle praying him to send to Athens the Babylonian eclipse records which were centuries old; and Aristotle mentions, when speaking of the motions of the planets, that the Babylonians and Egyptians had furnished trustworthy information about each one of them. Even before this, we find that the Greek descriptive names of the planets were changed for names of Greek deities which are believed to correspond with the Babylonian gods and goddesses who presided over the planets. Thus Plato speaks of “the star sacred to Hermes” as well as Stilbon the Glitterer, and he is the last to use commonly the name of Phosphor for the planet which henceforth was known as Aphrodite among the Greeks, and Venus among the Romans, corresponding with the Babylonian Ishtar; and so on with the rest. Instead of vague records of journeys in Egypt or Babylonia, we have a definite statement that Eudoxus, who was the founder of the new school, went to Egypt about 378 b.c., with letters from the king of Sparta to the king of Egypt, and we are told that he studied the planetary motions under a priest of Heliopolis. It seems highly probable, to say the least, that Eudoxus was the first Greek to appreciate the value of those methods of observation and continuous recording of phenomena which he found among the Egyptians, and to understand the wonderful regularity which was hidden behind the seeming irregularities of the “wandering stars.” He was also, apparently, the first Greek to write a detailed description of the forty-eight ancient constellations.

But if Egypt and Babylonia gave to Greece records of celestial phenomena, and set the example of accurate and long-continued observations, Greece made the new knowledge her own, and transformed it. The legend that Eudoxus applied his mathematical skill to the ancient monuments of the Egyptians, and showed them how to calculate the height of the Great Pyramid by measurements of its shadow, is typical of the history of Greek treatment of Oriental astronomy. One geometrical theory after another was invented to represent the planetary motions, was compared with the skies, and rejected or improved, and meanwhile observation became much more close and accurate; new instruments were introduced, new methods of calculation invented, new motions discovered which had to be accounted for; finally, five hundred years after Eudoxus’ visit to Egypt, the result of all this labour was summarized in a truly epoch-making work, which remained the standard treatise on astronomy until the time of Copernicus.

Plato c. 427-347 b.c.

Eudoxus was born at Cnidos, in Asia Minor, but at the age of twenty-three he went to Athens, and studied under Plato. It is said to have been Plato who inspired the young man with the idea of devoting his brilliant mathematical powers to solving the problem of celestial motions, and with this view he went to Egypt. The story is easy to believe when we recall the many passages in the Dialogues in which Plato uses the splendid imagery of the skies to illustrate his philosophic doctrines, dwelling especially on the perfect though little understood symmetry of the celestial motions, and it will be remembered that astronomy was one of the subjects to be learned by the rulers of his ideal state.

It is true that Glaucon is gently but decidedly snubbed by Socrates in the Republic, for suggesting that the study of astronomy is valuable because of its use in navigation, husbandry, and the arts of war. This is “vulgar praise,” but has there ever been nobler praise of astronomy than that which Socrates himself then proceeds to give? Although he believes that true knowledge, knowledge of realities, is only to be obtained by the exercise of pure reason without the aid of sense, he considers that the study of celestial motions is one of the best means of training the mind to reach those heights, and he does not hesitate to say that sight was given to us in order that we might look at the skies. For the embroidery of heaven, says Socrates, though wrought upon a visible ground, is the fairest and most perfect of visible things; and it is displayed to our mortal eyes as a pattern of the eternal realities which are granted to the vision of the soul.

In the Timaeus this idea is elaborately developed, and it undoubtedly had an effect on Plato’s contemporaries, although his direct influence on astronomy cannot be compared with that of Aristotle. The Timaeus was widely read also in the Middle Ages, during the long period when Plato’s other writings were unknown, and it is quoted by Dante. We are often reminded of him when reading the astronomical and quasi-astronomical parts.

Timaeus, who is introduced to Socrates by Critias as “the most of an astronomer among us, and one who has made a special study of the nature of the Universe,”30 describes the Creation as he conceives it most probable that it took place. He assumes a chaos to begin with, where there is no order, and no matter which can be distinguished by name, but all is confused and seething with random restless motions.

Of this, in order to produce something which should express his own goodness,31 the Creator formed the four elements,—earth, water, air, and fire,—and of them he made a world, which became a fair and intelligent being, animated by a living soul. He made it in the most perfect form, that of a sphere, polished and smooth on the outside, “as if from a lathe.” The soul was placed in the centre, and hence diffused throughout the whole bodily frame. It is the cause of the harmonious motions of the stars, and of these there are two kinds: the motion of the Same (the diurnal revolution of the whole heavens) is in the noblest direction, simple and uniform; the motion of the Diverse is in the opposite direction and diagonal to the first, and it is divided into seven parts (the seven orbits of the planets), which bear certain definite ratios to one another.

Timaeus does not name the planets, but in the Republic Socrates names some, and indicates the rest by their colour or other characteristic,32 so we know that the order which he assigns to them, counting outwards from the central earth, is: Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn.

It was in order to make the world like its eternal pattern that the Creator made a “moving image of eternity,” which we call Time, in the revolutions of the heavenly bodies; and to make it visible he “lighted a fire which we now call the sun, in the second of these orbits, that it might give light to the whole of heaven [note that the stars shine by reflected sunlight, as well as moon and planets], and that the animals who were by nature fitted might participate in number: this was the lesson they were to learn from the revolutions of the Same and the Like. Thus, then, and by these means, the night and the day were created, being the period of the one most intelligent revolution. And the month was created when the moon had completed her orbit and overtaken the sun; and the year, when the sun had completed his own orbit. The periods of the other stars [the planets] have not been understood by men in general, but only by a few, and they have no name for them, and do not estimate their comparative length by the aid of a number, and hence they are hardly aware that their wanderings, which are infinite in number and admirable for their variety, make up time. And yet there is no difficulty in seeing that the perfect number of time completes the perfect year when all the eight revolutions, having their relative degrees of swiftness, are accomplished together, and again meet at their original point of departure, measured by the circle of the Same moving equally.”

The heavenly bodies, according to Timaeus, are all divine intelligent beings. In form they are perfect spheres, like the world of which they form part, and they are composed of fire. The stars have two motions, for each rotates on its own axis while it is carried round the centre on the rotating star sphere.

Earth is also a sphere, immoveable at the centre of the World. Of her Timaeus says: “The earth, which is our nurse, encircling the pole which is extended through the universe, he made to be the guardian and artificer of night and day.”

This passage has given rise to the idea that Plato believed the apparent diurnal revolution of the heavens to be caused by earth’s rotation on her axis; but the word here translated “encircling”33 may mean—as that does—either motion or situation round about something, and the whole context ascribes the diurnal movement so clearly and emphatically to the heavens, that it seems evident Plato could only have meant that earth was guardian and artificer of day and night by virtue of her position. The only strong argument in favour of the other meaning is that Aristotle, when speaking of Earth as supposed by some to be central in the Universe but moving, quotes Plato and the Timaeus. It might easily happen, however, that Aristotle knew from other sources, perhaps from conversation with Plato, that at some time the latter had inclined towards belief in Earth’s motion, and remembering the ambiguous expression in the Timaeus he quoted it from memory as a statement of Plato’s belief.

There is some evidence that late in life Plato accepted the doctrine of Philolaus that Earth was not only in motion, but in motion round a Central Fire. There is a legend that he bought the books of Philolaus at a great price, and Theophrastus, a disciple of Aristotle, is reported by Plutarch to have said that “Plato when old assigned to Earth another place, the central and nobler place being reserved for something else more worthy of it.” However this may be, he does not teach either theory in his writings. His views seem to be quite the same as those of Pythagoreans of the old school, whom he sometimes quotes.

After describing the creation of the Universe, Timaeus relates that the Creator deputed the gods whom he had made (including the stars) to create living beings on the earth, he himself creating directly only their immortal part, which he made of the same essence as the World-Soul, but diluted. Then follows the passage which came to the mind of Dante when he met the first spirits of Paradise in the moon.

“And when he had framed the Universe, he distributed souls in equal numbers to the stars, and assigned each soul to a star; and having placed them as in a chariot, he showed them the nature of the Universe, and the decrees of destiny appointed for them, and told them that no one should suffer at his hands, and that they must be sown in the vessels of the times severally adopted to them.... He said that he who lived well during his appointed time [on earth] would return to the habitation of his star, and there have a blessed and suitable existence.” If he lived ill, he would be a woman at his second birth, if a bad woman, then a beast, and as long as he continued to do ill he would “not cease from his toils and transformations until he followed the original principle of sameness and likeness within him.... When he had given all these laws to his creatures... he sowed some of them in the earth, and some in the moon, and some in the other stars which are the measures of Time.”

The creation of man’s body and all the remainder of the Timaeus does not concern us here, except that when speaking of the highest use of man’s faculty of sight, we realize how near Dante and Plato are in their feeling for the revolving heavens:

“God invented and gave us sight to this end, that we might behold the courses of intelligence in the heaven, and apply them to the courses of our own intelligence which are akin to them, the unperturbed to the perturbed; and that we, learning them and being partakers of the true computations of nature, might imitate the absolutely unerring courses of God and regulate our own vagaries.”

2. Eudoxus

Eudoxus 408 b.c. to c. 355 b.c.

With words like these ringing in his ears, Eudoxus went from the Greek philosopher to the Egyptian priest, and studied “the courses of intelligence in the heaven.” Legend says that the sacred Egyptian Bull licked his garment, and the priests no doubt were encouraged by this omen to divulge their secrets to a person so highly favoured by the gods. They prophesied that he would have a short but very illustrious life.

After a year, or perhaps more, spent in Egypt, Eudoxus returned to his own city, set up an observatory of his own, received pupils, and worked out an exceedingly ingenious and original planetary scheme. He did not accept (if he knew of them) the risky theories of the Pythagoreans as to Earth’s motion, but assumed a central stable earth, round which circled the stars and the seven planets, according to the teaching of Plato and the general belief among educated Greeks of his day. But Egyptian observation and Greek geometry enabled him to describe for the first time the complicated movements of the planets, and to represent them by an imaginary mechanism.

This was a series of spheres, or hollow balls, fitting inside one another, and gradually diminishing in size like the ivory boxes of a Chinese puzzle, or the coats of an onion. Their size was stupendous, for the outer one, which contained all the rest, was nothing less than the sky we see, and was encrusted all over with stars. Of the inner smaller spheres, one bore, fixed in it like a jewel set in a ring, the sun; and six others bore, in the same way, the moon and the planets, one in each. All these hollow spheres were symmetrically placed so that all centred in a single point, and at this point was a solid sphere, exceedingly small in comparison, which was the earth. The star sphere, without moving from its place, rotated round this central Earth, and this caused the diurnal motion that we see in the stars. Each planet-bearing sphere rotated also, but the special characteristic of Eudoxus’ system is that each of these was surrounded by its own complete set of spheres, bearing no planet, but all attached together, the poles of one sphere resting on the surface of the next, and moving with different speeds, in different directions, and with differently inclined axes: these motions being all communicated to the innermost sphere on which the planet was fixed, the net result was the movement of the planet as we see it in the sky. Each planetary set was quite separate from the rest, and did not interfere with their movements, although each set was enclosed within the next larger. Since all the planets have a diurnal motion like the stars, as well as their own proper motions, each set had to be provided with a sphere which moved exactly like the great all-enclosing star sphere.

Thus, the sun had one sphere turning like the star sphere, and within this was a second, on which the sun was fixed, which turned round in a year, in a west to east direction. The sun, carried along by the combined motion, travelled through the sky with the daily and yearly motions, as we see them.

The planetary spheres were much more difficult to arrange. Eudoxus used four spheres for each, and these had in every case to be carefully adjusted to the very different periods and amplitudes of the planetary oscillations. It must be confessed that the scheme failed with the difficult case of Mars, and was not quite satisfactory with Venus, but it represented remarkably well the movement—so far as then known—of Sun and Moon, Saturn, Jupiter, and Mercury. It was certainly a feat for those days, whether we consider it merely as the solution of a mathematical problem, or as an embodiment of astronomical knowledge. The periods of the planets as known to Eudoxus, stated in round numbers only, are given in the following table. They are taken from Simplicius, who describes the system of Eudoxus, but as in the so-called Papyrus of Eudoxus the synodical revolution of Mercury is given as 116 days, the same as the modern value, Eudoxus may have had much more exact data. It will be seen that his synodic period for Mars is the only one which is totally wrong, and the large error is difficult to explain.

Planet.	Synodic Period.	Modern Value.	Zodiacal Peroid. 34	Modern Value.
Mercury	110 days	116 days	1 year	1.0 year
Venus	19 months	584 ″	″	1.0 ″
Mars	8 months, 20 days	780 ″	2 years	1.88 ″
Jupiter	13 months	399 ″	12 ″	11.86 ″
Saturn	13 months	378 ″	30 ″	29.46 ″

It is disappointing, after the splendid hypotheses of the Pythagoreans, to be back again on a central stationary Earth among mechanical contrivances for moving the heavenly bodies, which remind us of Anaximander’s series of hemispherical heavens and heavenly wheels, but at least the earth is spherical, owing to the Pythagoreans, and the sky extends like a sphere all round, and we shall never have a flat Earth or a hemispherical sky again among the Greeks. We do not know whether Eudoxus regarded his spheres as convenient mathematical abstractions only, or whether he reasoned that the stars were evidently set in an invisible uniformly rotating sphere, and Plato considered this kind of movement the most suitable for all heavenly bodies; that therefore he would try whether a series of similar spheres interacting on one another would account for the complicated motions of a planet, and finding that they would, taught that they must truly exist. In any case the basis of his system was a detailed knowledge of planetary motions hitherto unapproached by the Greeks, and its chief merit was that it challenged comparison with the skies.

3. Calippus

Calippus c. 330 b.c.

The challenge was soon taken up, for twenty or thirty years later one of the pupils of Eudoxus, Calippus of Cyzicus, undertook to improve the system. The defects in the theories of Mars and Venus had evidently been discovered, for Calippus added another sphere to each of these, as well as one to Mercury, which would be quite enough to bring the theories into better agreement with the facts.

With regard to the sun and moon, Calippus had paid special attention to their movements, for he made an improvement in the old luni-solar cycle of Meton, to which we shall return later. Eudoxus had ignored a very important fact discovered by Meton and Euctemon about b.c. 430, viz.: that the seasons are of unequal length, showing that the sun takes unequal times to pass over the four arcs of his orbit lying between the four points of the vernal and autumnal equinoxes and the summer and winter solstices. “Why,” exclaims a later writer 35 “are there unequal numbers of days in the four seasons, seeing that the course of the heavenly bodies must be regular, not being swayed by human passions or affairs?”

