PART II.

FIG. PAGE

A MEDIÆVAL ASTRONOMER. _From a painting by Gerard Dow_ 200 ASTRONOMY. _From a fresco in the Spanish Chapel of Santa Maria Novella, Florence_ 217 38. The Half-Moon shape of the Habitable Earth (Ristoro) 247 CLIMATE MAP OF ABOUT A.D. 1110. _Reproduced from Beazley’s Dawn of Modern Geography_ 248 39. Sun, Moon, and zenith. To illustrate _Par._ xxix 1-6 267 40. The Zodiac and the Months 276 41. The Ram on the Ecliptic. _From the Cosmi Historia of Robert Flud_, A.D. 1612. _Reproduced from Brown’s Aratos._ 279 MAP OF STARS VISIBLE BEFORE DAWN IN PURGATORY 295 42. Ursa Minor as a Horn. _Par._ xiii. 10 299 43. The Sun at the Equinox, seen from the poles and the equator. _Conv._ III. v. 327 44. Lunar and Solar Eclipses 339 MAP OF THE WORLD BY HEINRICH OF MAINZ, about A.D. 1110. _Reproduced from Beazley’s Dawn of Modern Geography_ 344 45. The Universe of Dante 355 46. The Signs of the Zodiac at sunrise from the Mountain of Purgatory 375 47. Northern Slope of the Mountain of Purgatory 377 48. Dante’s View of Earth from the stars. _Par._ xxii. 395 49. do. Six hours later. _Par._ xxvii. 396 50. An impossible interpretation of _Par._ xxvii. 399 51. The Rising Sun at the spring equinox. _Par._ i. 39 403 52. The Moon’s Epicycle and Deferent 449 53. Comparative sizes of the Sun and his satellites 490

ABBREVIATED TITLES OF BOOKS USED IN THE TEXT.

Dante’s Works:— _Inf._ Inferno. _Purg._ Purgatorio. _Par._ Paradiso. _Canz._ Canzone. _Son._ Sonetto. _Ball._ Ballata. _Ecl._ Eclogue. _V. N._ Vita Nuova. _Conv._ Convivio. _De Mon._ De Monarchia. _V. E._ De Vulgari Eloquentia. _Ep._ Epistola. _Qu._ Quæstio de Aqua et Terra.

_El. Ast._ Elementa Astronomica (Alfraganus). _Comp. del Mond._ Della Composizione del Mondo (Ristoro).

DANTE AND THE EARLY ASTRONOMERS.

INTRODUCTION.

In a beautiful passage of the _Convivio_ Dante describes how he first began to devote himself diligently to science and philosophy. When the gentle soul of Beatrice had passed to heaven, a great darkness fell upon him: the streets of Florence were to him as a deserted city, and his life empty and purposeless. It was long before he could find any comfort, but at last he bethought himself of studying a book by Boëthius, who when exiled, imprisoned, and unjustly condemned to death, had strengthened his soul with the “Consolations of Philosophy.” This led him on to Cicero’s book “On Friendship,” in which Lælius explains how he is consoled for the death of Scipio.

Books in those days could only be had in manuscript, full of abbreviations, and often also of errors, and at first the young student found the Latin hard to master; but as he struggled on, half deciphering and half divining the meaning, the mists cleared a little, and the weight was lifted from brain and heart. With elation he discovered that obscure passages were becoming luminous, and to the exhilarating sense of conquest was added the joy of finding, beautifully expressed, thoughts which had already floated in his own mind, but dimly, as in a dream. He compares himself to one who, seeking silver, should light (not without Divine guidance) on a treasure of gold; for he found not only relief from his tears, but a door into a new world of literature, philosophy, and science. Henceforth, he tells us, he eagerly frequented the schools of the religious orders and the discussions of the philosophers; and how extensive and thorough was his learning we can see in his writings. In them we find a reflection of thirteenth-century thought in every field of intellectual research.

Among all his studies was one which evidently had a great attraction for him, even in the early days of the _Vita Nuova_, before learning had become a passion. Astronomy appealed to many sides of his nature. The beauty of the skies stirred his imagination; their suggestive symbolism touched his religious sense; the harmony of the celestial movements and the accuracy with which they can be foretold delighted his instinct for order and precision. He must have read, and perhaps possessed, some of the best text-books then available, and he grasped with singular clearness the phenomena observed and the theories taught in his day. His works are full of allusions to astronomy. In the _Vita Nuova_ he finds pleasure in connecting the story of his lady with the revolutions of the spheres; in the _Convivio_ he teaches the elements of the science; in the Vision of the _Divine Comedy_ he journeys through the universe as it was depicted by mediæval astronomers; and throughout his works are scattered similes drawn from celestial phenomena and descriptions of “le belle cose che porta il ciel.”[1]

------------------------------------------------------------------------ [1] “The fair things that Heaven holds.” Inferno XXXIV. 137, 138. ------------------------------------------------------------------------

Therefore, for full enjoyment and understanding of Dante’s works it is necessary to have a rudimentary knowledge of astronomy.

Many of his readers think that Dante’s astronomy is very complicated and difficult to understand. What makes it seem difficult is that in this age we are generally unfamiliar with the skies. We do not eat our breakfast or go to our office by the sun, nor do we watch the stars to see when grouse-shooting begins or the summer holidays end. If it is important for us to know at what hour the sun sets and lamps must be lighted, or if we wish to see a view by moonlight, we consult an almanac. When we think at all of the movements of the heavenly bodies, our notions are usually taken from diagrams and tables, not from what is actually seen in the skies. We only think, for instance, of the seasons as caused by the earth’s journey round the sun, and the tilt of her axis: therefore, when Dante speaks of Venus as a Morning Star veiling the Fishes with her rays, or the horn of the Celestial Goat touching the sun, it conveys little, although the seasons of spring and of winter are as clearly indicated as if he had spoken of the blossoming of primroses or the fall of snow. When Cacciaguida, in the heaven of Mars, tells the date of his birth by counting how many times the planet had since then returned to his Lion, those who only think of Mars as circling round the Sun, and have never traced his path among the stars, are at a loss, and think the method very far-fetched. A short description, and especially a little individual watching, of the apparent movements of the heavenly bodies, would put us in a position to realize the meaning of a large number of Dante’s astronomical descriptions and allusions, without any knowledge of any theory.

Others complain that the subject is dull. Dante’s astronomy, when interpreted only by means of notes on single passages, is undoubtedly dull—as dull as the history of his own times learned in the same way. But when either subject is studied as a whole these passages acquire a special interest; and they in their turn give new life to the subject they illustrate.

Other readers say that Dante’s astronomy is so entirely false and obsolete that it is not worth study. This is hardly true. Where Dante speaks of appearances he is remarkably accurate, far more so than most modern artists and writers of fiction. Where he speaks of the heavens as he supposes them actually to exist, he is interpreting the appearances according to the astronomical theories of his day, with which he was very well acquainted. This interpretation was not correct, but it was an ingenious and beautiful system, and very successful in so far as it enabled astronomers to calculate the positions of sun, moon, stars, and planets for any date. Its main outlines can be explained in a few pages, with the help of a couple of diagrams, but when presented thus, especially to those unfamiliar with the skies, it seems very strange and artificial. To appreciate it at its true worth, we must know just what are the phenomena it was intended to explain, and trace its gradual development out of man’s first clear perception that the movements of sun, moon, and stars follow unchanging laws.

The story of this development is of enthralling interest, and after the system had been completed by one of the greatest mathematicians the world has seen, its later history reads like a romance. Though of classical Greek origin, it was almost wholly lost to Europe for many centuries, it returned at last in Oriental dress, and its final form was given by a devout and learned Dominican friar.

It was at this time that Dante was born, and the scholar-poet immortalized the Ptolemaic system of astronomy in his verse, adding to its popularity in his own day, and making it known to thousands of readers since, who might otherwise scarcely have heard of it.