Calippus considered this question very seriously, and made a careful determination of the length of the four seasons. It seems at first sight impossible to reconcile their inequality with uniform circular motion of the sun round the earth, but he found that he could do it by adding two more spheres to the sun’s set, rotating uniformly but so arranged that their motion, added to the others, would result in an actual velocity in the sun itself varying just in the way required by the facts. The same had to be done for the moon, for the same reason, so the number of spheres, which Eudoxus had made twenty-seven, was brought up to thirty-four (including the star sphere). The varying velocity of the five planets had not yet been perceived.36

4. Aristotle

Aristotle b.c. 384-322.

Calippus went up to Athens about 330 b.c. to lay his scheme before the great master, Aristotle, and it had his cordial approval. But Aristotle definitely accepted the spheres as things having a concrete existence, for he says (De Cœlo II, 12) that we must regard them as heavenly bodies like the stars and planets, and that they are composed of the same celestial stuff.

He made one change, when incorporating the system in his scheme of the Universe. He was not satisfied that each set of spheres should work quite independently of the rest, and thought that the outermost sphere of stars ought to communicate its motion to those below (i.e. nearer Earth); and no doubt it did seem rather clumsy to have a separate sphere in every set rotating in exactly the same manner as the star sphere. But how could the impulse be communicated without disturbing the other movements? Aristotle introduced below each set another set of “unrolling” spheres, as he called them, which successively neutralized the rotations of all spheres in that set except the one with diurnal rotation, hence this movement alone was communicated to the set next below. This seems, however, more clumsy than the defect it was intended to remedy. Aristotle was perhaps led to it by his wish to give greatest importance to the star sphere; and if so, he acted on the principle which he blamed in the Pythagoreans, of making deductions not from things as they are seen, but as, according to his own ideas, they ought to be.

For indeed Aristotle, in spite of his own doctrines, and the great impulse which he gave to truly scientific methods of observation and experiment, could not rise altogether above the prejudices of his age, and consequently his Cosmos is a curious mixture of sound reasoning, based on observation, and of metaphysics, the latter predominating. For instance, it is only at the end of his second book On the Heavens, after he has “proved,” from purely metaphysical reasons, that Earth must necessarily be spherical and at the centre of the World, that he adds in support of his assertions the fact that the curved line of Earth’s shadow seen on the moon during eclipses is always round, that stars vary in visibility as we change our horizon, and that astronomers say that the celestial phenomena occur as they would if Earth were at the centre of the World.

Nevertheless, Aristotle’s teaching had so overwhelming an influence, not only throughout this epoch, but in the age of Dante, and the latter was so greatly influenced by him, both directly and indirectly, that it is exceedingly interesting to know his ideas about the Cosmos. We find them in the two books On the Heavens, in the Meteorology, the Metaphysics, and some other works. A special treatise on Astronomy, to which he refers 37, is unfortunately not extant.

The form of the Universe, Aristotle says, must be a sphere, because a sphere is the most perfect of solids and a solid is more perfect than a surface or a line, because it is in three dimensions, and three means completion, perfection.38

The Universe had no beginning, and will have no end; and this conclusion, drawn from reasoning, is supported by the belief which all have who believe in gods, “whether Greeks or not Greeks,” that the gods, who are immortal, live in the highest heaven, which is therefore also immortal; and by the fact that no one, throughout the ages, so far as we know, has ever seen any change in it.

But it is of finite dimensions, for no infinitely great body could rotate in a finite time; and it is the only universe which exists or ever can exist: outside is neither space, nor void, nor time. For space is that which is or may be occupied by matter, and time is the measure of motion occurring in matter, and no matter exists or can exist there. Therefore that which exists there is not in space nor is altered by time, but lives for ever the best and the self-sufficing life (i.e. the purely spiritual).

As matter has three dimensions, so motion is of three kinds: viz. (1) in a straight line down, that is, towards the centre of the World; (2) in a straight line up, that is, towards the circumference; (3) in a circle round the centre. Thus simple heavy bodies such as all kinds of earth, have a simple motion downwards; simple light bodies such as fire, move upwards; and when they reach their respective goals they remain where they are, unless disturbed by external force—earthy things on the earth, fiery vapours in the upper atmosphere. Composite bodies have composite motions, the motion proper to the predominant substance predominating. But for the heavenly bodies the only possible motion is in a circle, where there is neither beginning nor end, no goal and no limit, hence this motion is eternal.

Thus Aristotle solved for himself the problem of the early philosophers: how the stars in the sky remain there, for ever circling round us, and never falling to the ground. There is no need, he says, to assume an Atlas to support the sky on his shoulders, as in the old myths, nor a whirlwind such as Empedocles suggested, nor a Soul of the World, as Plato said; for the heavenly bodies are not heavy things like Earth to need support, and they are not moved by force, but are eternally in motion from the nature of their being.

In the same way he disposes of the difficulty of supporting Earth, having first “proved” that because there is an ever-circling spherical Heaven, there must also be an ever-resting spherical central Earth; there must be its opposite, the ever upward-striving Fire; and there must be the intermediate pairs of opposites, Air and Water. It is indeed, he says, a strange thing, and one to set any thoughtful man thinking, that the smallest clod of earth, when thrown up into the air, immediately falls down, and presumably would never stop falling if the earth were suddenly removed from beneath it; yet here is Earth herself, so large and heavy, not falling, but remaining steady in one place. But the explanations given by philosophers are more difficult than the fact they seek to explain. Xenophanes of Colophon said that the earth roots in the infinite, which simply saved him the trouble of considering further; others that the earth rests on water, which is our oldest tradition, said to be derived from Thales; but on what then does water rest and how can water, which is lighter than earth, support it? Do we not see that even small pieces of earth sink in water, and larger ones still more quickly? Anaximenes, Anaxagoras, and Democritus said that Earth rests on air, through her flat shape, as a leaf can float on the wind, and they added that the air cannot escape because the flat earth fits close down upon it, like a lid, which is also the reason that it can support the earth, because it is compressed, and they brought forward many proofs to show that air, when compressed and still, can support great weights. Others, like Anaximander, said that Earth rests because she is in equilibrium, for there is no reason why she should move in one direction rather than another. But all earthy things (says Aristotle) do not merely remain at the centre when there, they move thither whenever displaced. They are not suspended like a hair which is powerfully but uniformly stretched, and so never breaks, nor like a man who is equally hungry and thirsty, and has meat and drink at equal distances from him and therefore starves.39 No, the truth is that Earth, and every particle of Earth, tends naturally towards the centre of the Universe, and rests when at its goal. We must remember that on every part of the sphere of Earth, heavy bodies fall vertically to its surface, showing that it is not to the surface in general that they fall, but exactly to the centre, which is also the centre of the Universe.

Of course it was no solution of the mystery, but only moving it a step back, to say that the stars circle because it is their nature to do so, and heavy bodies fall to Earth because that is their nature. But the interesting point is that the Greeks did reason about these two motions, and compare them; that they clearly grasped the fact that “weight” simply means a tendency to move, and that the motion of falling bodies at Earth’s surface is invariably towards Earth’s centre, accelerating as it appproaches the surface (De Cœlo I. 8). It is only the fresh mind of a little child, or of a really intelligent man, which is forcibly struck by the mystery of everyday sights, such as stones falling, and stars not falling but eternally moving in the sky. The force which makes bodies move towards one another we still call “heaviness,” i.e. gravity, and the mystery of its ultimate nature and mode of action is still unsolved. It is so weak and so often complicated by other forces that, except in very delicate experiments or with the mind’s eye, we can only see it in action when bodies fall to the ground; and thus Nature guarded for centuries the secret that every tiny particle on the whole earth attracts every other, and also the earth itself, as surely as the earth attracts them. The further grand secret concerning this force Eudoxus had unwittingly set out to discover, with his planetary periods learned from the Egyptians, and his three motions of the moon. For when this study was far enough advanced, the necessary data were at hand for Newton, as he pondered the mystery which had baffled Greece; and he was able, from the moon’s motions, to verify his guess, that even the heavenly bodies are in truth always falling, falling, towards one another, exactly as Aristotle’s “smallest clod of earth” fell to the ground.

From the theory of the three simple motions, it obviously follows that Earth must be at the centre of the world, that her particles must be arranged in a spherical form round the central point, also the sphere must be at rest.

But all are not agreed about this, says Aristotle. All who consider the Universe finite say Earth is at the centre; but the philosophers in Italy, the so-called Pythagoreans, on the contrary, say that in the centre is Fire, and that Earth, which is one of the stars, is in motion round the centre, and so causes day and night. They also assume a Counter-Earth, merely from pre-conceived ideas, not from observation of facts. And some agree about the Central Fire, from pre-conceived ideas, because they think that the noblest should have the noblest place: fire is nobler than earth, and boundary nobler than what is bounded, and circumference and centre are both boundaries; therefore (they say) Fire and not Earth is at the centre. Moreover, the Pythagoreans say that the most important part of the Universe is the best guarded, and that the centre is such a part, and they call it the Watch Tower of Zeus.

To these metaphysical reasons Aristotle replies that the centre is not a true boundary, it is rather an end than a source, it is the material, the limited, while it is the circumference which limits, encloses, and gives the form. Besides, the centre of a thing is not necessarily the centre of its being; as with animals the centre of their life (meaning the heart) is not the centre of their body. So the philosophers need not disturb themselves to put Earth out of her local centre, but they would be wiser to examine that other centre of the Universe (meaning the sun), and find out what is its nature and its place, for it also is a point of origin, and noble.

He continues “Some also assert that though Earth is at the centre, it is wound and moving round the axis which is extended through the Universe, as is written in the Timaeus.” Plato’s actual words in the Timaeus will not bear this interpretation, as we have already seen (p. 85). It is a little surprising that Aristotle does not mention the names of Ecphantus the Pythagorean and Heracleides of Pontus in this connection, since the latter was his contemporary, and perhaps the other also, for they are mentioned together as teaching the doctrine of Earth’s rotation on her axis.40 Also Aristotle seems hardly fair to either this or the Central Fire theory, in that he only answers the metaphysical reasons of the Pythagoreans, and omits to mention that either would unify the diurnal celestial motions in a much simpler way than all his “unrolling” spheres. If he had not especially mentioned that Earth’s motion was supposed by the Pythagoreans to cause day and night, we should be inclined to think that he did not understand that the period was twenty-four hours, and that its effect would be to produce the apparent diurnal rotation of all the heavens.

The passage, however, has been a cause of endless controversy from the earliest commentators of Aristotle to the present day, and such a thorny question would have been avoided altogether in this book were it not that it is actually quoted by Dante in the Convivio.

As to the size of the earth, Aristotle held that it was not a large sphere, and small when compared with the stars. For, he says, if we take quite a short journey to north or south, our horizon changes markedly, so that the stars above us look quite different, and we do not see the same stars; for some which are well seen in Egypt and near Cyprus are not visible at all in northern parts, and those which in the north are always in the sky, set when we go south. And therefore, he adds, those who say that the regions near the Pillars of Hercules are connected with India, so that the ocean is one, are not saying anything altogether incredible; and their proof is that there are elephants both in the extreme east and the extreme west. He does not mean, evidently, that there was no sea at all between, but only that one could quickly travel from one to the other, always going west: there is no immense stretch of land or sea between west Africa and east India, nor are they the extremities of a flat disc-like earth. Aristotle tells us, moreover, that the mathematicians, who have tried to measure the circumference of the earth, find that it is about 400,000 stadia. This is the first time we hear of an attempt to measure the earth, but unfortunately we do not know what stadium was used, nor what was the method employed.

Aristotle’s Cosmos is arranged as follows:—

Upon the central spherical Earth rests water, and above this is air, but these intermingle more or less, and are not sharply divided; in the same way, though fire rises highest of the four elements, there is not a distinct sphere of fire, but the higher part of the atmosphere is chiefly composed of it. It is in this upper fiery atmosphere that shooting stars are produced: hot and dry exhalations rising from Earth take fire there, but are quickly consumed. Comets have their origin in the same place, when large masses of vapour rise and are directly below the sun (had the Greeks noticed that comets’ tails are always streaming away from the sun?). Aristotle also explains that the Milky Way is formed from these constantly-rising vapours, but under the influence of the stars, for it always has the same position amongst them, and that is where the most numerous and brightest stars congregate.

Thus within and below the fiery atmosphere constant changes are taking place, and all things are perishable, but as soon as we reach the lowest of the heavenly spheres, the moon’s, we enter another world. All is changeless, eternal, divine. Motion is in circles, space is filled with ether, the heavenly bodies as well as their spheres are of an ethereal substance.

The Pythagorean idea of music made by the spheres, Aristotle dismisses as very pretty but unfortunately not true. For if in truth these immense spheres made a sound as they moved, even if we could not hear it (as they said) we should feel it, for even earthly thunder bursts rocks asunder! And there is no reason why they should make any sound, for nothing moves out of one place: the spheres are simply rotating, which is the natural movement for a sphere, unless it rolls along, which they are not doing. If nature had wished the spheres or the stars and planets to move forward, she would not have treated them worse than terrestrial animals, in giving them no limbs by which they could progress! The stars and planets have no motion themselves of any kind, but are simply carried along by their rotating spheres, as we can plainly see by the moon turning always the same face towards us: hence they make no more noise than a ship’s mast set in a ship, or the whole ship as it glides down a river.

Stress is laid both by Plato and Aristotle on this absence of any motion of translation in the heavenly bodies and their spheres; both insist that a movement of rotation, in which the moving body continually occupies the same place, is the only movement existing in the heavens. One wonders whether the spheres of Eudoxus suggested or resulted from this idea.

Aristotle does not enter into detail about the separate planetary motions, in any extant work, but explains as the general principle that the outermost, the prime movement of the whole universe, is simple, and the most rapid, while the inner are complex, slower, and in the contrary direction; so that the planet nearest to the prime movement (Saturn) is longest in making his own revolution, because most affected by it, and the others less so in proportion to their distance. He refers his readers to the mathematicians, and quotes the Egyptians and Babylonians as having furnished satisfactory proofs of the relative positions of the planets, by such observations as occultations of other planets by the moon, which show that she is below them (i.e. nearer to us). The passage is quoted by Dante 41, in which Aristotle describes how he himself once saw an occultation of Mars. “When the moon was a half sphere, she passed beneath Mars and he disappeared under her dark side, but came forth again on her bright illumined side. And the same kind of thing,” he adds, “is reported to happen with the other planets also, as those tell us who for a vast number of years have made observations, viz. the Egyptians and Babylonians.”

There is one point which is elaborately discussed in the De Cœlo, which seems very curious to us, but the main point must be noted here, since it is of some interest to the Dante student. Aristotle tells us that he considers the sphere of the Universe to have a top and a bottom, and that the Pole which is not seen by us (the south) is at the top. One cannot help thinking that Dante had this in mind when he chose the southern hemisphere for the mount of Purgatory, whither, after all their mistakes and wrong-doing on this underside of the earth, souls go to purify themselves on the upper side, under the stars of the southern pole.

In his book on metaphysics, Aristotle gives a very brief sketch of the spheres of Eudoxus and his own “unrolling” spheres; and says that all these planetary movements prove the existence of Essences, eternal and immoveable themselves, who cause these movements. And it has been handed down to us in a mythical way, from the most ancient teachers, that these eternal Essences are gods. Above all these must be a First Mover, the Primum Movens Immobile, who is one, eternal, and enjoys for ever the kind of existence which we only experience in our best moments. Upon this First Mover depend the whole heaven and all nature.

5. Aristarchus

With a system of revolving spheres accepted by the mathematical astronomers, and sanctioned by the great philosopher Aristotle, it may be thought that we are within sight of our goal, the system of Greek astronomy which was to dominate the scientific world for many centuries, including the age of Dante. But so exacting had the careful observers become that the system of Eudoxus must be completely transformed, by aid of two quite new hypotheses, before it would satisfy their demands. Also, about half a century after the consultation of Calippus and Aristotle in Athens, a strange new theory was propounded, the boldest and strangest of all.

Aristarchus c. b.c. 281.

Nearly two thousand years before Galileo was summoned before the Inquisition, and forced to recant upon his knees his “most damnable heresy” that the earth goes round the sun, Aristarchus of Samos was accused of impiety by his countrymen for the same crime. But he met an even sadder fate than Galileo—neglect. His daring scheme was almost ignored by his contemporaries, and but for a casual mention by Archimedes and by Plutarch, we should know nothing about it.42

He was, however, very famous as a mathematician, and also as an observer. Ptolemy quotes his determination of the summer solstice of the year b.c. 281, and this tells us the date at which he flourished. He was renowned for a very ingenious method by which he tried to discover how much further from us the sun is than the moon. When the moon is half full the angle sun-moon-earth is a right angle, and if the angle sun-earth-moon be measured, by pointing the astrolabe first to sun and then to moon, the third angle, at the sun, may be computed, and then the ratio sun-earth to moon-earth will be known. The method is perfect theoretically, and if the sun were comparatively near, say about ten times the moon’s distance, it would be practicable; but the distance is really so much greater that the angle at the sun almost vanishes, and a very small error in estimating it causes an error equal to many millions of miles in the result. It is also impossible to determine from looking at the moon the exact time when the division between light and dark is a straight line. Aristarchus made the angle at Earth 87° instead of 89° 50′, and this gave the sun a distance of about 19 times as far as the moon, instead of 400 times, which is the true value.

The foolish fad (as they thought it) about Earth’s motion, held by this otherwise great man, is described quite clearly by the two writers above-mentioned. He suggested that the stars might be immoveable, and Earth be turning on her axis at the same time that she moves in a circle round the sun. Moreover realizing all that this implies with regard to the immense distance of the stars, he said that the circle in which Earth revolves round the sun, compared with the sphere of the stars, is as the centre of a sphere compared with its circumference. That is, not only Earth, but Earth’s whole orbit, shrinks to a point when compared with the infinite distance of the stars.

We have unfortunately absolutely no information as to the way in which Aristarchus was led to these remarkable truths, and can only make conjectures from what we know of his times. Evidently the Central Fire theory was a suggestive step, and so was another theory which was afloat about this time, and has been called the “Egyptian system” on the authority of Macrobius in his commentary on Cicero’s Dream of Scipio. No one really knows where it arose, but it is ascribed with much probability to Heracleides of Pontus. According to this, the two planets Mercury and Venus circled round the sun, and all three together circled round Earth, which still remained the centre of the Universe and of the other celestial motions. It was an idea which might have occurred to any unprejudiced observer, since the oscillations of Mercury and Venus from side to side of the sun are more striking than their movements through the stars. They never go far from him in the sky, like the other planets, and seem to belong to him.

Further, the clear understanding of the periodic motions of Mars, Jupiter, and Saturn, and the accurate observation which had been introduced by Eudoxus, must have revealed the fact that the loops in the orbits of these planets are connected with the apparent movement of the sun; and the varying brightness (especially noticeable with Mars) is inconsistent with the assumption of unvarying distance from Earth.

The great importance of the sun, above all the other planets, had of course always been recognised, and it is possible that Aristarchus was struck by an unconscious suggestion in Aristotle’s advice to the Pythagoreans to examine the nature and place of the sun, “that other centre of the Universe,” for that was also a point of origin, and a noble one.43 His own work, too, would lead him to attribute a commanding position to the sun, for as it was nineteen times as distant as the moon, it must also be nineteen times as large (since they appear equal), so he must have felt certain that it was a very great size, probably much the largest of all bodies in the Universe.

It was the grandest and truest of all the Greek astronomical theories. But it was not accepted, it was hardly even discussed, and we can scarcely be surprised at this. Such an improbable theory needed many more convincing proofs than Aristarchus could bring forward. Observation, calculation, comparison of theory with facts, this was what was needed before safe ground could be won for belief, and in this Eudoxus was a true pioneer. But freedom of thought and courage in imagination is needed also in science, and Aristarchus seems to have been almost the last to possess this.

Seleucus b.c. 160.

Aryabhata born a.d. 467.

A certain Babylonian, named Seleucus, who lived about b.c. 160, perhaps on the Tigris, and an Indian astronomer, Aryabhata, of the fifth century a.d., both taught that Earth turns on her axis, but Aristarchus stood alone in suggesting that she also has a movement of revolution round the sun. The possibility of Earth’s motion was alluded to but seldom by classical and mediæval writers, and then almost always as a foolish fancy hardly worth discussion;44 until at last Copernicus, hardly daring to publish his bold idea in sixteenth century Europe, for fear of persecution, sought and found among the followers of Pythagoras, and in Aristarchus of Samos, kindred spirits with his own.

6. The School of Alexandria

The spheres of Eudoxus would not work. The system was already overladen, and more variations in velocity were becoming known. Observation shows, too, that the planets, especially Mars and Venus, vary greatly in brightness, in regular periods which correspond with their movements, and this could not be accounted for by any possible number or arrangement of spheres if all were to remain concentric to Earth, so that every planet remained always at a uniform distance. Yet Aristotle had said that Earth must be at the centre of the Universe. The new philosophers of the Stoic school agreed with him, and among mathematicians only Aristarchus dared to disagree.

But they were not long at a loss. The homocentric spheres 45 were thrown aside, and during the third century two new hypotheses were suggested (beside that of Aristarchus), and although we do not certainly know by whom, there is little doubt as to the place in which they originated. By a strange fate, Egypt, the home of astronomy many centuries before, became the seat of the latest, most brilliant, and most successful astronomical school of ancient times, and the knowledge won there in the five centuries between b.c. 300 and a.d. 200 spread, following in the wake of Alexander’s conquests, over the whole of the civilized world.

It was a purely Greek school, however. Greece lost her independence under Alexander, and was finally crushed by Rome in 146 b.c., but never was Greek learning and culture so much honoured and sought after as in this age. In Egyptian Alexandria, Greek men of science found a welcome, and opportunities of research which did not exist in any other place in the world. In the Museum, founded and liberally endowed by the royal Ptolemies, was a great library whose custodians were bidden to obtain every book that had ever been written, and it is said that when any stranger arrived with a new book it was taken from him and copied for the Museum, and the copy returned to the owner. Within the great marble colonnaded building were lecture-halls, and reading rooms, and laboratories; there were gardens for botanists and zoologists, and observatories for astronomers. These astronomers were all Greeks, and though now living in Egypt they do not seem to have learned anything more from the Egyptians. Perhaps the priests resented the intrusion, and kept their secrets jealously to themselves; perhaps Eudoxus and his immediate followers had learned all they had to teach. This seems the more probable because, although the Greeks of this age did use Babylonian records of eclipses to form a lunar theory, they complained of the insufficient accuracy of all available planetary records. Moreover, they were not hindered from learning astrology: the sacred books of the Egyptians which taught its principles were translated into Greek about 300 b.c.; but it was always treated by them as quite a separate branch of study. Their geometrical methods were entirely their own. They introduced a system of notation which greatly simplified calculation 46; their discovery of the principles of spherical trigonometry inaugurated a new era in astronomy; and they invented a new class of astronomical instrument.

We know what these instruments were like, and it is even possible to give an illustration; for, from descriptions in Ptolemy’s Almagest, we find that the “well-made copper circles,” the gnomons, and the celestial globes, which were set up in the Square Portico of the Museum, were of the same pattern as instruments which existed in Pekin, in the ancient observatory on the ramparts, until they were looted by the Germans during the late Chinese war. The Alexandrian instruments were not supported on their stands by beautiful bronze dragons, but on the other hand the circles were more accurately divided, which after all was of more importance from the astronomers’ point of view. Fig. 21 gives a general view of the Pekin Observatory, and Fig. 22 one of their astrolabes dating from the 13th century a.d.

At first glance there seems to be here absolutely nothing like our modern observatories. Ancient and mediæval astronomers had indeed no telescopes, being ignorant of the properties of lenses: therefore they were unable to study the features of any heavenly body except the moon, and they had no way of finding out anything about their physical constitution; but they had many ways of measuring their distances and motions, and even the angular sizes of sun and moon, and their instruments were the forerunners of our sextants, micrometers, and transit instruments, our chronometers and sidereal clocks.

The gnomon has been already described 47, and it was one of the most valuable instruments used by the Greeks. The Pekin gnomon at the right of figure 21 was more than 40 feet in height, and on the top had a little plate of copper which was pierced by a hole as fine as the eye of a needle: the observations made with this were much more exact than observations of the end of the shadow, which must always be vague, and the Chinese records of the sun’s movements made with this instrument between 1270 and 1280 a.d. are of great value in modern research. Ptolemy explains that his gnomon was made accurately vertical by the use of a plumb-line, and that one way of testing the level of the surface on which the shadow fell was to flood it with water.

Clepsydras, or water-clocks, were used by the Greeks, and many kinds of sundials for telling the time by day. Tables were also made of the risings of bright stars which served for clocks by night.

The instrument in the middle of the platform is a quadrant, and beyond this on the left is a large celestial globe, which, however, only dates from the Jesuit missionaries of the seventeenth century. Ptolemy says that his globe was made the colour of the night sky; Sirius being marked in his proper place, all other stars were placed relatively to him, and in their own colours as nearly as might be; the Galaxy was drawn, and the figures of the constellations outlined. The globe was arranged to turn on either the poles of the ecliptic or of the equator; circles of wood represented the horizon and meridian, and the pole could be arranged at any altitude according to the latitude of the place.48

But perhaps the most interesting are the astrolabes, and these owe their origin to the Greeks. The essential part of any instrument for determining angular distances is a divided circle and a pointer: the pointer is directed first to one object then to another, and the angle between them is then read off on the circle. In the astrolabe, the pointers themselves were also circles, provided with little perforated rods for “sights.” (These are not visible on the instrument in Fig. 22, and have probably been broken off.) There were two fixed circles, set in the plane of the ecliptic and perpendicular to it. Three other circles could be rotated round the poles of the ecliptic. One of these was directed (by means of the sights), to some body whose position was already known, another to the body whose position was to be ascertained, and the angle between them was read off on the ecliptic circle; on the third the angular distance north or south of the ecliptic circle could be read. This last and the ecliptic circle were both divided into 360 degrees, and as many fractions of a degree as space and skill would allow.

The equinoctial astrolabe was similar, but the fixed circle was in the plane of the equator, instead of the ecliptic. One of each of these is seen in the view of the Pekin Observatory.

But how did the old astronomers know how to find the ecliptic and the equator in the sky, and set their circles in those planes? This they did by means of the sun’s motion. The gnomon told them the day of the equinox (see p. 25), and on that day the sun was in the equator: therefore, if a circle was set up so that the shadow of the upper part fell symmetrically upon the lower, with a little line of light each side, it must be exactly in the plane of the equator. In the Square Porch such a circle was erected, a large one of copper, and when once correctly adjusted it was a standard plane, and also showed the date of the equinoxes, as accurately as the gnomon itself. Since the ecliptic is the path of the sun as seen in the sky, it is obvious that it could be determined from a number of different observations of his position at different times of the year.

A PEKIN ASTROLABE OF THE 13th CENTURY, a.d.

From a photograph taken in 1888, and published in the “Bulletin de la Société belge d’Astronomie”.

Finally, accurate solar tables were drawn up, showing the sun’s position in the sky in degrees for different dates, and then from these it was possible to find the places of planets and stars. They could not of course be compared directly, but the position of sun and moon were compared during the day, when both were in the sky, and then after dark the planets and stars were compared with the moon, allowing for her motion among the stars in the meantime. Or secondly, when the moon was eclipsed, and therefore known to be in the ecliptic and exactly opposite the sun, the places of stars could be found directly.

This very brief description will give some idea of the chief instruments and methods used, and when we see how very rough and elementary they were, and remember that the Greeks had to work out their observations without algebra, or decimal notation, we are amazed at their results, and their far-reaching ambitions.

Eratosthenes b.c. 276-194.

Already in the very early days of the Museum, Eratosthenes, a celebrated geographer, made a bold attempt to utilize observations of the sun measuring the size of the earth. It was known that in Syene (the modern Assuan) on the day of the summer solstice at noon no shadows were thrown, and the bottoms of wells could be seen: evidently therefore the sun was in the zenith. Eratosthenes found that the sun’s distance from the zenith in Alexandria at noon on the same day was 7° 12′, or one-fiftieth of the circumference of the heavenly sphere, consequently the two towns must be distant from one another (assuming them to be nearly in the same meridian) one fiftieth of the circumference of the earth. The distance from Alexandria to Meroe was known, and from Meroe to Syene had been paced by the king’s professional pacers; the whole was 5000 stadia. 50 times 5000 = 250,000. The figure always quoted by the ancients is however 252,000. If the stadium used by Eratosthenes was the measure generally used for long distances which have been paced, this estimate is equal to 24,662 miles, only about 200 miles less than the modern value. It was partly by luck that Eratosthenes got such a good result, for he was evidently only working with round numbers, and the extra 2000 stadia seem to have been added in order to make one degree equal to exactly 700 stadia. But in any case it was a highly creditable performance.

Euclid c. b.c. 300.

Apollonius c. b.c. 270.

There were celebrated mathematicians and geometers at Alexandria, whose work was most useful to astronomy, such as Euclid, and Apollonius of Perge. The latter is specially mentioned by Ptolemy in connection with the new theory of “moveable eccentrics,” which was invented to account for the varying brightness of the planets, as well as their peculiar movements.