Dante’s astronomy, therefore, is of wide and deep significance. To study its history is to learn a chapter in the development of the human intellect; to see the universe with his eyes is to know how it appeared, not only to his contemporaries but to men in many lands and many centuries. The system of Ptolemy was already a thousand years old when Dante studied it, and it continued to be taught long after Copernicus had introduced a truer one; nor has it ever been completely swept away, for much that it taught was accurate. The new astronomy has developed from the old, and bears traces to this day, in its phraseology, its written symbols, and its methods, of the many races and ages which have contributed to its progress.

This book, therefore, is divided into two parts. In the first, I put before my readers the elementary facts which form the foundations upon which all astronomy is based, the movements of sun, moon, stars, and planets, so far as they can be easily observed by the naked eye; then follows a sketch of the attempts which were made to interpret these observations from very early days until Dante’s time. Unnecessary technicalities are avoided, but we shall try to enter into the thoughts of past generations concerning the stars, to see why they were interested, how they worked, what hindered and what helped them in their search for truth.

In the second part, we shall examine Dante’s works, and see how familiar he was with the movements of the skies, and how well he understood the theories which in his time were held to explain them. We shall see how astronomy was generally regarded in his day, what books he read, and which authors influenced him most. We shall see how false is the assertion often made that in the Middle Ages men studied astronomy only for the sake of astrology, and how closely the science of the stars was connected with religion and the loftiest speculations of philosophy.

We shall also examine in particular some difficult passages connected with astronomy which occur in Dante’s works, but my aim is not so much to explain all the astronomical references as to put the reader in a position to attempt an explanation himself.

My greatest ambition is to share with others the pleasure I have had in learning what Dante knew and thought about the stars, and who were the master builders who had erected through the ages the system so vividly pictured in his immortal poem.

_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).

[Illustration: Fig. 1. The Sun’s path in the sky at different seasons.]

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.

------------------------------------------------------------------------ [2] Greek _gnomon_, an interpreter. A pole set up in order to show the length of shadow thrown by the sun. ------------------------------------------------------------------------

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.

[Illustration: Fig. 2. The Moon at Sunset.]

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.

[Illustration: Fig. 3. The Path of Mars among the Stars, 1909.]

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.

------------------------------------------------------------------------ [3] Greek _planetes_, a wanderer. This name was originally given to Mercury, Venus, Mars, Jupiter, Saturn, and also to sun and moon, for it indicated all the known heavenly bodies which changed their places among the stars. In modern usage it is not applied to the sun, but only to his satellites, of which many more are now known. ------------------------------------------------------------------------

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.

[Illustration: Fig. 4. The star sphere.]

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.

[Illustration: Fig. 5. Diagram illustrating Synodic and Sidereal Periods.

The arrows show the direction of the Moon’s monthly and the Sun’s yearly revolutions in the zodiac, as seen from Earth.

When the Moon is opposite the Sun, for instance in Libra while he is in Aries, she is full. In 27½ days she returns to the same place among the stars, and this is a SIDEREAL MONTH. But the Sun meanwhile has moved into Taurus, and not until the Moon has reached Scorpio, opposite to him, will she be full again, and complete her SYNODIC MONTH (29½ days).]

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. 365 5 48 45·5 (Our civil year is based on this). 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 ”

------------------------------------------------------------------------ [4] Fractions omitted. ------------------------------------------------------------------------

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_.

II. THE BEGINNINGS 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.

------------------------------------------------------------------------ [5] Conv. IV., xxiii. 56, 57. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [6] Dr. C. Hose, in “Travel and Exploration,” for Feb. 1910, quoted in “Nature,” Feb. 17, 1910. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [7] Journal of the British Astronomical Association, June 24, 1909, report of a lecture on Chinese astronomy by E. B. Knobel, F.R.A.S. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [8] Acts, xvii. 28.

[9] _The Phainomena of Aratos, done into English verse by Robert Brown_, lines 1-13. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [10] _Ibid._, 373-382. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [11] Ptolemy says he made a few changes, as his predecessors had done. (Delambre, _Histoire de l’Astronomie Ancienne_, ii. 261). ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [12] _Origine de tous les cultes, ou Religion universelle_, by C. F. Dupuis. ------------------------------------------------------------------------

[Illustration: THE OLD CONSTELLATION FIGURES.

SOUTHERN HEMISPHERE.]

[Illustration: NORTHERN HEMISPHERE.

THE OLD CONSTELLATION FIGURES ACCORDING TO ARATUS.

_In Ptolemy’s Catalogue Equuleus and Corona Australis are added to these._

_(From Peck’s “Constellations and How to Find Them.”)_]

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.

------------------------------------------------------------------------ [13] _Journal of the British Astronomical Association_, “The Oldest Astronomy,” July 1898, June 1899, April 1904, May 1909; _The Observatory_, December 1898; _Knowledge_, October 1904; and elsewhere.

[14] _The Phainomena of Aratos_, by Robert Brown. See also his _Eridanus, River and Constellation_; _Primitive Constellations_, and other works. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [15] We are not sure what limits Aratus intended to set in the south to Centaur and Argo, and notably to the River Eridanus, which used to flow beneath the Sea-Monster (Cetus), joining the Water poured out by Aquarius. It changed its bed (like the Euphrates, of which it is perhaps the heavenly counterpart), and now has left the Sea-Monster high and dry, while on its ancient banks a chemist’s furnace and a sculptor’s workshop have been set up.

The Celestial Equator of Aratus fails to agree with the Equator of B.C. 2084, not only in passing over the head of Orion, instead of through his belt, as Brown himself points out, but also in running through the eye of the Bull, instead of his “crouching legs alone,” so this part is altogether too far north. The Equator some 1200 years later agreed better here, and equally well elsewhere, except in the opposite part of the sky where it was then too northerly for Aratus, leaving Corvus to the south of the line. Much the same may be said about the tropical circles. Either Aratus was careless, or the globe from which he took his descriptions was incorrect: in any case, there results an uncertainty of many centuries and many degrees in date and latitude.

[16] Epping and Strassmeier, _Astronomisches aus Babylon_, Kugler’s _Babylonische Mondrechnung_, and _Babylonische Sternkunde_. Schiaparelli’s two monographs on Babylonian Astronomy, from which much of the information here given is derived, are chiefly based on these works. ------------------------------------------------------------------------

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.

[Illustration: The Moon-God of Ur. [_To face p. 36._

From a cylinder-seal in the British Museum, dated about B.C. 2400.

Reproduced by permission of the Trustees.]

[Illustration: Fig. 6. The triple star-sign of the Babylonians.]

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, [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.

------------------------------------------------------------------------ [17] King, History of Sumer and Akkad, p. 246. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [18] Schiaparelli, _L’ Astronomia nell’ Antico Testamento_, chap. vii.; Wellhausen, _History of Israel_, chap. iii. ------------------------------------------------------------------------

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,”

------------------------------------------------------------------------ [19] Sayce and Bosanquet identify Dilgan with Capella, not with part of Aries, and consider that a date of about B.C. 2000 is indicated—(_Monthly Notices_ xxxix, 454). But in any case the method of calendar formation is the same. ------------------------------------------------------------------------

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).

------------------------------------------------------------------------ [20] Sayce and Bosanquet understand Capella here also. ------------------------------------------------------------------------

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.

[Illustration: Fig. 7. First Year, normal. New Moon near the Pleiades after sunset on the 1st of Nisan.

The position of the young moon (which always closely follows the sun) showed that the sun was not far west of the Pleiades; and about 1000 B.C. this proved that it was near the vernal equinox. The sun’s position is given for about half an hour after sunset, when the Pleiades would first be visible.]

[Illustration: Fig. 8. Second Year, normal. New Moon not far from Pleiades on the 1st of Nisan.