Fig. 23 explains this theory. Let P A be a great revolving circle upon which Mars is fixed. (In the hands of the Alexandrian mathematicians the spheres almost disappear, and they deal practically only with circles.) If the earth were at its centre, as Eudoxus demanded, Mars must always be at the same distance, but if we make the circle eccentric to Earth, by putting its centre at C while Earth is at E, then the distance and consequently the brightness will constantly vary, and Mars will be brightest when at perigee P (point nearest Earth), and faintest when in apogee A (point furthest from Earth).49

But, as the Greeks had discovered, Mars attains his greatest brilliance at different points of the zodiac, so P must be made moveable, and it always happens when he is opposite the sun, therefore P must keep pace with the sun’s apparent motion in the zodiac and P E always point towards him. This was accomplished by making P C A turn round upon the fixed point E, so that for instance when the sun had moved through a quarter of his circle (in three months) P A had moved to P′ A′, and the whole eccentric had moved into the new position shown in the diagram, its centre C being now at C′. In other words, the centre of the eccentric moves round Earth in the same time and in the same direction as the sun, that is in one year, and “with the signs” (from west to east).

At the same time, Mars is moving in an opposite direction on the eccentric, and without entering into all the details of the problem, we may add that the Greek geometers found that by determining the proper relative sizes of the large and the small circle they could make the two motions neutralize one another when the planet reached its stationary points, and the retrograde motion prevail over the direct when it retrograded. A similar arrangement was made for Jupiter and Saturn.

In this very ingenious way the varying brightness as well as the varying motions of these three planets were accounted for, without violating the principle of uniform circular motion, and without removing Earth from the centre of the Universe. She was also still the centre of planetary motion, in a certain sense; but to place the true centres of these planets’ spheres outside Earth and in the direction of the sun was a very suggestive step, and may well have helped Aristarchus to his bold hypothesis. For he had only to put the sun, not at some indefinite point along the line E A, but exactly at the point C, and it became the centre of motion for Mars, Jupiter, and Saturn, just as in the “Egyptian theory” it was the centre of motion for Venus and Mercury. In this way he would arrive at the conception of the sun circling round Earth and carrying all the planets with him, (a theory which was held by the great astronomer Tycho Brahé in the sixteenth century a.d.). Then a flash of insight may have revealed to him the fact that this motion of the sun is apparent only, being but the reflection of Earth’s own motion; for she is circling round the sun like all the other planets.

It is, however, only a guess that the Moveable Eccentrics played this part in the theory of Aristarchus. They did not long hold the field, because they were not applicable to Venus and Mercury, which are never seen in opposition to the sun. So they were thrown aside for another system, the Epicycles, which illustrates much more simply the stations and retrogressions of the planets, and can be used for them all.

Later on, when more irregularities of motion were discovered, it was found necessary to combine eccentrics and epicycles, and by means of this joint system it became possible at last to represent completely, and as accurately as they could be observed, all the apparent movements of the heavens. First, however, an immense amount of work had to be done, and new methods devised, both in observation and mathematics. The man who contributed most, in both ways, to make it possible, was Hipparchus.

7. Hipparchus

Hipparchus c. 140 b.c.

Of this great man we know scarcely anything but what can be gathered from the work he did, and this corroborates Ptolemy’s description of him: “Hipparchus, lover of toil and truth φιλοπονον και φιλαληθεα.” He lived about b.c. 140, since this is the date of the only book of his still extant, and his work was not done in Alexandria, though he may have studied there in his youth, and he used the Museum records. We count him among the Alexandrians, as he belongs to this era, but he seems to have been a private astronomer, who set up an observatory of his own in Rhodes, his native place. Here we seem to see him, surrounded by his primitive instruments and his papyrus books, patient, eager, modest, seeking no fame and no reward but the joy of his work. By day he would keep watch over the sliding shadow of his gnomon, would write up his observations, make long calculations, and devise new methods in mathematics, improve and modify his astrolabes and his clepsydras; at night he would spend long hours with moon, planets, and stars, making up for the defects and shortcomings of his instruments by the skill and care with which he applied them to measure positions in the sky. Nothing but the most loving and conscientious care could have raised his work to such a pitch of accuracy, and made such rude means suffice for such splendid achievements.

The book we possess, apparently an early one, is chiefly concerned with the positions, the risings and the settings, of stars, and at the end is a list of sixteen which came to the meridian at intervals of an hour: from this list and the knowledge of spherical trigonometry which he possessed, it would be possible to calculate the time at night to within about a minute.

Hipparchus was able to construct a satisfactory theory of the sun and to some extent of the moon, but he found more irregularities in the planetary motions than Eudoxus had suspected. The records of his predecessors were not accurate enough for him to construct a theory for the planets, and he soon realized that one life-time would not be long enough to collect all the data necessary, so, as Ptolemy tells us, “Hipparchus, who loved truth above all things,” quietly set to work to make as good and as many observations as possible, leaving it to his successors to complete and explain them.

In the same spirit he undertook the laborious task, of which Pliny speaks with awe as a presumptuous scheme, even for a god, “rem etiam Deo improbam,” of numbering the stars. Pliny says he was led to do this by the appearance of a New Star, which blazed out suddenly in the constellation of Scorpio in b.c. 136, just as Nova Persei did in Perseus in February 1901. He saw that even in the upper regions of the eternal heavens, which Aristotle had supposed absolutely changeless, changes may occur, and in order that even the least of these should not pass unnoticed, he set to work to note the number, brightness, and position of all he could see. This great catalogue of 1080 stars, copied by Ptolemy in his Almagest, was the basis for all succeeding catalogues, from Spain to Turkestan, until quite modern times. In it, for the first time, the places of the stars were not merely described according to their position in the constellation figures, but were noted in degrees on the sphere, as is done to-day.

Timocharis c. b.c. 280.

One day, when comparing his notes with those of Timocharis, who had worked at Alexandria about a century and a half earlier, he found that the brilliant star Spica, the Ear-of-Corn which the Virgin carries in her hand, had apparently moved nearer to the autumnal equinox by about 2°. (Two degrees is about four times the angular diameter of the sun). Of course he or Timocharis might have made a mistake, or Spica might really be moving among the stars, or she might be carried along with the rest by a slow movement of the whole star sphere. Apparently Hipparchus satisfied himself that he could rely upon Timocharis’ observation, and took pains to verify his own; the second hypothesis could be disproved by the fact that Spica does not change her place perceptibly among her neighbours; and finally it became clear that her motion is part of a slow apparent movement of the whole heavens.

Here was a discovery of first importance, an unexpected reward of patient accuracy, of which the white Spica, flashing down from summer skies, may always remind us. Hipparchus had discovered the grand cycle which we call the “Precession of the Equinoxes,” and before Spica returns to the same position in which he saw her then, when she led him to his great discovery, she will have been watched by generations of astronomers for another twenty-four thousand years. No notice of the cycle has been found as yet among the records of any other nation, although it seems as if the astronomers of Babylon and Egypt, and other countries where observations had been carried on for many centuries, must have been aware of it. We can only imagine that at long intervals of time they found that the stars had somehow changed, and made corrections accordingly, but without understanding the nature of the change. What Hipparchus thought about its cause we cannot tell: probably he left all speculations to future astronomers, and confined himself to noting the fact.

The displacement of Spica which he observed is shown in the diagram.

Both Timocharis and Hipparchus evidently measured her position indirectly by comparing it with that of the moon, which was eclipsed at the time,50 and therefore known to be in the ecliptic and opposite the sun. To find the sun’s distance from the equinox was an easy matter, since his yearly course had long been carefully studied, and the days on which he passed the equinoxes were regularly observed with the gnomon. Spica, then, had moved eastward along an arc parallel to the ecliptic, and since celestial latitude and longitude are referred to the ecliptic, we may define her apparent movement in astronomical language by saying that while her latitude had remained constant, her longitude had increased by about two degrees; and further, as the celestial equator is oblique to the ecliptic, this implied that her declination (position north or south of the equator) had also varied. The diagram shows that she had a less northerly declination than before.

At this rate, Spica, which was now only 6° from the autumnal equinox, would reach it in less than five hundred years, and thereafter would lie east instead of west of it; and that she has in fact done so, may be seen by consulting a modern star atlas. She is now 22½° of longitude east of the autumnal equinox, and nearly 11° south of the equator. Her south declination will continue to increase for about five thousand years, after which she will come north again.

Ptolemy says that Hipparchus examined other stars, and found that they also were increasing their longitude at what appeared to be the same rate as Spica. The yearly amount of the movement, derived from the Spica observations, is within a few seconds of arc of the true value, which is 50¼ seconds; but Hipparchus would not fix any value until it had been tested by further observation, and merely stated that it could not be less than one degree in a century i.e. 36 seconds per annum.

This is a very uncomfortable phenomenon for astronomers, since every star is for ever changing its measured position on the celestial sphere. Take three stars, one at the north pole, another on the equator, and a third in the southern hemisphere. After some years, the first will no longer be a pole star, the second no longer an equatorial star, and the third may have so far increased its south declination that it will be invisible at latitudes in our northern hemisphere where formerly it used to rise above the horizon. One compensation for this inconvenience is that if we know what star was near the pole, or which stars lay along the equator, on any given occasion, we can calculate the date. Thus it is believed that the Great Pyramid was built when Alpha Draconis was the Pole Star, that is, nearly 3000 years b.c.; and by a similar method Mr Maunder determines the epoch at which the ancient southern constellations were invented, as we have already seen.

The greatest inconvenience, and also the greatest historical interest, attaches to stars like Spica which belong to constellations of the zodiac, for if they are not stationary with regard to the equinoxes and solstices they are not such simple guides to the length of the solar year as the ancients supposed them to be. The scheme of the Babylonians for beginning their month Nisan when the stars of Dilgan rose just before the sun was an excellent one for a time, but if they had continued it for many centuries they would have found that their year was too long, and the months were all falling in the wrong seasons. This has actually happened with Hindus and Parsis, who now keep their New Year in the middle of our April, although when their calendar was fixed, about thirteen hundred years ago, the years began at the spring equinox. For the sun is like a runner in a circular race-course who thinks he has completed a lap when he returns opposite a group of spectators originally standing at the starting-point, but after several laps he finds that the spectators and the goal no longer coincide; either they, and also all the others surrounding the course are walking away from it, or an unseen hand has been moving the flag towards him, and so shortening the lap.

It is the flag which must count, in any case, not the spectators, and with the sun it is the equinox which must count, and not the stars, for this is the point at which he crosses the equator, making day and night equal, and from this we count the beginning and ending of our seasons. So our year is counted from equinox to equinox, and is twenty minutes shorter than the “sidereal,” or star year, of the ancient Babylonians. Hipparchus, from observations of equinoxes and solstices, made the year 365 days 5 hours and nearly 55 minutes, which is only 6 minutes longer than the correct value.

After Hipparchus had made his discovery, astronomers agreed upon a somewhat clumsy and very confusing device, by which the zodiac was divided into twelve equal “signs” of 30 degrees, which bear the same names as the zodiacal constellations, but whose beginning is always reckoned from the vernal equinox. These twelve “signs of the zodiac,” therefore, do not now agree with the twelve constellations of the zodiac, and our present “first point of Aries,” which marks the vernal equinox, is in the constellation of Pisces.

What is the true cause of this strange phenomenon? Are the stars really all in motion, or is it the equinox which moves?

The successors of Hipparchus, who believed that the stars were fixed on a sphere, found no great difficulty in conceiving that this sphere had a very slow easterly motion, round the poles of the ecliptic, completing a revolution once in 36,000 years (i.e. one degree in century). To us, however, it is impossible to believe that the stars, which we have found to be at enormous and varied distances, are all revolving at one rate, parallel to the ecliptic. The ecliptic, to us, is simply the plane of Earth’s own orbit, and as she moves in it she has a very slow “wobbling” motion on her axis, as well as the rapid spinning of the diurnal motion, like the “wobble” of a spinning top. The top has this motion because gravity is trying to pull it down from its upright position; the earth because the sun is trying to drag her slightly protuberant equator into the plane of her orbit.

The resulting motion is not a revolution of the earth, nor an apparent revolution of the star sphere round Earth: what really happens may be illustrated with the traditional orange and knitting needle.

Ignoring all motions but the one we are speaking of, let the points of the knitting needle (Earth’s axis of rotation) trace out small circles in space, and the equator of the orange will be seen to alter the direction of its tilt, but without turning round (Fig. 26). Stick a pin in the equator, and others in north or south latitudes, between equator and pole; these will always remain facing you, but while the pole makes its small circle, the equatorial pin will be seen to move up and down, while the tropical and temperate pins trace out ellipses. These are the movements which we see reflected in the stars; and if Earth’s diurnal rotation were suddenly to cease, while her revolution in her orbit and the movement of “precession” continued, we should see Spica, for instance, sink slowly lower in the southern sky and after ages rise again northwards, but there would be very little preceptible movement east or west.

The movement observed by Hipparchus, then, was not a movement of Spica and other stars, but a movement of the equinox. For the celestial equator is simply a reflection of Earth’s equator in the skies, and as it keeps changing the direction of its tilt in the way described, it changes the point at which it cuts the ecliptic. This may best be seen by taking two rings or hoops (two large curtain rings, for instance), one of which just fits inside the other. Tilt the inner ring, so that half of it is above and half below the other ring, and they touch at two points, 1 and 2 (Fig. 27). The outer ring is the Ecliptic, the inner the Equator, and where they touch each other are the Equinoxes. Now move the inner ring, not sliding it round, nor making any difference in the angle between the two, but simply so that they touch at fresh points, 1′ and 2′. In this way you may make the points of contact revolve entirely round. This is what the real equinoxes are doing: while the equator opposite the group of stars in figure 25 rises and falls, the equinox travels on, and finally returns to the same place.

The phenomenon is called “precession of the equinoxes,” because they thus move on to meet the sun in his yearly course.

The discovery of precession is what has chiefly made Hipparchus famous, but the invention of the astrolabe and of spherical trigonometry, both believed to be due to him, his star catalogue, and his many observations, more accurate than any made before, were so valuable as pioneer work that Ptolemy justly called him the Father of Astronomy. If Hipparchus could visit one of our observatories to-day, and see the clock-driven equatorials, the transit instruments, the beautifully divided circles read with microscopes, and the sidereal clocks, one wonders whether he would be more astonished at the advance on his astrolabes and clepsydras or at the homage paid to him as one in whose footsteps all astronomers are proud to tread.

8. Ptolemy

Claudius Ptolemœus. I know that I am mortal and ephemeral, but when I scan the multitudinous circling spirals of the stars, no longer do I touch Earth with my feet, but sit with Zeus himself, and take my fill of the ambrosial food of the gods.

For more than two centuries after Hipparchus very little original work was done in astronomy, and no one seems to have had the courage to take up his unfinished task and study seriously the difficult problem of planetary motions.

Posidonius c. 135 b.c. to c. 50 b.c.

Posidonius the Stoic, who lived for some years in Rhodes, made a fresh determination of the earth’s circumference, basing it not on observations of the sun, like Eratosthenes, but of the star Canopus, which in his time was just visible at Rhodes while in Alexandria it rose “a quarter of a sign” (i.e. 7½ degrees) above the horizon. By his method, the earth was a little smaller, (240,000 stadia instead of 250,000), but it must have been difficult to measure the distance between Rhodes and Alexandria over the sea, and it is impossible to say when a star is exactly on the horizon. Posidonius also observed the tides in the Mediterranean, and showed that “Ocean follows the movements of the heavens,” and especially of the moon, having daily and monthly periods.