It takes the sun 365 days to return to the same place among the stars, but the Babylonian year of 12 lunar months (each of 29 or 30 days) was 11 days short of this: therefore on the 1st of Nisan in this year the sun had still 11 days’ march before him ere he returned to the position of Fig. 7. This is equal to about 11°, so the young moon was also about 11° west of her former position, near the Pleiades. But as she travels about 13° eastward every day, she would be near the Pleiades on the following evening, the 2nd of Nisan, so this year was also counted normal.]

[Illustration: Fig. 9. Third Year, “full.” New Moon distant from the Pleiades on the 1st of Nisan.

The sun is now 2 × 11 = 22 days’ march, or about 22°, short of his first position, and the young moon consequently about 22° west of the Pleiades, so she will not come up with them until the 3rd Nisan, after travelling 2 × 13 = 26°. The year was therefore “full,” that is an extra month of 29 days was added, which is more than the 22 days needed to enable the sun to reach his first position by the 1st of Nisan in the fourth year.

It appears, therefore, that the extra month must have been added once in three or four years.]

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]

------------------------------------------------------------------------ [21] If Taurus was originally considered the first constellation of the zodiac, instead of Aries, of which there are some indications, the change may well be explained by this change of method. It does not necessarily imply that the equinox was in Taurus when our zodiac was invented. It was near ω Arietis in B.C. 1000. ------------------------------------------------------------------------

[Illustration: Fig. 10. The Scorpion.

From a boundary stone (now in the British Museum) set up in the reign of Nebuchadnezzar I., king of Babylonia, about 1100 B.C.]

[Illustration: Fig. 11. The Goat, with Fishes’ Scales.

From a Babylonian boundary stone.]

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]

------------------------------------------------------------------------ [22] A Babylonian treatise on astronomy recently published by the trustees of the British Museum supports Kugler’s view that truly scientific methods were not adopted before the sixth century B.C. This treatise formed the subject of a lecture given by Mr L. W. King before the Society of Biblical Archæology on Feb. 19, 1913. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [23] Gen. i. 6, 7; vii. 11.

[24] Ezek. xxxii. 18, 24. ------------------------------------------------------------------------

[Illustration: The Boat of the Sun travelling over the sky. [_To face p. 46._

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, [glyph] which consists of the sign for sky [glyph] 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, [glyph]. 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.

[Sidenote: Homer _c._ 900 B.C.]

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: B.C. 585.]

[Sidenote: 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!

[Sidenote: 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]

------------------------------------------------------------------------ [25] _De Cœlo_ I. 3, and II. 1. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [26] But see note, pp. 75, 76. ------------------------------------------------------------------------

[Illustration: Fig. 12. The Universe according to Anaximander.]

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.

[Sidenote: Anaximenes _c._ 550 B.C.]

[Sidenote: Empedocles _c._ 450 B.C.]

[Sidenote: 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.”

------------------------------------------------------------------------ [27] His life was saved by his illustrious pupil, Pericles, of whom the story is told that on one occasion, just as his army was embarking for an expedition, the sun was eclipsed, and his pilot was terrified. Pericles snatched off his cloak, and held it so as to hide himself from the man’s eyes. “Is that terrible? is that an evil omen?” he cried. “Then do not fear the disappearance of the sun, for it is just the same, only the thing that hides it is larger than my cloak.” ------------------------------------------------------------------------

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.

[Illustration: Fig. 13. The Universe of Leucippus.]

[Sidenote: Leucippus _c._ 450 B.C.]

[Sidenote: 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.

[Illustration: Fig. 14. The Universe of Democritus.]

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.

[Sidenote: 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.

------------------------------------------------------------------------ [28] Some late followers said that Pythagoras, alone amongst men, could hear the music of the spheres. ------------------------------------------------------------------------

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.

[Sidenote: 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.

[Illustration: Fig. 15. The Universe of Pythagoras.]

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.

[Illustration: Fig. 16. The System of Philolaus: night on earth.

Only the side turned away from the centre is inhabited: consequently the Central Fire and Antichthon are invisible.]

[Illustration: Fig. 17. Twelve hours later: day on earth.

Earth has made half a revolution and her outer side is now lighted by the sun, which has only moved about half a degree forward in its yearly orbit. Antichthon has also made half a revolution, therefore remains invisible.]

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?

[Illustration: Fig. 18. Earth and sun according to Heracleides.

In the upper figure it is day, in the lower, night, on the inhabited side of Earth. The sun is on the equator, as at the time of equinox.]

[Sidenote: 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.

------------------------------------------------------------------------ [29] See Heath’s _Aristarchus of Samos_, pp. 187-189 and 251, 252. I very much regret that as Mr. Heath’s book was only published this year, I have been unable to make use of it while writing of early Greek astronomy. I can now only advise any readers who may be interested in my brief sketch of this period to read Mr. Heath’s history, where they will find the opinions of modern writers summarized and discussed, and also the full text (in English) of the most ancient and reliable sources of information. It is a great encouragement to find that my statements are in agreement with his in nearly all essential points, but readers will mark the following important differences:—

1. Anaximander’s heavens are said to have been spherical, not hemispherical, and this seems to be clearly proved by the evidence quoted from ancient writers.

2. Anaxagoras, not Thales, is said to have been the first to explain correctly the cause of solar eclipses and of the moon’s phases, viz. that the moon is an opaque body, shining only by reflected sunlight, and periodically hiding the sun from us when she passes in front of it. Mr. Heath regards the authorship of Anaxagoras as conclusively proved: readers will be able to judge of this from his quotations. Personally they seem to me to prove no more than that Anaxagoras agreed with others on this point, and was the first to express it clearly in writing. It is difficult to see why Mr. Heath denies that Parmenides held the same views before Anaxagoras: Parmenides’ own words seem to prove it, and his theory that the moon was composed of air and fire mingled is rather in favour of it than otherwise. He surely meant that the moon was not wholly bright, like the sun; yet that she had some light of her own must have seemed evident from the faint illumination we see during total lunar eclipses and on the part of her surface not lighted by the sun. (See Dante’s views, p. 402 of this book.)

The connection between her phases and her distance from the sun in the sky is so extremely obvious that I can hardly think the Greeks drew no inference from it until the fifth century B.C., and I cannot see why we should refuse to credit Thales with the discovery attributed to him that her light came in some way from the sun. Gruppe acutely observes that the reason why Thales’ pupil Anaximander did not accept the true explanation of lunar phases and solar eclipses may have been because he felt it necessary to have a theory which would apply equally well to eclipses of the moon; and as he believed in a flat earth he could not advocate the true explanation here. This was why he invented a new theory (viz. that both sun and moon were fire shining through holes in hollow rings, and that the occasional stopping up of these holes caused both lunar and solar eclipses, and also the lunar phases).

But Parmenides had learned the Pythagorean doctrine of Earth’s spherical form, hence he was able to accept the older theory that the moon obtains her light from the sun, and sometimes eclipses the sun by her opaque spherical body, for he could have added that the moon is eclipsed in like manner by the opaque spherical body of the earth.

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.

[Sidenote: 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.

[Sidenote: 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.

------------------------------------------------------------------------ [30] I follow the translation of Jowett. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [31] Compare _Par._ vii. 64-66. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [32] See his famous description of the eight spheres, on each of which stands a siren, singing, while the whole system turns upon a diamond spindle, the end of which rests upon the knees of Necessity. This book was not known in the Middle Ages. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [33] ειλλομενη. ------------------------------------------------------------------------

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.

[Sidenote: 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.

[Illustration: Fig. 19. The spheres of the sun in the system of Eudoxus.

The outer sphere turns on its axis _A A_ in a day and night; the inner on its axis _a a_ in a year, in the opposite direction.]

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.