Geminus c. 70 b.c.

A little later Geminus wrote an Introduction to Astronomy, which was an excellent little book as far as it went, but although he was apparently a native of Rhodes, and speaks of Hipparchus, he seems to know nothing of his work, for he does not quote his careful determination of the length of the year, nor his discovery of precession.

Cleomedes c. 20 b.c.

Theon of Smyrna c. 100 a.d.

Nor were other writers, such as Cleomedes and Theon of Smyrna, better informed, and they added nothing new to the advance of astronomical science.

Ptolemy c. 140 a.d.

But at last a worthy successor arose at Alexandria, the immortal Ptolemy, whom Dante met in that Limbo of antique spirits which was almost Elysium, although on the brink of the Inferno.

We do not know when Ptolemy was born nor when he died, nor where was his native town: we only know that his first recorded observation was made in the eleventh year of the Emperor Hadrian, that is a.d. 127, and his latest in a.d. 150, and that he lived and studied in Alexandria. He had splendid opportunities for carrying on the work of Hipparchus, for besides the use of the instruments in the Museum Observatory, he had at hand all the Museum records, which included the writings of Hipparchus. Ptolemy was not so painstaking and accurate an observer as Hipparchus, but he was a very able mathematician to whom it was evidently a joy to handle figures and work out problems. By examining a number of observations spread over several centuries, and combining them with his own, he was able to accomplish the task in which so many others had failed, and to frame a system which embraced all the celestial motions then observed. The monumental summary in which he set forth this system contains a great deal of interesting information about his methods and instruments, and about the work of Hipparchus, for whom he always expresses the most generous admiration. The original name of his book was the “Mathematical System of Astronomy,” but his admirers having called it the “Great System,” Megiste Syntaxis, the Arabs affixed their article al and gave it the name it preserves to this day, of Almagest. It remained the standard treatise on astronomy until the De Revolutionibus Orbium Celestium of Copernicus appeared in 1543.

The name of his book indicates the scope of Ptolemy’s work. It was to represent all the observed motions of the heavenly bodies by means of a mathematical system, so that they became amenable to calculation; but to explain the causes of these motions was thought to lie quite outside an astronomer’s province. It was not for a mere observer and calculator to determine which motions were real and which apparent, else Ptolemy must have decided in favour of Earth’s rotation, for he says that it would be much easier to account for celestial motions on this assumption. Nor was it his business to investigate the substance of the stars. Little did he dream that astronomers would one day solve such problems, and uphold their conclusions in the face of all the world: for him, as for his contemporaries, the decisions of the philosophers, and especially of Aristotle, were final, and his task was to describe what he saw in the light of their teaching.

He brings forward, in the introduction to his book, a few arguments against the absurd notion, taught by some, that Earth is in motion, turning on her axis or moving through space; but all that he proves is the immense difficulty, even to a trained mind, of accepting these theories, and the great authority of the philosophers who denied them on abstract principles. Educated Greeks might still discuss the nature of the heavenly bodies, as in Plutarch’s delightful dialogue On the Face of the Moon, (written about half a century before the days of Ptolemy), and might ridicule the law of gravity, laughing at the absurdity of supposing that if the middle of a man’s body were at the middle of the earth, his feet as well as his head would be “up,” and that falling weights if they reached this point would stop short, or oscillate to and fro. Yet even they all agreed that the fixed stars do most probably move “in a circle of eternal and never-ending revolution,” and that they are of a pure and eternal substance unlike Earth; and for the professional astronomers of Alexandria these axioms were assumed as the basis of all their work. Earth must be immoveable at the centre of the Universe because the heavy stuff of which she is made sinks necessarily to the centre and there remains in globular form without need of support; the heavenly bodies must be in motion, because, being of ethereal substance, it is their nature to revolve eternally in circles.

This being granted, we can feel nothing but admiration for the extent of Ptolemy’s knowledge, the comprehensiveness of his scheme, and the skill and patience with which he overcame its difficulties.

Earth, according to Ptolemy, is but a point compared with the immense surrounding sphere in which the stars are set, and this turns always round us, communicating its motion (he does not inquire how) to sun, moon and planets, so that day follows night, and the heavenly bodies daily rise and set. For the slow movement of precession, which also affects all heavenly bodies, Ptolemy accepted the least value of Hipparchus, one degree in a century, only testing it in rather a perfunctory way, which was a great pity, for he might have determined it much more closely after an interval of some 250 years. But one man cannot do everything, and he doubtless thought it best to spend more time on the planets, whose intricacies had baffled Hipparchus and gave him also a great deal of trouble.

He retained the great spheres which were supposed to carry them round Earth, inside the star sphere, but the chief feature of his system is the use of small spheres, which were fixed on the larger, and therefore called “epicycles,” while the large were known as “deferents” or carriers. The general principle of epicycles is very simple, as may be seen by comparing the two diagrams.

Fig. 28 shows the path of Mars as we saw it among the stars of Pisces in the year 1909. Throughout July the planet was travelling in its usual direction, “with the signs,” but on August 22nd it came to a stop, then turned and travelled backwards “against the signs” until October 26th, when it stopped again, reversed its direction once more, and during the rest of the year moved rapidly forward.

Fig. 29 shows the principle on which Ptolemy would have explained this curious track. Each planet was supposed to be fixed on a small circle, the epicycle, and this was fixed upon a large circle, or deferent, upon which it travels in the direction shown by the arrow, at a uniform speed, returning to the same place in the sidereal period of the planet. Thus Mars, as seen from Earth, which is near C the centre of the deferent, makes a great circle through all the zodiac in two years, Jupiter in twelve, and so on. But meanwhile the epicycle is rotating round its own centre, C1, and when the planet reaches the point marked S, the two motions neutralize one another, so that it appears stationary, as Mars did on August 22, 1909. After this, the motion of the epicycle more than counter-balances the motion of the deferent, and the planet seems to reverse its direction until it reaches the point on the epicycle marked S′. After this the two motions are once more in the same direction, so the planet is seen to move rapidly forward, as Mars did after October 26.

In this extremely ingenious way the strange planetary oscillations were accounted for, without violating the law of uniform circular motion, and in a more convenient and satisfactory way than by the concentric spheres of Eudoxus or the moveable eccentrics of Apollonius. Each of the five planets was provided with an epicycle and a deferent, and these were made of the proper relative size and given the right speed, so that the motions should correspond with what we see in the sky.

Ptolemy calls the oscillation a planet’s “anomaly with regard to the sun,” because (as we have seen when discussing the moveable eccentrics) it was known to be connected in every case with a planet’s angular distance from the Sun. On September 24, when Mars was in the middle of his retrograde arc in Pisces, the sun was exactly opposite, in the constellation of Virgo. This is found to be always the case, not only with Mars, but with Saturn and Jupiter too. Whenever one of these planets has the position O on its epicycle, and therefore is retrograding, the sun will be found to be exactly opposite in the sky. Mars comes into this position, and is opposite the sun, once in 780 days; this, therefore, Ptolemy called the period of his epicycle, while a little less than two years was the period of the deferent. The two periods of Saturn are 378 days and 29½ years nearly; of Jupiter 399 days and nearly 12 years.

Venus and Mercury betray their dependence upon the sun in more striking fashion, for since these planets simply oscillated from one side to the other of the sun, their epicycles must be supposed to be keeping pace with him all the way round the zodiac. Fig. 31 shows their relation to one another. On September 25, 1911, Mercury was seen from Earth as a morning star as far west of the sun as it is possible for him to travel, while Venus, after shining as an evening star all the summer, had come into line with the sun and become invisible.51 On December 7 following, the rotation of the epicycles (Ptolemy would say) had brought both planets to new positions, Mercury now being an evening star at his “greatest elongation east,” and Venus a morning star. But the centres of the two epicycles always remain in a line with one another and the sun, and so their periods on the deferents are the same as his, viz. one year. The epicyclic periods, or intervals between two “greatest elongations” west or east, are 116 days for Mercury, 584 days for Venus.

We still explain the complicated course of the planets by resolving it into two approximately circular motions, but we know now that only one belongs to the planet itself, the other is Earth’s own motion. The reason why the sun’s position affects the position of every planet is simply that the epicycles of Mars, Jupiter, and Saturn, and the deferents of Venus and Mercury are reflections of Earth’s yearly journey round the sun.

Ptolemy had by no means finished with the planets when he had provided each one with an epicycle to represent the “anomaly with regard to the sun.” Hipparchus had noticed that there was another lesser irregularity, which seemed to be periodical likewise, although no former system had taken it into account; and this he called the “anomaly with regard to the zodiac,” because the speed of each planet and the amplitude of its loop varies slightly according to the part of the zodiac it happens to be in. He suggested that this might be dealt with by combining the two theories of epicycles and eccentrics, and this suggestion Ptolemy adopted with success. He placed each deferent with its centre not exactly at the earth, but at a certain small distance which was different for each planet. (This is not shown on our small-scale diagrams, therefore Earth appears at the exact centre.) The true explanation of this irregularity is that each planet’s path is not strictly circular, but elliptical.

Besides this, Ptolemy had to represent the planet’s movements north and south (note how this varies in fig. 28.). This was partly managed by the aid of small wheels, rotating in such a way that they lifted and lowered the epicycle as required.

Although Ptolemy quotes Babylonian observations of lunar eclipses dating back as far as the eighth century b.c., the oldest planetary observations that he uses were made only four hundred years before his time, and they were probably Greek. Even these were generally very rough. For instance:—

In the 496th year of Nabonassar, on the 17th day of Choeac, in the morning, Mercury was three moon-breadths north of the tail of Capricorn.

In the same year, Phamenoth the 30th, Mercury was three moon-breadths south of the horn of Taurus which is also the foot of the Charioteer.

The first year of Nabonassar (a Babylonian epoch) corresponds with b.c. 747, so the 496th year is b.c. 251. The months used by Ptolemy are usually Egyptian. The later observations, made with an astrolabe, were much more precise; Ptolemy quotes one from Theon of Smyrna, which states that Mercury was 3° 50′ in advance of the Heart of the Lion (Regulus), and for his own observations he also usually gives the sign, degree, and minute. Sometimes the planets had been observed so near stars that their positions could be very accurately determined by the aid of Hipparchus’ star catalogue. Timocharis, on a certain morning in the 13th year of Ptolemy Philadelphus (b.c. 273), saw Venus beside the last star in the wing of the Virgin (Beta Virginis); Ptolemy himself saw her so close behind a certain star in Aquarius that she seemed to touch it with her rays; and in the 83rd year after the death of Alexander, Jupiter had been observed to eclipse the Southern Ass, that is the southernmost of the pair of stars on either side of the little cluster in Cancer which the ancients called the Manger.

The sun was much easier to manage than the planets. Moving always in the same direction, he needed no epicycle, and remaining always in the ecliptic, no wheels. His one irregularity, the varying speed in different parts of the zodiac, which Meton had discovered and Calippus confirmed, Hipparchus accounted for by placing him on eccentric deferent; Ptolemy adopted this without change, and made the year the same length as Hipparchus had done. As the slowest motion was observed when the sun was in the sign of Gemini (at the time of year corresponding with the end of our month of May), the eccentric was placed as in the diagram; and the sun, supposed to be revolving uniformly round the centre C, had a slower motion as seen from Earth when he went north, because he was then more distant.

We know now that it is really Earth which revolves round the sun, but the elliptical shape of her orbit is not unlike the eccentric deferent which the Greeks gave to the sun, and they guessed quite rightly from his motion that he is further from us in one part of the year than in the other. This is easily proved to-day by the fact that he grows apparently smaller, as shown by photographs or measurements taken at different times of year, but the change was not perceptible to the rougher methods of the ancients.

It was a pity that Ptolemy did not take more pains to verify the work of Hipparchus on the sun, for the sun’s “apogee,” or point of greatest distance from Earth, has an extremely slow motion among the stars which ought to have been quite perceptible in nearly three centuries;52 but here again he seems to have thought that where Hipparchus had given so much attention he might pass on to something else, and so missed an interesting discovery.

1911, July 1.1912, Jan. 3.

Two half photographs of the Sun, taken at Kodaikanal Observatory. The smaller was taken two days before apogee, the larger on the day of perigee.

Instead, he worked very hard at the moon, and added another periodical irregularity to those already known. Perhaps his feelings were somewhat mixed when this happened, his pride and pleasure in his important discovery being counter-balanced by the consciousness that it would still further complicate his lunar theory. Our satellite is acted upon by ourselves as well as by the sun, so that she suffers many perturbations, for Earth, though so small compared with the sun, is comparatively near. Ptolemy’s discovery was a difference in her speed at full and new, as compared with her intermediate phases, and this periodic difference is called by modern astronomers the “evection.” It was already known that her nodes, or the points at which she crosses the ecliptic, are in constant retrogressive motion, just like the equinoctial points, where the sun crosses the equator; but the moon’s crossing points, instead of taking thousands of years to circle the zodiac, run round in about eighteen years. This was discovered early, because observations were chiefly made during eclipses, and at these times the moon is always at a node, that is to say, she is crossing the ecliptic, the sun’s path; otherwise the eclipse could not happen. It was also known that she has a varying speed in the zodiac, and that her apogee, where the motion is slowest, instead of being apparently fixed, like that of the sun, also runs round the zodiac, but with a direct motion, and in a period of about nine years.

We need not enter into all the details of Ptolemy’s arrangements for the moon, which are exceedingly complicated, but it is interesting to note that he does not explain her varying velocity by an eccentric, as with the sun and the planets. She has an eccentric, but Ptolemy needed it for representing his own discovery, the evection, so he gave her an epicycle, using it in quite a different way from the epicycles of the planets. This epicycle also revolved while moving on the eccentric, but in the opposite direction, and there was so little difference in speed between the two motions that it never brought the moon to a stop, nor reversed her direction, but simply increased and retarded her motion alternately during her monthly revolution. Thus, when the moon was at M, in what Ptolemy called the upper apsis (or arc) of her epicycle, or as we should say in her apogee, the motion on the epicycle was contrary to her motion on the eccentric, and made it seem slower. When the epicycle had travelled halfway round the eccentric, it had also made nearly half a revolution on its own axis: consequently the moon was at M¹, near the lower apsis, or perigee, and the motion on the eccentric seemed to be accelerated.

The slight difference in speed between the two motions accounted for the continuous displacement of the apogee in the zodiac, as may be seen from the diagram. For suppose that when in apogee at M the moon is seen from Earth among the stars in the middle of Taurus. At the return of the epicycle to this place next month, she has not yet quite completed a revolution on her epicycle but is at M², and will not be in apogee until the centre of her epicycle is advanced 3° further in Taurus. After some time (five months), apogee does not occur until the moon is in Gemini, and it will be nine years before it occurs again in Taurus.

These are the leading features of the system by which Ptolemy represented the motions of the planets, the sun, and the moon. He is uncomfortably conscious that it may strike us as very complicated, and in his last book he makes a kind of apology. We must remember, he says, that we are not dealing with earthly machines which jar and wear, but with celestial bodies which have no weight, cause no friction, and are eternally the same. Delambre somewhat cruelly retorts that he need not have wasted time in writing such rubbish, but have been content to put his results into tables.

But what true astronomer could be content with tables and nothing more? He must try to understand their significance. Nearing the end of his great work, which had cost so much labour, and was so brilliant a success within its limits, Ptolemy allows us to see in this little paragraph that he felt he had but touched the hem of Nature’s veil, and longed in vain to lift it. The circles which he manipulated so skilfully were only mathematical abstractions to him:53 what was the reality behind? What were the stars? whence came their unwearied strength, their eternal calm? The power of Egypt, of Assyria, and of Persia had declined, Greece was now laid low, and it was the day of Rome, but still Venus pursued her ancient path among the little stars of Aquarius, and when all faded in the solemn dawn, the sun arose in his ancient majesty. Then Ptolemy looked at his circles and triangles, and felt how inadequate they were; yet it was the nearest approach he could make to truth.

They did indeed represent very beautifully the celestial motions, and also in a general way the variations in brightness or diameter, but their unreality is betrayed by the fact that the latter was often grossly exaggerated, as for instance with the moon, whose epicycle had to be so large, in order to represent her motions, that at perigee she ought to appear twice as large in diameter as at apogee! Ptolemy can hardly have failed to notice this, though he does not mention it. With regard to the planets, he is careful to tell us that he knows no way of finding their real distances: the ratios of their epicycles to their deferents he had carefully computed in each case, but to estimate the diameters in stadia was utterly beyond his powers. He believed, however, that all were very much nearer than the stars, and more distant than the moon, and he found universal agreement among astronomers in placing Saturn, Jupiter, and Mars, beyond the sun, in order of the periods of their deferents, which were all longer than a year. Venus and Mercury, however, had periods the same as the sun: on which side of him, then, must they be placed? Some modern authors, Ptolemy says, thought they were beyond the sun, but he agrees with the most ancient, and places them between sun and moon. The general disposition of the heavenly bodies according to Ptolemy is shown in Fig. 35, with the periods of epicycles and deferents, and the directions of the several movements, but epicycles and spaces between deferents are all made equal. It will be noted that the sun has no epicycle and that the moon turns on hers in a reverse direction, that the centres of those of Mercury and Venus are in a line with the sun, while the lines joining Mars, Jupiter, and Saturn to the centres of theirs are in each case parallel with the line joining Earth and Sun. Beyond all the wandering stars is the sphere of the fixed stars, moving in its vast period of 36,000 years; and the whole system is carried round Earth in one great revolution of a day and a night.

And here we have to note one astonishing fact. Although the planets were all beyond reach of measurement, it was not so with the moon, which the Greeks rightly recognized as our nearest neighbour. They had actually achieved the long-desired feat of measuring her real size and distance.

The fundamental principle on which they worked is easily explained. If we look out of a window at a tree in the garden, it appears against a background of some distant scenery; if we alter our position by walking to another window, the tree changes its place with regard to the relatively motionless background, and its apparent change of place bears a definite proportion to its distance from us. A tree near the house changes its position greatly, a tree at the far end of the garden much less. From careful measurements of the angle through which the tree appears to have moved and the distance we have walked between the two windows, the distance of the tree from the house may be easily deduced.

The tree in the garden is the moon, the distant landscape is the star-spangled sky. The space between the two windows must be increased to thousands of miles, but the astronomer need not walk it. If he makes his first observation when the moon has just risen, carefully measuring her position among the stars, the revolving Earth will carry him to a new position in a few hours, when with the moon high in the sky he can once more compare her position with the same stars, and from the change he then finds he can deduce her distance. The Greeks thought it was the sky, and not the earth which moved, but this makes no difference, as the question is one of relative motion only.

The problem, however, when applied to the moon, is a complicated one, implying not only skill in trigonometry and the possession of suitable instruments for measuring the necessary angles, but also accurate knowledge of the size of the earth and the motions of the moon, since her progress eastward among the stars during the interval between the two observations must be allowed for. Hipparchus and the astronomers of Alexandria were the first to qualify themselves for attacking this difficult problem, and the proof of their success is that Ptolemy’s value for the distance of the moon is very near the truth as obtained by modern methods. The same method is now used, only it is found better to do what was not possible for the Greeks, namely to compare observations made at places several thousands of miles distant, for instance Greenwich and the Cape, instead of allowing the same place to be moved by the earth’s rotation.

When the distance of the moon had been thus discovered, it was a very simple matter to find her real size from her apparent size.

The distances of all other heavenly bodies are too great to be determined by naked eye methods, for the displacement (technically called “parallax”) is so small that it is quite invisible without a telescope. Hipparchus had tried repeatedly to measure the distance of the sun, but recognized that neither the method of Aristarchus nor any other was really conclusive. It was, however, the best attempt that had been made, and Ptolemy assumed that he knew the distance to be about twenty times that of the moon, so he gave the sizes and distances of these two bodies as follows, taking Earth’s semi-diameter as unit:—

	According to Ptolemy.		Modern Values.
	Semi-diameter.	Distance.	Semi-diameter.	Distance.
Moon	⁵/₁₇ (=0·290)	59	0·273	60·3
Sun	5½	1210	109·4	23,439

In Books VII and VIII of the Almagest Ptolemy describes the 48 ancient constellations and the course of the Milky Way among them. The position of each star is noted as it appears in its constellation-figure, but the celestial latitude and longitude is also given, and this great catalogue is evidently taken from Hipparchus.

PTOLEMY’S FORTY-EIGHT CONSTELLATIONS.54

Ursa Minor	Pegasus
Ursa Major	Andromeda
Draco	Triangulum
Cepheus	Cetus
Auriga	Orion
Corona Borealis	The River (Eridanus)
The Kneeler (Hercules)	Lepus
Lyra	The Dog (Canis Major)
The Bird (Cygnus)	Canis Minor (Procyon)
Cassiopeia	Argo
Perseus	Hydra
Böotes	Crater
Ophiuchus	Corvus
Serpens	Centaur
Sagitta	The Wild Beast (Lupus)
Aquila	Ara
Delphinus	Corona Australis
Equuleus	Piscis Australis,
Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra,
Scorpio, Sagittarius, Capricornus, Aquarius, Pisces.

Ptolemy sometimes remarks on the colour of the brighter stars, and always mentions the brightness, or “magnitude” as we call it now, for the classification of Ptolemy (or Hipparchus?) was found convenient and accurate enough to be retained by modern astronomers, and the same system is now continued with the faint telescopic stars.

The stars ranked as “first-magnitude,” or brightest of all, are fifteen in number, and as these are evidently the “quindici stelle”55 alluded to by Dante in Par. xiii. 4, it will be interesting to give a list of them here.

PTOLEMY’S FIRST-MAGNITUDE STARS.

	Name and Description	Modern Name and Meaning. in the Catalogue.
1.	Arctouros, fire-coloured	Arcturus (the Bear-Watcher).
2.	The brightest star in the Lyre	Vega, in Lyra. (Falling Eagle, Arabic).
3.	Aichs (the Goat)	Capella (Little Goat, Latin).
4.	The brightest star of the Hyades, fire-coloured	Aldebaran. (The follower, because following the Pleiades, Arabic).
5.	Basiliskos (the royal), the heart (of Leo).	Regulus (Latin equivalent).
6.	The tip of the tail (of Leo)	Denebola (Lion’s Tail, Arabic).
7.	Stachys (Ear-of-Corn)	Spica (Latin equivalent).
8.	The last of the Water and Mouth of the Southern Fish.	Fomalhaut. (Mouth of the Fish, Arabic).
9.	The fire-coloured bright star on the shoulder of Orion.	Betelgueux. (Shoulder of Giant, Arabic).
10.	On the left foot of Orion, common to the Water.	Rigel. (Foot of the Giant, Arabic).
11.	The last of the River	Achernar (Arabic equivalent).
12.	The very brilliant star, fire-coloured, at the mouth of the Dog, called the Dog.	Sirius (Greek Seirios, or Sothis, from the Egyptian Sept), in Canis Major.56
13.	Prokuon (the preceding Dog), on the thigh of Prokuon	Procyon (in Canis Minor), which rises before Canis Major.
14.	Canopos, on the rudder (of Argo)	Canopus (an Egyptian god, and a town on the Nile delta).
15.	The tip of the right forefoot (of the Centaur).	Alpha Centauri.
Altair and Antares were counted as second magnitude, though we now class them among the first.

It will be seen from the above that only two of these fifteen brightest stars of Ptolemy’s still bear their Greek names, Arcturus, and Procyon; but most of the other modern names are direct translations, either into Latin or Arabic, of Ptolemy’s description or name for the star, while Vega and Aldebaran have preserved their original Arabic names (much corrupted), and Canopus and Sirius are derived from the Egyptian. Regulus-Basiliskos apparently comes from Babylon, for the name of this star on tablets of the second century b.c. was Shar-ru, which means “royal.”

Ptolemy’s “Last of the River” was taken by his Arab and other commentators to be the first-magnitude star which consequently they named Achernar, but this was too far south to be visible at Alexandria, though possibly he heard of it or saw it himself at Syene, where it rose over the horizon in his times. Delambre thinks it is the same as Fomalhaut, which already belongs to two other constellations in the star catalogue; Brown suggests it was Theta Eridani, which may have been brighter sixteen centuries ago. Perhaps it was the star we now call Alpha in the Phoenix, for this lies between the last bend of the River and the Water of Aquarius, and its magnitude is between first and second. The stars of the Southern Cross are included by Ptolemy in the stars about the hind feet of the Centaur, though it is difficult to identify each one with certainty: the positions are not very accurately given.

Ptolemy wrote also on Astrology, or as it was then called Judicial Astronomy, and his work on the subject, which is in four books, received the name of the Tetrabiblios. It seems that astrology was not very much believed in by the Greeks, for he protests that the influences of the stars are real, and can be known and predicted, but allows that this part of astronomy is much more difficult than the mathematical part, with which he had dealt in the Syntax, and that it has not yet been perfected, and therefore it is sometimes slandered as untrue. Astrologers sometimes make mistakes, like doctors, yet both astrology and medicine are useful arts. He mentions especially the Egyptians as practising it.

Only second in importance to the Almagest, and even better known in old days, was Ptolemy’s work on Geography. In this he shows how the size of the earth and the latitudes and longitudes of places on Earth, can be discovered by observations of the heavens. For Earth’s diameter he adopts the value found by Poseidonius. His terrestrial globe had a moveable half-circle attached to the poles, which was divided into 90° from the equator in both directions, so that by placing this against any spot on the globe, its latitude north or south of the equator could be immediately read off. Only half the equator was marked on this globe, and divided into 180°, for the known part of the earth all lay within these limits. The parallels of latitude marked were not the same as we use, though the most northerly fell very close to the Arctic Circle: it showed the latitude of the Island of Thule, far away “towards the Bears,” as Ptolemy expresses it, meaning that it lay under the constellations near the North Pole. The most southerly was not far below the equator, and others were marked between these which divided the known Earth into “climates,” according to the height of the Pole and the length of the longest day in each. Among the many towns which figured on this globe we may mention Alexandria, Rome, Athens, Jerusalem, Florence, Cadiz, Paris, Strasburg, London, Bath. Meridians were marked at every 5 degrees. From this globe Ptolemy shows how a plane map may be constructed. He took Rhodes as the central meridian, because it had a nearly central position among the “climates,” and was the place in which Hipparchus had observed.

Ptolemy also wrote books on Optics, on the theory and construction of Dials, and on Music!

V — Retrospect

The Almagest is the last word of Greek astronomy. We have seen how from the dawn of Greek history, as far as we can trace it back in literature, the Greeks were familiar with the skies, and how the most ancient of their philosophers had tried, chiefly by abstract reasoning, to discover the cause of the circling motions—never changing, never ceasing—of sun and stars. When the seemingly unruly movements of the planets were known, they still felt sure that there must be some underlying principle which would bring all into harmony. Inspired by Plato, and helped by the Egyptians, Eudoxus took the first step towards finding this principle by careful study of the planetary motions, and at last, after many generations of observers and mathematicians, Ptolemy was able to describe these motions as accurately as was possible with the methods available.

At first the heavenly bodies had been thought of as gods, then as worlds like our own, then as spheres of ethereal fire. They were swept round by a mighty wind, they ran on wheels, they floated in the ether, they were set in crystal spheres; the controlling force was the principle of number or harmony, an all-pervading World-Soul, a host of immaterial intellectual Beings subject to one eternal First Mover. It was also suggested that the greater part of the motions were apparent only, that Earth was really in motion, spinning on her axis, revolving round a Central Fire, or revolving round the Sun. But these ideas had not enough evidence to support them when suggested. Had a great imaginative thinker, a Pythagoras or an Aristarchus, arisen after Ptolemy, he could have shown in detail how by assuming these two motions the phenomena could be more simply accounted for, and he could have made out a very good case for their probability.57 But the time was past then for such bold originality, and the explanation of Aristotle was universally adopted. He, as we saw, placed the abode of the gods, the rulers of the universe, beyond the outermost sphere, and found the principle for which all were seeking, which should be the key to all celestial motions, in the law of circular motion.

The Greeks had at first thought that the earth was a disc, under a tent-like sky; then it was a cylinder, with the sky in tiers above; then a huge hemisphere filling half the universe. But they discovered that it was a sphere, surrounded on every side by the heavens; and they found its true size, and that the portion of it which was known to them was less than a quarter of its whole extent. They explained the marvel of Earth’s remaining unsupported in space by the known facts of gravity, arguing that the falling of every particle of earth towards Earth’s centre proved that it was also the centre of the Universe, and that every heavy thing tended thither by a law of nature.

They also knew the size and the distance of the moon; they realized that the planets were all immeasurably remote, and the stars vastly more distant still. They believed that there were great intervals between the planets, corresponding to the differences in their periods of revolution, but the stars were always thought of as set in a great sphere, and therefore all at the same distance from Earth at its centre. The relative positions of the stars on this great sphere, and times of rising and setting of many of them had been known in a rough way for many ages, through the familiar appearance of the constellations, named we know not by whom; but Hipparchus measured their positions in degrees, and was able to foretell where any star would be in the sky for any place or time. He also discovered the Precession of the Equinoxes, and this was thought to prove a slow rotation of the star sphere.

Astrology was learned by the Greeks in Egypt and the East, but was never practised with the enthusiasm shown by their teachers.