_Modern Zodiacal Modern_ _Planet. Synodic Period. Value. Period._[34] _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 ”

------------------------------------------------------------------------ [34] The period in which a planet is seen to revolve round the zodiac, and return to the same star, varies greatly, because complicated by its retrograde movements; but if the average of a sufficient number of periods be taken, it coincides for Mercury and Venus with the sidereal year; for Mars, Jupiter, and Saturn, with the period in which each is actually revolving round the sun (its “sidereal period”). ------------------------------------------------------------------------

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.

[Sidenote: 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?”

------------------------------------------------------------------------ [35] Geminus. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [36] This varying velocity is due to the fact that all celestial orbits are not true circles, but ellipses, which was first discovered by Kepler (1609 A.D.). ------------------------------------------------------------------------

4. ARISTOTLE.

[Sidenote: 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.

------------------------------------------------------------------------ [37] _De Cœlo_ II. 10. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [38] Thus, (he adds) time also is threefold, for we have Beginning, Middle, and End. Therefore we apply three to Divine things, and also in common speech we call two “both,” and only say “all” when we reach three, following Nature’s law. The Pythagoreans say “The all and all things are bounded by the number three.”—_De Cœlo_ I. 1. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [39] _Par._ iv. 1-3. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [40] See p. 75, note. ------------------------------------------------------------------------

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.”

------------------------------------------------------------------------ [41] _Conv._ II. iii. 59-65. ------------------------------------------------------------------------

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.

[Sidenote: 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]

------------------------------------------------------------------------ [42] It is also mentioned in a compilation of philosophers’ opinions, probably made in the fifth century A.D. by Stobæus, who is very likely quoting Plutarch. ------------------------------------------------------------------------

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.

[Illustration: Fig. 20. Method of Aristarchus for finding the distance of the sun.]

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.

------------------------------------------------------------------------ [43] See page 101. ------------------------------------------------------------------------

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.

[Sidenote: Seleucus B.C. 160.]

[Sidenote: 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.

------------------------------------------------------------------------ [44] Indian astronomers also refused to accept the doctrine of Aryabhata. Varâha Mihira (sixth century A.D.) says:—“Others maintain that the earth revolves and not the sphere: if that were the case, falcons and other birds could not return from the ether to their nests.” ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [45] Spheres all centring in one point. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [46] Mahaffy, _The Progress of Hellenism in Alexander’s Empire_, p. 119. ------------------------------------------------------------------------

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.

[Illustration: PEKIN OBSERVATORY. [_To face p. 114._

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

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.

------------------------------------------------------------------------ [47] See p. 26. ------------------------------------------------------------------------

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]

------------------------------------------------------------------------ [48] _Almagest,_ Bk. viii. ------------------------------------------------------------------------

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.

[Illustration: A PEKIN ASTROLABE OF THE 13TH CENTURY, A.D. [To face p. 116

_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.

[Sidenote: 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.

[Sidenote: Euclid _c._ B.C. 300.]

[Sidenote: 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]

------------------------------------------------------------------------ [49] Greek _peri_ near, _apo_ away from, _ge_ Earth. ------------------------------------------------------------------------

[Illustration: Fig. 23. The Moveable Eccentric.]

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.

[Sidenote: 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.

[Sidenote: 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.

[Illustration: Fig. 24. The movement of Spica.]

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.

------------------------------------------------------------------------ [50] _Syntaxis_, book VII.; Delambre, _Histoire de l’Astronomie Ancienne_ Vol. II. page 247 (1817 edition). ------------------------------------------------------------------------

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.

[Illustration: Fig. 25. The Sun and the Equinox.]

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.

[Illustration: Fig. 26. The movement of Earth’s axis, which is the true cause of Precession.

_V_ is the vernal equinox, at the intersection of the equator and plane of the ecliptic: _APX_ the earth’s axis, which always preserves the same inclination (23½%) to the plane of the ecliptic. As _APX_ slowly revolves round _T_ in the direction of the arrow, the vernal equinox is gradually shifted to _V_′, and so on.

(_From Young’s “Manual of Astronomy,” 1902._)]

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

[Illustration: Fig. 27. Precession of the equinoxes.]

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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: Cleomedes _c._ 20 B.C.]

[Sidenote: 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.

[Sidenote: 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.

[Illustration: Fig. 28. The Path of Mars among the Stars, 1909.]

[Illustration: Fig. 29. The Epicycle.

Ptolemy’s method of accounting for movements such as those shown in Fig. 28.]

[Illustration: Fig. 30. Planet retrograding, and in opposition (_i.e._ in opposition to the sun.)]

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.

[Illustration: Fig. 31. Venus, Mercury, and the sun.]

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.

------------------------------------------------------------------------ [51] Venus had passed her “inferior conjunction with the sun” on Sept. 15. ------------------------------------------------------------------------

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.

[Illustration: Fig. 32. The sun’s Deferent. (Its eccentricity is exaggerated).]

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.

------------------------------------------------------------------------ [52] It amounts to 5 degrees of longitude in 300 years. ------------------------------------------------------------------------

[Illustration: 1911, July 1. 1912, Jan. 3.

Fig. 33. Apparent Variation in the Size of the Sun. [_To face p 146_

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.

[Illustration: Fig. 34. The moon’s epicycle and deferent.]

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.

------------------------------------------------------------------------ [53] This is evident from the way he treats them, picking up an epicycle or a deferent just as best suits the purpose in hand and explaining sometimes that either would answer equally well. ------------------------------------------------------------------------

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.

[Illustration: Fig. 35. The Ptolemaic system.

The arcs of circles are portions of the deferents which carry round the smaller circles (the epicycles) in the periods named at the side.]

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]

------------------------------------------------------------------------ [54] Taken from the _Almagest_ catalogue, as given in Delambre’s History. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [55] Fifteen stars. ------------------------------------------------------------------------

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 Vega, in Lyra. (Falling Eagle, Lyre Arabic). 3. Aichs (the Goat) Capella (Little Goat, Latin). 4. The brightest star of the Aldebaran. (The follower, Hyades, fire-coloured because following the Pleiades, Arabic). 5. Basiliskos (the royal), on Regulus (Latin equivalent). the heart (of Leo). 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 Fomalhaut. (Mouth of the Mouth of the Southern Fish, Arabic). Fish. 9. The fire-coloured bright Betelgueux. (Shoulder of star on the shoulder Giant, Arabic). of Orion. 10. On the left foot of Orion, Rigel. (Foot of the Giant, common to the Water. Arabic). 11. The last of the River Achernar (Arabic equivalent). 12. The very brilliant star, Sirius (Greek _Seirios_, or fire-coloured, at the _Sothis_, from the Egyptian mouth of the Dog, _Sept_),in Canis Major.[56] called the Dog. 13. Prokuon (the preceding Procyon (in Canis Minor), which Dog), on the thigh of rises before Canis Major. Prokuon 14. Canopos, on the rudder Canopus (an Egyptian god, and (of Argo) a town on the Nile delta). 15. The tip of the right forefoot Alpha Centauri. (of the Centaur).

Altair and Antares were counted as second magnitude, though we now class them among the first.

------------------------------------------------------------------------ [56] Lockyer, _Dawn of Astronomy_, p. 196. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [57] The changing latitudes of the planets, for instance, which gave Ptolemy much trouble, are much more easily explained when it is granted that they partly depend upon Earth’s motion in an orbit whose plane is slightly inclined to the planes of their orbits. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [58] It therefore really approached more nearly the sidereal year, although the cycle was based on the tropical year. ------------------------------------------------------------------------

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.

[Sidenote: 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]

------------------------------------------------------------------------ [59] _De Mon._ II. vii., “Temple Classics” edition. ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [60] _De Senectute._ ------------------------------------------------------------------------

[Sidenote: Ovid B.C. 43-A.D. 17.]

[Sidenote: Virgil B.C. 70-19.]

[Sidenote: Manilius _c._ A.D. 10.]

[Sidenote: 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.

[Sidenote: Strabo born _c._ B.C. 63.]

[Sidenote: Seneca B.C. 3-A.D. 65.]

[Sidenote: Pliny _c._ A.D. 23-79.]

[Sidenote: Proclus died _c._ 480 A.D.]

[Sidenote: Martianus Capella, 5th century A.D.]

[Sidenote: 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!

[Sidenote: 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]

------------------------------------------------------------------------ [61] The _average_ year was the same, 365¼ days, in the old 8-year cycle of the Greeks, and also in the Calippic cycle, which did not come into practical use. The average year of the Metonic cycle was longer, and therefore departed further from the true tropical year. ------------------------------------------------------------------------

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.

[Sidenote: Cosmas _c._ 540 A.D.]

[Sidenote: 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.

------------------------------------------------------------------------ [62] See p. 45.

[63] _Ezekiel_, v. 5. ------------------------------------------------------------------------

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.

[Sidenote: Martianus Capella 5th cent. A.D.]

[Sidenote: Cassiodorus _c._ 530 A.D.]

[Sidenote: 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.

[Sidenote: Charlemagne 732-814.]

[Sidenote: Isidore died 636.]

[Sidenote: Bede _c._ 673-735]

[Sidenote: Fergil, 745.]

[Sidenote: 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.

ARAB ASTRONOMY.

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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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]

------------------------------------------------------------------------ [64] Arabic _gib_ = Latin _sinus_, a fold; _i.e._ the chord folded in two. ------------------------------------------------------------------------

[Sidenote: Alfraganus _c._ 840 A.D.]

[Sidenote: Albategnius _c._ 900 A.D.]

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: Arzachel _c._ 1080.]

[Sidenote: Averroës 1126-1198.]

[Sidenote: Al Betrugi _c._ 1150.]

[Sidenote: 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.

------------------------------------------------------------------------ [65] The Arabian mile was equal to 4000 “black cubits,” and if this is the Egyptian and Babylonian cubit, the values are rather too large, being in round numbers 26,500 and 8,500 English miles, instead of 25,000 and 8000. ------------------------------------------------------------------------

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.”

------------------------------------------------------------------------ [66] The Catalogue of Hipparchus is said to have contained 1080 stars, but Ptolemy’s has only 1022. ------------------------------------------------------------------------

[Illustration: Fig. 36. Method (erroneous) of estimating planetary distances, described by Alfraganus.

The distance _E A_ being known, and _E p_ being assumed equal to it, the distance _E a_ can be calculated from the known ratio _E a_: _p a_.]

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.

------------------------------------------------------------------------ [67] Earth’s diameter, and even Earth’s distance from the sun, is too small a unit. Light, travelling 186,000 miles a second, takes 4¼ years to reach us from the nearest star. ------------------------------------------------------------------------

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. Modern Values._ Sun 5½ 109½ The 15 first-magnitude { Arcturus, Sirius, stars 4¾ { Spica, and others, 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.

------------------------------------------------------------------------ [68] It is impossible to measure the diameter of any star, even with the help of the most powerful telescopes, but in the case of a double star at a known distance the movement of the components as they travel round their common centre of gravity enables us to determine the gravitational force they exercise on each other, and thus their combined mass; and their spectra give some idea of their density. For instance, the mass of the double star Alpha Centauri is nearly twice that of our sun; and as the components appear to be about equal to each other, and both show a spectrum resembling that of the sun, we may conclude that Alpha Centauri consists of two stars, each of which has about the same diameter as our sun. Arcturus has a diameter far greater, some say ten times, some not less than twenty-five times as great as the sun! ------------------------------------------------------------------------

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.

------------------------------------------------------------------------ [69] The mean length of Earth’s shadow (which varies a little with her distance from the sun,) is 857,000 miles, or 216 times her semi-diameter. ------------------------------------------------------------------------

[Illustration: Fig. 37. Earth’s Shadow.]

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.

[Sidenote: 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.

[Sidenote: Nasir-ed-din 1201-1274.]

[Sidenote: 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.

[Illustration: A MEDIÆVAL ASTRONOMER. [_To face p. 200._

_From a painting by Gerard Dow._]

[Sidenote: 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!

[Sidenote: 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.

[Sidenote: Frederick II. 1194-1250.]

[Sidenote: Sacrobosco died _c._ 1256.]

[Sidenote: 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:—

------------------------------------------------------------------------ [70] It was also translated from Arabic into Latin at Toledo, in 1175. ------------------------------------------------------------------------

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.

[Sidenote: 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!”

[Sidenote: 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!

[Sidenote: Albertus Magnus 1193-1280.]

[Sidenote: 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.

_SECOND PART._

THE ASTRONOMY OF DANTE.

I. POPULAR ASTRONOMY IN ITALY IN DANTE’S TIME.

In the first part of this book we have sketched the story of man’s thoughts about the stars, from primitive days until the thirteenth century of our era. We have seen what a wealth of imagination and invention the Greeks brought to bear on the purely empirical science of Egypt and Babylon and Homeric Greece, and how out of all the systems devised by them between 600 B.C. and 100 B.C. one survived, which was completed and expounded by Ptolemy in the second century after Christ in his great _Syntax_ or _Almagest_. Its fundamental principles were that Earth is a sphere, at rest in the centre of the Universe, surrounded on all sides by spherical heavens, and that the movements of all the heavenly bodies are explained by a combination of uniform circular movements.

In the succeeding centuries there were few who could appreciate his work, and during the Dark Ages it was scarcely known in Europe, but was preserved by Nestorian Christians in schools and monasteries of Persia, whence it was unearthed by Mahomedan princes, five centuries after Ptolemy’s death; and when another five centuries had passed it was brought back to Europe, tinged with Oriental thought, and almost immediately became immensely popular among scholars.

Then there arose one of the world’s greatest poets, and, a thousand years after Ptolemy’s death, immortalized his work, writing in a tongue unknown to Ptolemy, and for nations which in his day were only just struggling into existence. As Homer reflects to us man’s primitive conceptions of the Universe, so Dante reflects the ideas of Ptolemy and his school.

And because he lived just at this time he was able to write with perfect confidence, quoting Ptolemy and the Catholic Faith side by side as infallible authorities in astronomy. Had he lived in the early Christian centuries he would have been obliged to choose between classical and orthodox views; had he been born three centuries later, he would have found Copernicus and Galileo ranged against Ptolemy and the Church. Even Milton writing a hundred years after the death of Copernicus, could not make up his mind which system to adopt, and the astronomy of _Paradise Lost_ is a curious jumble of ancient, modern, and transitional ideas. He describes the Primum Mobile as a “firm opacous globe”[71] on which Satan alights and walks about, yet later on tells us that we need not believe in its existence if Earth is turning on her axis;[72] the archangel Raphæl describes to Adam the Creation, at which he was present, yet declares that he himself does not know whether the sun circles round Earth, or Earth round the sun. This the great Architect had wisely concealed from man and angel,

------------------------------------------------------------------------ [71] _Paradise Lost_, II. 418.

[72] _Paradise Lost_, VIII. 34-38.

“perhaps to move His laughter at their quaint opinions wide, Hereafter when they come to model heaven, And calculate the stars, how they will wield The mighty frame, how build, unbuild, contrive, To save appearances; how gird the sphere With centric and eccentric scribbled o’er, Cycle and epicycle, orb in orb.”[73]

[73] _Paradise Lost_, VIII. 77-84. ------------------------------------------------------------------------

Such inconsistencies are not found in Dante’s work, and nothing could have been further from his thoughts than to imagine the Creator mocking at man’s mistakes and ignorance. Like the angelic doctor, Thomas Aquinas, he considered man’s desire for knowledge as one of his highest attributes, and believed that it had been given to him in order to be satisfied.