As regards the division of time, the Greeks adopted from the Babylonians the twenty-four hour day which we still use, and their months began with the young moon. Their year therefore had to contain a whole number of months, and it had sometimes twelve, and sometimes thirteen, as with the ancient Babylonians, but the system by which this was arranged was quite different, as they did not depend upon observations of the stars, but counted the number of days between equinox and equinox by means of gnomons. Great difficulties were found in trying to reconcile the lunar and solar periods. The ancient 12-month year, used in the time of Hesiod, was found to be much too short, and alternate years of 12 and 13 months made the period too long; then an eight-year cycle was invented, but this had to be constantly corrected, which led to great confusion. As we have seen how carefully Meton and Euctemon had determined the length of the tropical year, even before the days of Eudoxus, surprise may be felt that a calendar year was not fixed to correspond accurately with the movements of the sun, ignoring the irreconcileable movements of the moon, but it is difficult for us to realize in these days how wrong and strange it seemed if a new moon occurred in the middle or at the end of a month, instead of at the beginning. In Aristophanes’ play of The Clouds, which was acted in b.c. 423, the moon was said to grumble because men would not keep the months as she showed them:—

“Yet you will not mark your days
As she bids you, but confuse them, jumbling them all sorts of ways,
And she says the gods in chorus shower reproaches on her head,
When in bitter disappointment they go supperless to bed,
Not obtaining festal banquets duly on the festal day.”

Then Meton made his celebrated discovery that nineteen tropical years correspond almost exactly with 235 synodic months (the difference is in fact only a few hours), and a cycle of 19 years was arranged, which was adopted by all Greek states and dependencies. Some of the years had twelve and some thirteen months, and some of the months 29 and others 30 days, but all followed in a regular order, and when one cycle was completed another was begun. The total number of days in each cycle was 6940, and as this is only 9½ hours longer than 19 true tropical years, it follows that the average year in the Metonic cycle was only half an hour longer than it should have been.58 The average month was not quite two minutes longer than the true synodic month.

An improvement even on Meton’s cycle was made by Calippus, who proposed to correct its too great length by quadrupling the period, and then deducting one day from the whole. This would have given a cycle of 76 calendar years, in which the average year was 365¼ days, or only 11¼ minutes too long. It does not seem, however, to have been ever brought into actual use as a calendar, but Ptolemy often refers to the Calippic epoch as a date from which to calculate celestial phenomena.

Theon of Alexandria c. 380 a.d.

After Ptolemy, the Alexandrian school of astronomy produced only copyists and commentators, the last of whom was Theon, who saw his daughter Hypatia murdered and the library burned by fanatical mobs. It only remains for us to see how the Greek system of astronomy, brought to so great perfection in the Almagest, was neglected for many centuries, and by whom it was at length rediscovered and made to live again.

VI — Astronomy Under Imperial and Christian Rome

b.c. 46 to a.d. 1000.

Vos O clarissima mundi
Lumina labentem cœlo quæ ducitis annum.
Georgic I.

No new school of astronomy arose under the Roman Empire, nor do we even know of one Roman who devoted his life to the science. The genius of this people lay in other directions, and Dante truly says:—

‘“Nature ordained in the world a place and a people for universal command... to wit, Rome and her citizens or people. The which our poet too has touched upon right subtly in the sixth [Virgil, in the sixth book of the Æneid], introducing Anchises admonishing Æneas, the father of the Romans, thus:—

“Others shall beat out the breathing bronze more softly, I do well believe it! And shall draw the living features from the marble; shall plead causes better, and trace with the rod the movements of the sky, and tell of the rising stars. Roman! do thou be mindful how to sway the peoples with command. These be thy arts: to lay upon them the custom of peace, to spare the subject and fight down the proud.”’59

Yet there were some enthusiastic amateur astronomers in Rome, for Cicero tells us of one who had felt old age to be no burden because he was so eager over his astronomical studies, sitting up sometimes all night to finish his calculations, and delighted when an eclipse he had foretold came to pass.60 This ardent amateur, Sulpicius Gallus by name, had found such knowledge of practical value in his younger days, when he was with the legions in Macedonia, for he had been able to persuade the troops not to be alarmed by an eclipse of the moon which was about to happen, explaining how it was due to natural causes; and while the soldiers in the opposite camp were shrieking and moaning, believing that the eclipse portended the death of their king, the Roman soldiers remained quite calm. This was on the eve of the battle of Pydna, in b.c. 168, a little before the time of Hipparchus.

Ovid b.c. 43-a.d. 17.

Virgil b.c. 70-19.

Manilius c. a.d. 10.

Cicero b.c. 106-43.

In Cicero’s own life-time, and throughout the early days of the Empire, it was the fashion to have at least a smattering of Greek astronomy. Ovid tells legends of the constellations; Virgil, at his farm where he lingered happily among his vines, his cattle, and his bees, studied the varying aspects of the constellations in connection with the seasons and the weather; Manilius wrote a long poem in five books on astronomy and astrology; Cicero himself was quite learned in the subject, and made a translation of Aratus, which had a great vogue.

Very popular also, both in classical and mediæval times, was his Dream of Scipio, which was an imitation of Plato’s fable of the vision of Er, in the Republic. The moral is that earthly fame is valueless, since Earth itself is insignificant compared with the starry heavens, but that those who practice virtue for its own sake shall return to the stars whence their souls originally came. The youthful Scipio is transported to the skies in a dream, and meets the souls of his father and of the elder Scipio Africanus in “a radiant circle of dazzling whiteness, which you have learned from the Greeks to call the Milky Way.” There he sees “stars which we never saw from this place, and their magnitudes were such as we never imagined, the smallest of which was that which, placed upon the extremity of the heavens, but nearest to the earth, shone with borrowed light.” But the shining globes of the stars are so great that Earth seems to have contracted to a point, and Scipio gazes at it, grieved.

“How long will your gaze be fixed on Earth?” cries Africanus. “Do you not see into what temples you have entered?” and he points out nine spheres which compose the whole universe. The outermost, in which the stars are fixed, is most divine, and within this are seven, one of which contains the planet called Saturn upon earth, the next the glorious Jupiter, friendly and helpful to mankind, then Mars, ruddy and terrible, and the next place in the middle region is held by the sun, the leader, prince, and governor of all other luminaries, the soul of the world, filling all things with his light. Venus and Mercury follow him in their courses, like attendants, and in the lowest sphere rolls the moon, kindled by his rays. Below this, all is mortal and transitory, except the souls given to the human race by the grace of the gods; above the moon all is eternal. Earth, which is at the centre and forms the ninth sphere, is immoveable and below all the rest; and all weights, by their natural gravitation, fall towards her.

Scipio then asks what is the sound which fills his ears, so loud and yet so sweet? and he is told that he hears the music of the spheres, which is too great for mortal ears, just as the sun is too bright for human eyes to look upon. Yet those who make music upon Earth, with strings or voice, like all others who follow heavenly pursuits, are opening for themselves a path by which to return to the stars, the true home of the soul.

Strabo born c. b.c. 63.

Seneca b.c. 3-a.d. 65.

Pliny c. a.d. 23-79.

Proclus died c. 480 a.d.

Martianus Capella, 5th century a.d.

Simplicius 5th century a.d.

Other famous Latin authors who wrote on astronomy were Strabo, Seneca, and Pliny, who quote Eudoxus and Aristotle, Poseidonius, and Hipparchus. When Ptolemy’s work was done there was no great writer to popularize it. Three hundred years later Proclus writes a commentary on it, and Martianus Capella mentions it, but Simplicius, in his commentary on Aristotle’s De Cœlo, though he speaks of “the admirable Ptolemy,” is evidently unacquainted with his work.

No Roman added anything new to astronomy, and the most precious parts of their writings for the history of astronomy are some fragmentary notes of early Greek astronomers whose original works are lost.

The practical use of astronomy for measuring time appealed, however, to the Roman people. The most ancient Roman year (said to have been introduced by Romulus) had only ten months, March being the first, which explains why the ninth to the twelfth of our present months have the names of September, October, November and December, as if they came in the order of seventh to tenth. Two more months were added later, and at some unknown date the old Octennial or 8-year Cycle was adopted from the Greeks. This involved the use of intercalary months of varying length, and the priests were entrusted with the business of arranging them. But the priests thought it much more important that the length of the year should suit their convenience than that it should conform to the celestial movements, so they made it long or short according as they approved or not of the persons holding office at the time; and by the time of Julius Cæsar the calendar had fallen into such confusion that March 25, which was supposed to be the date of the spring equinox, came in the middle of winter!

Julius Cæsar and
Sosigenes b.c. 46.

A drastic reform was necessary. Julius Cæsar called in the Alexandrian astronomer Sosigenes, and gave the Empire the calendar which, with the exception of one small reform made since, we still use. The moon was thrown over altogether: there were to be no more intercalary months, and every year was to be exactly like the last, except for the addition of one day in every fourth year, so as to make the average year equal to 365¼ days. Since the tropical solar year is only 11 minutes, 14 seconds shorter than this, many centuries would elapse before the months of this calendar would depart from their proper seasons. March 25 was restored to the time of the vernal equinox, but the first day of the new year was to be January 1, and Julius Cæsar gave his own name to the old fifth month of Quintilis. Each month was to be alternately of 31 and 30 days, except February, which would only have its full complement of 30 days in the fourth year (Leap Year), and 29 every other year. This reform was regarded by some as an unwarrantable interference by a despot. Cicero, when some one mentioned that the constellation Lyra would rise at a certain hour, answered bitterly, “Yes, if the edict allows it!”

Unfortunately, the simplicity of the scheme was a good deal spoiled by the folly of Augustus, who could not bear that the month of his predecessor should have 31 days while the next, the old Sextilis, which he turned into August, named after himself, should have only 30. So he made two months of 31 days come together, and took away a day from February. Afterwards, Nero gave his name to April, and Domitian his to October, but this was more than a long-suffering world could bear, and the new names were gladly forgotten as soon as the tyrants were dead.

Although, therefore, Rome was obliged to apply to Alexandria, that is to Greek astronomy, to carry out the project, it was Rome that gave us the most correct and convenient calendar which exists, better in both respects than that which had been used in Greece itself.61

But alas! the celestial science, a willing servant as time-measurer for the daily uses of humanity, a docile captive to adorn the triumph of literature, was doomed to a baser servitude. It was in the early days of the Empire, and all through the Middle Ages, that the pseudo-science of Astrology was pursued with passion, and men spent their lives in studying the paths of planets and positions of the stars, urged solely by the delusive hope of being able therefrom to read the book of fate and guide the lives of their superstitious clients. From Chaldea, its ancient home, came the most famous astrologers, but their art was soon learned in every country of Europe, and its professors were sought after by peasants and kings—now reviled and banished as impious and leagued with devils, now loaded with honours and rewards, revered, hated, welcomed, forbidden, but always believed in. Although when Christianity was established the seven planets could no longer be regarded as great gods ruling over the lesser gods of the stars, they were still thought to be mighty revealers of fate. Each had his special attributes and influence over man: the fiery colour of Mars no doubt suggested the warlike and hostile spirit ascribed from time immemorial to this planet-god; the slow motion of Saturn in his distant sphere gave an impression of a mournful morose being, the “frigida Saturni stella” of Virgil; Venus was the planet of love; the sun, of honour and power, and so forth. Each planet was also mysteriously connected with a colour, and, the alchemists said, with a metal; the sun with gold, the moon with silver, Saturn with pale heavy lead, etc. Each also influenced a special part of the body: thus, if Mercury were unfavourably placed at the moment of a child’s birth it would be liable to suffer from lung-disease; the moon’s position affected the brain; the sun’s the heart, etc.

As the planets had distinct and often contrary influences in different positions, it was necessary, in determining a man’s fate, to consider the aspect of the whole heavens, especially at the moment of his birth, but horoscopes were also cast for any period in his career, past, present, or to come, enabling him to guard against threatening evils or bad tendencies, and to seize favourable opportunities. The method was as follows: the sky-sphere, as it appeared at the given time and place, was divided into twelve “houses,” by drawing meridians (called “circles of position”) 30° apart. The house just about to rise on the eastern horizon was called the “ascendant,” and was the first and most important, planets situated there having more power than anywhere else; but each house had its special significance, the second (just above the eastern horizon) being the House of Riches, the seventh of Marriage, the twelfth of Enemies, etc. The kind and the strength of each planet’s influence depended mainly upon the house in which it happened to be, and was strongest when the planet was in its own house and also in its favourite zodiacal sign. The sun was considered to be most at home in Leo, the moon in Cancer, and each of the other five planets owned two of the remaining signs. Another important point was the “aspect” of the planets with regard to one another, that is, their angular distance apart on the sky-sphere. If Mars and Jupiter, for instance, were in “opposition,” i.e. 180° apart, the portent was unfavourable, but in “trine” or “sextile” aspect (120° or 60° apart), favourable.

It is evident that for casting horoscopes it was necessary to be able to calculate for any given time or place the positions of the heavenly bodies; and for this the skies must be watched, and the movements known of the stars, of sun and moon, and of planets. To this extent, therefore, an interest in genuine astronomy was kept alive; but on the other hand, the system fostered belief in the overwhelming importance of Earth in the Universe, and the existence of the heavenly bodies for the sole purpose of ruling and foretelling human destinies: no one cared to inquire what were the underlying laws, and what the real nature, of the heavenly phenomena.

Closely allied to this superstitious belief in planetary influences, was the dread of comets, meteors, and eclipses, which were everywhere regarded as omens. It was in vain that Seneca urged the greater importance of investigating the nature of the heavenly bodies about which something was already known, and of trying to solve the problem worthy of highest consideration, viz. whether the earth, as some had asserted, was turning rapidly, or was stationary in a turning World. His very protest, as well as his lengthy dissertation on comets, shows how far less interesting, alike to philosophers and public, were the ordered courses of stars and planets, than the startling apparition of such rare objects as that great “hairy star” which, appearing suddenly during the games instituted by Augustus after the assassination of Julius Cæsar, was thought to be the soul of the dead Emperor. Augustus erected a temple in its honour.

Rome, considered as the metropolis of the dominant temporal power, failed to encourage astronomy; Rome as the centre of the spiritual power directly discouraged it.

Cosmas c. 540 a.d.

Augustine 354-430 a.d.

In the fourth and fifth centuries after Christ “the old heathen theory” that Earth is a sphere was opposed by some of the Fathers, as inconsistent with certain expressions in the Bible; and in the sixth an Egyptian monk, Cosmas Indicopleustes, formulated a scheme of the Universe according to which the Jewish Tabernacle was a type and pattern of the World. The earth is the flat oblong floor, surrounded by four seas; these are enclosed by four massive walls which support a roof (the firmament or sky), and above this live the angels, who move the sun, moon, and stars across the firmament, and let down rain through its window. This childish cosmogony, supposed to be in entire accordance with Genesis, Isaiah, and the Psalms, bears a curious similarity to one of the oldest “heathen theories” of all, born in the land where Cosmas lived.62 Saint Augustine, however, author of the paralysing doctrine: “Nothing is to be accepted save on the authority of Scripture,” does not seem to have considered belief in a spherical Earth forbidden, but it was to him a matter of perfect indifference, while he upheld as an article of faith that in no case could any antipodean inhabitants exist. For they could not be descendants of Adam, nor ever hear the Gospel, since everyone knew the torrid zone to be an impossible barrier between north and south. Another favourite Church doctrine was that Jerusalem was the centre of the earth: this idea, which it will be remembered has a place in Dante’s cosmogony, was based on the words in Ezekiel:63 “This is Jerusalem: I have set it in the midst of the nations and countries that are round about her.” Good bishop Arculf, and other pilgrims, were shown a pillar “on the north side of the holy places, and in the middle of the city,” which marked the exact spot, and were told in proof of the assertion that at midday at the summer solstice this pillar cast no shadow! How this proved its central position is a mystery, and if true the pillar must have been deplorably crooked, for the sun can never pass overhead in Jerusalem, in a latitude of nearly 32° north.

The Church, like the State, saw that astronomy had one use, and applied, like the State, to Greek astronomy for a calendar. It was necessary that the ecclesiastical calendar should be luni-solar, since Easter, which corresponds with the Jewish passover, must fall on the Sunday following the first full moon after the Vernal Equinox. By 325 a.d., when the Council of Nice was held, at which this question was settled, the Vernal Equinox fell on March 21 instead of March 25, owing to the neglected eleven minutes in the Julian year. March 21 was therefore adopted by the Church as the date of the equinox, which was assumed to remain constant; and the old luni-solar cycle of Meton was used, and still is used in all churches which celebrate Easter, as a basis for the ecclesiastical calendar.

The custom of reckoning years forwards and backwards from the birth of Christ was first introduced by a Roman abbot, Dionysius Exiguus, in the sixth century, but it did not become general in Christian countries until the ninth century. Dionysius adopted as the first day of the epoch, not January 1, but March 25, the old Roman date of the vernal equinox. This was because it was Annunciation Day, and it was a belief of the Middle Ages that the Annunciation and also the Crucifixion actually took place on this day, and also that the Creation began on the same date.

Martianus Capella 5th cent. a.d.

Cassiodorus c. 530 a.d.

Boëthius died 525.

At the break-up of the Roman Empire some fragments of classical learning were saved from the wreck, mainly in the text-books of the “heathen” writers, Capella, Cassiodorus, and Boëthius. These were preserved by the Church, now the only repository of learning. The secular instruction given to churchmen included astronomy, for while the “Trivium” comprised the three elementary sciences of Grammar, Rhetoric, and Dialectic, the “Quadrivium” comprised the four advanced sciences of Arithmetic, Astronomy, Geometry, and Music. But only a mere smattering of the “Quadrivium” was taught in this period, and scarcely more of astronomy than was necessary for determining the date of Easter. The intimate knowledge and ingenious theories of the Greeks concerning the celestial motions interested no one any more.

Charlemagne 732-814.

Isidore died 636.

Bede c. 673-735

Fergil, 745.

Dicuil, 825

From the seventh century, however, the ignorance began to be less dense. Charlemagne established many schools, and there were enlightened monks here and there—Saint Isidore of Seville, the Venerable Bede, and Irish scholars like Fergil and Dicuil—whose teachings show that the elements of astronomy as taught by the Greeks were not totally forgotten everywhere. From the beginning of the ninth century all famous monasteries had schools for laymen as well as for monks.

In Italy the darkness was never quite so deep as in northern Europe, for traditions of classical culture never quite died out. And although throughout the long period from Ptolemy to the end of the tenth century, astronomy had been almost completely neglected in Europe, the way was slowly being made plain for a great revival. The ideal Empire, governing the whole world from the Eternal City, and the ideal Church making all men brothers, though neither has ever existed in fact, did so in men’s minds, as we see clearly in Dante, and both exercised a powerful influence. The Roman Empire and the Roman Church did impress a kind of unity on Europe as it grew: there was one civilization, one religion, one language in which new thoughts could be conveyed to all. Thus the ground was prepared, and whenever a new school of astronomy should arise or be imported, it would not remain the property of one nation surrounded by barbarians, but might at once be shared in and advanced by the whole of Europe.

VII — Arab Astronomy

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.

Al Mansur 753-775 a.d.

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.

Haroun al Raschid 786-809 a.d.

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 813-833 a.d.

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

Alfraganus c. 840 a.d.

Albategnius c. 900 a.d.

Abul Wefa 940-998.

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.

Ebn Jounis died 1009.

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.

Arzachel c. 1080.

Averroës 1126-1198.

Al Betrugi c. 1150.

Abul Hazan c. 1200.

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 Semi-Diameters of Earth.
Moon	64⅛
Mercury	167
Venus	1120
Sun	1220
Mars	8876
Jupiter	14,405
Saturn and Stars	20,110

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.

	Alfraganus.
Sun	5½	109½
The 15 first-magnitude stars	4¾	Arcturus, Sirius, Spica, and others,
The 15 first-magnitude stars	4¾	much larger than the sun.
Jupiter	4⁹/₁₆	11
Saturn	4½	9
Other stars, in order of		Various. Some certainly
magnitude, 2nd to 6th...		larger than the sun.
Mars	1⅛	½
Earth	1	1
Venus	³/₁₀	⁹/₁₀
Moon	⁵/₁₇	¼
Mercury	¹/₁₈	⅓

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.

Tabit ben Korra 826-901.

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.

Nasir-ed-din 1201-1274.

Alfonso 1223-1284.

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.

VIII — The Return of Greek Astronomy to Europe

a.d. 1000 to 1300.

“He hath made everything beautiful in His time; also He hath set
the infinite in their heart.”

In the whole cycle of the changing year there is no moment so wonderful in northern climes as that which comes in early February, when winter is not yet past, but for the first time the promise of spring is felt in the air. Not a leaf has unfolded its green, but the swelling buds on the trees make a purple flush all over the woods, the blackbird sings an exultant strain, and in some sheltered copse you may find a delicate daring primrose already in bloom.

Such a moment in the history of Europe was the year 1000 Anno Domini. After the apathy, the ignorance, the despair of the Dark Ages, a new spirit began to breathe hope into the hearts of men. A love of beauty, a new religious fervour, a passionate desire for knowledge took possession of them. Yet it was nearly a hundred years before the great universities which were one expression of this new spirit sprang up in Paris, Bologna, Oxford, to be followed later by similar centres of intellectual activity in all parts of Europe.

By the end of the twelfth century it is said that there were 100,000 students in Bologna. A large number were foreigners from many lands, for as Latin was the universal tongue in education, all nations could understand each other, and scholars often wandered from one university to another, attracted by the fame of some great master. Similarly the doctors would teach first in one town and then another. Men of all ages and classes met together, for among the students were young boys and elderly ecclesiastics, poor scholars who begged their bread, and rich nobles who came with a tutor, a chaplain, and a whole suite of servants. There were no colleges or even lecture-halls: the students joined together in small groups to take a house and share expenses, and the professor lectured in his own house, or in a hired room, or, if the audience was large, in a city square, speaking from an open-air pulpit. All were united in the ardent pursuit of learning, and none complained if the floors were merely covered with straw, and the lectures, which often lasted three hours, began before sunrise on winter mornings in rooms which had no light and no fire. Was it not enough that when leaving at the end of university life one was technically said to be “going home a wise man”?

One cause of this intellectual fervour was the influence of Arab culture, with which Europe came into contact through the crusades, and through the Saracens in Sicily, and the Moors in Spain. For this reason astronomy and astrology took a high rank among the new studies. To distinguish between the two is quite a modern idea, and in mediæval times either name was used indifferently to cover both subjects. In Bologna university in the thirteenth century an important school of medicine and arts arose, through Arab influence, and the Arab doctors of medicine introduced the system of astronomy which they had learned from the Greeks. “A doctor without astrology,” it was said, “is like an eye that cannot see;” and before prescribing for a patient it was thought quite as important to determine the positions of the planets, as the nature of the disease. By the beginning of the fourteenth century there were salaried professors of astrology in Bologna, and they were more highly esteemed than any other professors except those of philosophy.

Cecco d’Ascoli d. 1327.

One of their duties was to provide “judgments” (i.e. to cast the horoscope) gratis for students. But the dignity was a perilous one. Legitimate prediction by astrology bordered close on necromancy, which was banned by the Church, and one of Bologna’s most famous professors in astrology, the learned Cecco d’Ascoli, was burned at the stake in Florence in 1327 for the crime of sorcery.

Astronomy, like other subjects, was taught chiefly by lectures and “repetitions,” or classes for catechizing the students on what they had already heard. Books could also be had, though they were dear, on hire or purchase, from the university “stationers” or librarians.

The first books on Greek astronomy which found their way into European universities were Latin translations of Arabic commentaries and paraphrases of Aristotle, which travelled from Moorish academies in Spain to Paris. The astronomical treatises with strange technical terms in Arabic were hard work to translate, especially when they had already passed through several languages, as often happened. Thus it was possible to possess a work of Aristotle which was a Latin translation of a Hebrew translation of a commentary upon an Arabic translation of a Syriac translation of the original Greek text!

Urban IV., pope 1261-1264.

But meanwhile some of Aristotle’s works in the Greek entered Italy from the East, as a result of the crusading conquest of Constantinople in 1204. The first translations of these into Latin were very poor, but later on St. Thomas Aquinas, with the help of Pope Urban IV., had a better version made.

Frederick II. 1194-1250.

Sacrobosco died c. 1256.

Roger Bacon c. 1214 to c. 1294.

It was long before a good Latin version of Ptolemy’s Almagest could be obtained. A translation was made from the Arabic in 1230, at the bidding of the Emperor Frederick II., who did much, at his Sicilian court, to encourage Arab literature, but this translation was not much known or used.70 The teachings of the Almagest became known chiefly through popular expositions such as those of Alfraganus, Albategnius, and John Halifax of Holywood, an English monk who became famous under his Latinized name of Sacrobosco. He was not an astronomer but had studied Greek and Arab writings, and finding that the study of astronomy was neglected because books on the subject were difficult both to procure and to understand, he compiled a useful handbook, which became widely popular and remained so for several centuries. Several other writers, notably Roger Bacon, wrote on the spheres, on the use of astrolabes, and on astrology. The books prescribed in Bologna for the course in Astrology and Mathematics were as follows:—

A work on Arithmetic or Algebra.

Euclid, with a thirteenth century commentary.

The “Theorica Planetarum,” which was either a free translation of Ptolemy’s Almagest or an exposition of its principles.

The Alfonsine Tables.

The Canons of De Lignières (of Amiens, 1330 a.d.), i.e. rules for the use of astronomical tables to determine the motions of the heavenly bodies.

Portions of the Canon of Avicenna (the Arab philosopher).

A treatise on the Astrolabe by a Jewish astrologer of the ninth century.

A treatise on the Quadrant.

The astrological works of Ptolemy, with a commentary.

A book by Alchabicius (fl. c. 850 a.d.), probably his work on astrology.

A book on astrological medicine.

Alfonso X. 1223-1284.

From the above we gather that a past master in Astrology would understand the elements of mathematics, and all the astronomy that Ptolemy’s translator or commentator could teach; that he had learned—at least in theory—the use of astronomical instruments and tables, and a good deal of astrology, including its use in medical practice. The tables were intended mainly for astrological predictions. The standard Alfonsine Tables had been drawn up in 1252 by Christians, Jews, and Moors, under the direction of Alfonso X. king of Castile. They contained lists of positions of the planets, dates of Easter moons, “golden numbers” and “dominical letters” of the ecclesiastical calendar, times and other details of eclipses, together with methods for finding the places of planets, and for casting horoscopes. This is the Alfonso who was so much shocked at the complexity of Ptolemy’s multitudinous circles that “the ointment of his name is marred,” says Fuller, “with the dead fly of his atheisticall speech”: “If only the Creator had consulted me, when He made the world, I would have given some good advice!”

Sylvester II. (Gerbert) Pope, 999-1003.

Not one of all these books pretended to add any new discovery to astronomy: all intellectual energy was absorbed in eagerly assimilating the knowledge stored by Greeks and Arabs. Nor were any great observatories founded in Europe yet, in imitation of Alexandria, Rhodes, or Baghdad. The instruments in use were celestial globes and small portable astrolabes and quadrants for determining positions and angular distances between the heavenly bodies. The learned pope, Sylvester II., who had studied astronomy among the Moors in Spain, was so skilful in making astrolabes that some accused him of gaining the art by selling his soul to the devil!

Albertus Magnus 1193-1280.

Aquinas 1225-1274.

When Aristotle first came to Paris (about 1200 a.d.), in Oriental dress, and accompanied by Moslem authors, the Council of Paris denounced him as an infidel; yet in less than fifty years all his works were placed on the list of books prescribed in the university course. This was brought about by the Dominicans. In six of his twenty-one ponderous volumes the German friar Albertus Magnus paraphrased the whole of Aristotle’s works, and stripping his philosophy of the pantheistic and materialistic garb in which the Spanish Arab Averroës had clothed it, presented the Greek philosopher as an ally of Christianity. The Italian saint, Thomas Aquinas, pupil of Albertus, in his much more readable commentaries and treatises, popularized this idea so successfully that Aristotle—the Philosopher, as he was called—speedily became as great an authority on every other subject as he had always been on logic.

It was a mutual victory. Aquinas captured the Greek for the Christian faith; Aristotle won the western world to accept his theories. No longer was the doctrine of a spherical Earth called “an old heathen theory”: it was almost an integral part of the Catholic faith. Aristotle’s demonstration that there must be a First Mover, himself unmoved, became an argument for the existence of the Christian Deity; the intelligences which preside over the celestial movements were interpreted as the nine hierarchies of angels whose existence was taught by the Church. To the eight spheres of the Greeks and the Primum Mobile of the Arabs, the thirteenth-century Christians added the all-embracing heaven of heavens, the Empyrean, to be the abode of the Creator and blessed spirits. Within the central immoveable earth they placed Purgatory and the fires of Hell. They accepted the limits of the habitable earth as laid down by Ptolemy, but kept Jerusalem as the centre by asserting that it was situated 90° from the Pillars of Hercules, and 90° from the mouths of the Ganges. Eden, the earthly paradise of Adam and Eve, was represented on contemporary maps as in the extreme East, separated by sea from the eastern boundary of the inhabited earth.

Thus theology and science supported one another. All learning was sacred, and all that man’s mind is capable of understanding he might aspire to know, for the search if rightly pursued would lead at last to the perfect bliss of beholding with unveiled eyes the Source of all Truth.

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