But before we examine Dante’s writings, it will be interesting to form an idea of the spirit in which astronomy was generally regarded by his fellow-countrymen, and what were his opportunities of studying it.

Dante Alighieri was born in Florence in or about the year 1265, and died in 1321. There can be no doubt that the part of star-lore which appealed most to the general public in Italy at this time, educated and ignorant alike, was the art of the astrologers. The movements of the heavenly bodies were regarded not merely as omens, but as the actual instruments by which every event on Earth was brought to pass. Every class of plants, every race of animals, was thought to be under the protection of some planet or constellation; so if it was a bad year for certain fruits, or if an epidemic broke out among the cattle, this was because the guardian planet was unfavourably placed, or an evil planet was in the protecting constellation. Floods and drought, prosperity and death, properties of minerals such as the lodestone’s attraction for iron or the emerald’s alleged power of blinding serpents, the instincts of animals and the impulses of men, all were subject to the influences of the stars; and naturally the men who understood and interpreted their movements were held in great repute.

Some of them were unscrupulous quacks, like the one-eyed prophet of Brescia, mentioned by the gossiping friar Salimbene.[74] He “called himself an astrologer and diviner,” and received daily “ten great pennies of silver, and nightly three great Genoese candles of the purest wax” from a political party in Modena, as a recompense for advising them how to act. On one occasion he prophesied a victory for them, but he had little faith in his own words, for being threatened with violence if his prophecy should fail, he “carried off all that he had gained and went his way without saluting his hosts.” “Then,” adds the friar, “the men of Sassuolo began to mock them, as men who sacrifice to devils and not to God, as it is written in Deuteronomy.”

------------------------------------------------------------------------ [74] All quotations from Salimbene’s Chronicle are taken from Coulton’s _From Saint Francis to Dante_. ------------------------------------------------------------------------

But most of these men, like Asdente of Parma, sincerely believed in their own ability to foretell events, and they usually combined some other favourite forms of soothsaying, as well as a little alchemy, with astrology. Asdente is described by Salimbene as “a poor working cobbler, pure and simple, and fearing God, and courteous and urbane; illiterate, but with great illumination of mind.” His proper name was Master Benvenuto, but he was “commonly called Asdente, that is, toothless, by way of contrary, for he hath great and disordered teeth and an impediment in his speech, yet he understands and is understood well. He dwells at the bridge-head of Parma, hard by the city moat and the well, along the street which goes to Borgo San Donnino.” This humble prophet was said by Dante to be the best known citizen of all Parma (_Conv._, IV. xvi. 65-71): he was asked to dinner by a bishop, and consulted by the warring factions of Reggio and Parma. He was said to have foretold the death of two popes, and a naval defeat of Pisa by Genoa.

The greatest generals of the day governed their tactics by the advice of astrologers who regularly accompanied them to the field and the camp. The famous Ghibelline, Guido of Montefeltro, who is called by Villani the cleverest soldier of his times[75] retained Guido Bonatti[76] in his service and was believed to have gained his great victory at Forli (in 1282) through the advice of this astrologer. Bonatti is diversely described as a tiler and a lawyer, but whatever his original occupation may have been he found that the position of private astrologer brought him both more fame and more money. He wrote a book on Judicial Astronomy, and Vincent de Beauvais describes him as celebrated throughout the western world for his knowledge of the art.

------------------------------------------------------------------------ [75] _Croniche Fiorentine_, Bk. VII. par. 80.

[76] _Inf._ xx. 118. ------------------------------------------------------------------------

But Bonatti’s fame was faint and fugitive compared with that of the wizard Michael Scot. He is one of the picturesque figures of the thirteenth century, round whom so many legends have gathered that the facts of his life are difficult to glean. It seems that he was born in Fifeshire of a noble Scottish family, at the end of the twelfth or beginning of the thirteenth century, that he studied in Oxford and Paris, and then spent some time in Toledo. Here he learned Arabic, and probably also astrology, for it was so commonly practised there, especially among the Arabs and the Jews, that it was sometimes called the Toletan art. Afterwards he went to Germany, and was discovered by Frederick II., who took him to Italy. His great learning earned the admiration of Pope Gregory IX., who speaks of him quite affectionately in a letter to the Archbishop of Canterbury; and it is said that Honorius II. would have liked to make him an archbishop. But Sir Michael the Scot found Frederick’s court more congenial. The Emperor, who was himself a poet, was a munificent patron of literature and art, and attracted to himself men of talent from all parts of the world. The culture of both East and West met at that brilliant Sicilian court[77] which was his for fifteen years before the title of Emperor was added to that of King of Naples and Sicily. Indeed it was his “fellowship with Saracens”[78] which was one great reason for the accusation of heresy on account of which Dante placed him among the Epicureans in the _Inferno_. He knew Arabic, as well as French, German, Italian, Latin, and Greek. Michael Scot’s acquaintance with Moorish literature and language was a bond of sympathy between them; he became astrologer to Frederick, and at the Emperor’s wish he superintended a new translation of Aristotle’s works from Arabic into Latin. His taste for astronomy is evidenced by the fact that out of these he chose to translate the _De Cœlo_ himself.

------------------------------------------------------------------------ [77] _V. E._, I. xii. 20-35.

[78] Villani, _Croniche Fiorentine_, VI. 1 and 24. ------------------------------------------------------------------------

An absurd story is told by Salimbene about Frederick and Michael Scot, which, however, shows what was believed of his capabilities as an astronomer. The Emperor one day asked him, when they were in the palace together, how far they were from the sky, and the astrologer told him the distance. They then took a long journey together, during which the palace was secretly lowered, and on their return Frederick asked casually whether the sky could really be so distant as Michael had said. “Whereupon he made his calculations, and made answer that certainly either the sky had been raised or the earth lowered; and then the Emperor knew that he spake truth.”

Michael Scot is said to have warned Frederick that he would die in Florence, for which reason the Emperor would not enter that city; but having thoughtlessly gone to a town called Florentiola he died there; “for this,” adds the historian, “is almost always the way, the devil tricks one by a play upon words.” It is curious to contrast this remark, attributing Michael’s prophecy to the evil powers, with Salimbene’s quotation from him, in exactly the same spirit as if he were quoting from an Old Testament prophet:—“that the word of Michael Scot may be fulfilled in them, which he wrote in his verses wherein he predicted the future, ‘And the factions at Reggio shall hold ill words together.’” The same author brackets him with others who have foretold the future, in a list which reads curiously to us—“Abbot Joachim, Merlin, Methodius and the Sybil, Isaiah, Jeremiah, Hosea, Daniel, and the Apocalypse, and Michael Scot who was astrologer to the deposed Emperor Frederick II.”

Besides these prophetic verses, Michael wrote several books which treat almost exclusively of astrology, alchemy, and other occult “sciences,” and even in the fifteenth century it was said that his magic books could not be opened without danger, because of the fiends who were thereby invoked! He seems to have returned to his native Scotland to die, but the date is very uncertain. We do not know whether Dante’s picture of him is drawn from memory, or hearsay of some who had seen the lanky Scotsman among the southerners, by nature taller and thinner than they, and worn by his prolonged studies.

“Quell’ altro che ne’ fianchi è così poco Michele Scotto fu, che veramente Delle magiche frode seppe il gioco.”[79] (_Inf._ xx. 115-117).

------------------------------------------------------------------------ [79] “That other, round the loins So slender of his shape, was Michael Scot, Practised in every sleight of magic wile.” _Carey._ ------------------------------------------------------------------------

It was perhaps the winning personality or the prudence of the canny Scot which enabled him to bring a brilliant career to a peaceful close, favoured by the Church as well as by the excommunicated Emperor, although his studies were of so dubious a nature, and he was intimate with heretic Mahomedans and Jews. Cecco d’Ascoli was not so fortunate. This learned Italian received the high and honoured post of professor of astrology in Bologna, where he lectured and cast horoscopes for his students. He was well versed in natural science, but the shady side of astrology had a fatal attraction for him: he fell under suspicion as a sorcerer, was condemned, and burned at the stake in Florence in 1327 (six years after Dante’s death).

The reputations achieved by these and other thirteenth-century astrologers in Italy, belonging to such different ranks of life, show what an immense importance was attached to their art by the general public. Yet we shall be greatly mistaken if we think that it was only to acquire skill in this fascinating pursuit that men thronged to hear Cecco lecture, or pored over Latin manuscripts. The intense ardour for knowledge which marks this period made them eager to understand the world around them and the sky above their heads.

[Illustration: ASTRONOMY.

_From a fresco in the Spanish Chapel of Santa Maria Novella, Florence._

[_To face p. 217._}]

It would be a shame, writes one, to live in a house and not know how it is built or what shape it has, never to examine the walls, and floors, and ceilings, nor to consider the use of the wooden beams used in its construction. In like manner we should not be content without understanding the form and structure of the Universe in which we live. Man, with his upright attitude and his head held high, unlike the animals, was designed by his Creator to look and listen, to know and comprehend this marvellous Universe, and especially that noblest part of it above him, the heavens and their wonderful movements. For thus alone can he learn to know God Himself, the great Architect of the World.

In writing thus, Ristoro, the monk of Arezzo, was not only echoing the thoughts of Plato and Cicero, he was expressing the feeling for astronomy as a noble and elevating study which was general among thoughtful men of his time. It was expressed also in contemporary art. Visitors to the “Spanish Chapel” in the cloisters of a Florentine church will remember seeing on the frescoed walls the figure of Astronomy as she was personified in Tuscany in the fourteenth century. She sits among her peers, the sciences of the Trivium and Quadrivium, the only one who wears a crown; her fair hair frames a spiritual face, one hand is lifted heavenwards, the other holds a celestial sphere, on which the broad band of the zodiac crosses the “equator of the day.” At her feet sits a kingly figure in flowing robes, also crowned, and with a face of singular beauty and refinement; he gazes up into the skies with a rapt expression, and on his knee is a book in which he writes what he sees.

This nameless figure was identified doubtfully by Ruskin as Zoroaster, who was considered by many as the inventor of astrology, but surely it can be no other than Ptolemy with his _Almagest_. For Ptolemy, the prince of astronomers, was often and naturally confused with the royal race who had patronized astronomy at Alexandria; as for instance by Omons, a thirteenth-century writer, who says in his _Image du Monde_ that “Ptolemy king of Egypt” wrote the _Almagest_. The curious mode of dressing the hair and beard may have been thought by the artist to represent an ancient Egyptian fashion.

Ptolemy, we know, was universely acknowledged at the time to be “Master of Astronomy,” as Brunetto Latini calls him. His _Almagest_ was only known indirectly, but it was believed to contain all that could be known about the movements and the nature of the heavens. Some minor additions and corrections had been made, as we have seen, by the Arab astronomers, but the system was accepted as a complete and satisfactory explanation of all celestial phenomena. Hence no professional astronomer was expected to make discoveries; he was simply well versed in the work of those who went before him, skilful in the use of a few simple instruments and tables, and practised in applying the principles of astrology.

A general notion of the Ptolemaic system was widely diffused. For those who could not read Latin there were encyclopædic works written in the vernacular and in a popular style, such as the _Trésor_ of Brunetto Latini, and these always contained a section on astronomy. The average educated man probably had only vague ideas about epicycles and eccentrics, and perhaps had never heard of the Arab estimates of the sizes of the planets; but he would know that astronomy taught that Earth is a globe, motionless at the centre of the universe, and smaller than any of the stars; he would know the names of the seven planets (including among these the sun and moon), and probably also their colours, their periods, and their astrological significance; the zodiacal constellations would be familiar, especially as they were often used decoratively; and he would believe that stars and planets are set in crystalline transparent spheres.

Moreover, he would often be more of an astronomer than he knew, for he would learn almost unconsciously many things of which modern men are ignorant. The ill-lighted streets and the dangers of night journeys would force him to be better acquainted with the motions and phases of the moon than most of us are to-day; he would know when and where to look for different stars; and the want of a watch would make it necessary for him to be able to take his time from the sun at any season of the year. He could, however, sometimes consult a sundial on a church wall or in a private garden, and the church chimes rang out at tierce, and nones, and vespers. These were heard at intervals which were much longer in summer than in winter, for the system of “temporary hours” was used by the Church, and the service of tierce was held halfway between sunrise and noon (or nones), and vespers was halfway between noon and sunset.

_II. DANTE’S STUDIES._

DANTE’S STUDIES.

Dante was far above the level of the average educated man. Not that his scientific ideas were in advance of his age: on the contrary, one special interest that they have for us is that they illustrate, like his political and religious views, the beliefs and feelings of the period. His authorities were the authorities of all, but he had studied them and made their thoughts his own, as few others did, except some churchmen and professed scholars. The extent and depth of his reading is evident from his own writings, and his great learning is noted with admiration by all his biographers. Giovanni Villani, in the earliest account we possess of Dante, says that he was “a great scholar in almost every branch of learning, although he was a layman.” Boccaccio would have us believe that while still a child, so young that he might be expected to spend his time playing with other children or sitting on his mother’s knee, he gave the whole of his time to reading and learning. Lionardo Bruni, however, assures us that though he was an ardent student, and showed unusual powers at an early age, he by no means tried to “sever himself from the world, but living and moving about amongst other young men of his age, he approved himself gracious and skilful in every youthful exercise.” It was wonderful, he says, how Dante maintained all his social and civic intercourse while he pursued his studies so fervently.

In truth, the poet’s troubled life was far removed from that life of calm retirement which one thinks suitable for a scholar. In his early youth he experienced a passionate love and sorrow; a year before the death of Beatrice he was fighting for Florence in the great battle of Campaldino, nor was it the first time he had borne arms; in 1296 he spoke in the council of the Hundred; in 1300 he was ambassador for the Tuscan League to San Gemignano, and was elected to the highest office a citizen could hold in his native city, that of Prior; in 1301 he was ambassador to the Pope in Rome, and in the year following he was exiled. After this he was always wandering, often in great poverty, dependent on first one patron and then another, always hoping that some turn of affairs would restore him to Florence, always taking a keen and active interest in Italian politics, until he died, still in exile, at Ravenna. Add to this the difficulties common to all scholars of his day, viz. absence of printed books, public libraries, and journals, etc., and we must marvel how he ever found the opportunities and the serenity of mind for his prolonged studies.

Boccaccio adds another obstacle—his wife! To console him for the death of Beatrice, his friends and relatives persuaded him to marry a wife of their choosing with melancholy results:—

“Dante formerly had been used to spend his time over his precious studies whenever he was inclined, and would converse with kings and princes, dispute with philosophers, and frequent the company of poets.... Now, whenever it pleased his new mistress he must at her bidding quit this distinguished company, and bear with the talk of women, and to avoid a worse vexation must not only assent to their opinions, but against his inclination must even approve them. He who, whenever the presence of the vulgar herd annoyed him, had been accustomed to retire to some solitary spot, and there to speculate on the motions of the heavens, or the source of animal life, or the beginnings of created things, or may be to indulge some strange fancy, or to compose somewhat which after his death should make his name live into future ages, he now, as often as the whim took his new mistress, must abandon all such sweet contemplation, and go in company with those who had little mind for such things.”[80]

------------------------------------------------------------------------ [80] Boccaccio’s _Vita di Dante_; Translation from Toynbee’s _Dante Alighieri_ (Oxford Biographies), pp. 92, 93. ------------------------------------------------------------------------

However, after a long tirade against wives, Boccaccio owns that as far as concerns Dante the picture is entirely imaginary. He believes the marriage was an unhappy one, because after his exile Dante and his wife never met again, but we have no evidence whatever that while they were together their life was as Boccaccio depicts it. Doubtless family life and the care of four children interfered to some extent with Dante’s studies, but the one detail Boccaccio affirms as fact among his fancies, namely that the poet refused for nineteen years to see his wife, seems rather to imply that one thing poor Gemma did know how to do was to leave her husband in peace when he did not desire her company.

When and where Dante began to study astronomy seriously it is not easy to say. His favourite study in his youth was poetry, but his parents (says Bruni) gave him a good general education, engaging such teachers as could be found in Florence, where as yet there was no university. But seeing how clever the boy was, his relatives and friends helped and encouraged him, and among the latter Bruni mentions Brunetto Latini.

This famous Florentine was a very learned lawyer, who during Dante’s infancy and boyhood held high offices of state in the city. It is not possible, therefore, that he should have had pupils at this time, and he cannot have been Dante’s master in any strict sense of the word, as Vasari affirms, and as many commentators have assumed on the strength of the moving interview between these two in the _Inferno_.[81] Dante’s affectionate greeting mingled with reverence, and the fatherly solicitude of Brunetto, suggest just such a connection as Bruni indicates. The elderly man had taken an interest in the budding genius of the boy, and had held inspiring conversations with him from time to time on serious subjects, and by his own example had encouraged the youth to win fame through his pen. For Dante was no doubt well acquainted with Brunetto’s _Tesoretto_, and his more ambitious and voluminous _Trésor_, which Brunetto specially commends to his care.[82] This was a compendium of knowledge, a small part of which was devoted to the elements of astronomy, and it may well be that this short epitome was Dante’s first introduction to the science.

------------------------------------------------------------------------ [81] _Inf._ xv. 23 _et seq._

[82] _Inf._ xv. 119. ------------------------------------------------------------------------

Some have thought that Brunetto’s advice to Dante to follow his star “Se tu segui tua stella ...,”[83] indicates that he had cast the poet’s horoscope; but there is no evidence that Brunetto had ever practised astrology, or even that he took special interest in it above other branches of learning.

------------------------------------------------------------------------ [83] “If thou follow thy star,” _Inf._ xv. 55. ------------------------------------------------------------------------

Villani and other biographers tell us that after his banishment from Florence, therefore in middle age, Dante went to the University at Bologna, but they seem to have made this statement rather because of its probability than because they knew it for fact. It is, however, quite possible that he spent a couple of years there, between 1304 and 1306. He probably left his “primo rifugio”[84] at Verona when Bartolommeo della Scala[85] died in March 1304, and we know nothing of his whereabouts till August 1306, when he was in Padua, as is proved by a fifteenth century document.[86] Now in 1306 a number of Ghibelline students and professors left Bologna for Padua; and we know that Dante had friends among the Bolognese professors, for later on he seems to have corresponded with Cecco d’ Ascoli,[87] and Del Virgilio entreated him to come and receive the laurel crown, an invitation which the poet refused in one of his Latin Eclogues. Bologna and the Bolognese are referred to several times in Dante’s works, and the friar Catalano is no doubt alluding to the school of theology at the University when he says in _Inf._ xxiii. 142-144 that he used to hear at Bologna much about the wickedness and the lies of the Devil. One vivid passage can hardly be anything but a personal reminiscence of the Carisenda, the leaning tower at Bologna. The poet compares his fear when he saw the giant Antæus stooping over Virgil and himself to the sensation of looking up at the Carisenda from beneath the leaning side, when a cloud is passing over it, and the spectator feels that the tower is about to fall upon him.[88] (The tower was much higher in Dante’s day than it is now, part having been pulled down in the middle of the fourteenth century).

------------------------------------------------------------------------ [84] “First refuge,” _Par._ xvii. 70.

[85] _Par._ xvii. 71, 72.

[86] Imbriani, _Dante a Padova_.

[87] “_Torno a Ravenna e de lì non mi parto_ (I am going back to Ravenna, and shall not leave it again), is a line in the _Acerba_ which Cecco d’ Ascoli puts into the mouth of Dante, as though from a letter written to himself from the divine poet at the time” (about the year 1319). _Dante and Giovanni del Virgilio_, by Wicksteed and Gardner, p. 84.

[88] _Inf._ xxxi. 136-141. ------------------------------------------------------------------------

The University at Padua was also famous, and as it was originally an offshoot from Bologna and modelled on the same plan, it is sure to have included astronomy in its curriculum. But Dante does not seem to have stayed here more than a few months.

There is also a tradition that he went to Paris, the greatest intellectual centre of his times, and that he himself heard those lectures of Sigieri, the philosopher, in the Street of Straw, of which he makes mention in _Par._ x. 137. This is possible, but quite uncertain; the allusion to Sigieri is no proof, since it has lately been discovered that he died in Italy, and his story was well known there.

After sifting all the evidence available, we can only echo Boccaccio, and say of Dante that “As it was at divers ages that he studied and learned the divers sciences, so likewise it was at divers places of study that he mastered them under divers teachers.”

_III. BOOKS ON ASTRONOMY USED BY DANTE._

BOOKS ON ASTRONOMY USED BY DANTE.

We shall probably be right if we conclude that Dante’s knowledge of astronomy was principally gained from independent reading, and from conversation and discussion with learned men. Like a true scholar, he was learning all his life, for in the _Paradiso_ he corrects the opinion expressed earlier in the _Convivio_ about the origin of the markings in the moon.

Boccaccio’s description of his planning out a course of study and attacking some subjects alone in his youth agrees with his own account of his lonely struggles with Latin authors;[89] and it is quite credible that he suffered heat and cold, and went without food and sleep in his eagerness to learn, since he himself mentions quite casually that at one time he injured his sight by constant reading, so that the stars appeared blurred to him, until by rest and bathing with cold water it became strong again.[90]

------------------------------------------------------------------------ [89] _Conv._ II. xiii. 22-26.

[90] _Conv._ III. ix. 146-157. ------------------------------------------------------------------------

His diligence must have been great, and his memory wonderful, judging from the numerous quotations from classical and contemporary authors to be found in his writings. They seem to be chiefly from memory, and it is not likely that he can often have had many books by him when writing. If he gives a reference it is often a vague one, and occasionally wrong: his authorities on astronomical questions are sometimes “the mathematicians,” “the astrologers,” or “the sages of Egypt,” by whom he means the Alexandrian astronomers.

One does not, of course, expect mediæval writers to verify their references, or to have our modern scruples about quoting other authors without acknowledgement: in those days they were only too glad to get their information wherever they could, often at second or third hand, and to make it their own by storing it in their memories. Nevertheless, from a careful study of Dante’s direct quotations, and his allusions and reminiscences, which are sometimes unconscious, a good idea may be gained of his range of reading, and of the books and authors on whom he chiefly relied for his astronomical data.

His supreme authority was of course Ptolemy. But it would only be by a rare chance that he could see the _Almagest_, even in a translation, and all the evidence that we can find in his own writings points to its being entirely unknown to him. On each of the three occasions that he quotes Ptolemy’s opinion on subjects dealt with in the _Almagest_ he is wrong: once it is Ptolemy’s view on the physical nature of the Galaxy,[91] as to which none had been expressed, although its appearance was carefully described; in another case he implies that Ptolemy discovered precession, and says that he added a ninth heaven to account for it,[92] and this double mistake was apparently copied from Albertus Magnus or Averroës.[93] As we know, it was Hipparchus who discovered precession, and Ptolemy gives him the credit for in the _Almagest_; it was the Arabian astronomers who added the ninth sphere.

------------------------------------------------------------------------ [91] _Conv._ II. xv. 73-77.

[92] _Conv._ II. iii. 36-52, _V. N._ xxx.

[93] Averroës, in his commentary on Aristotle’s _De Cœlo_, says that the ancients believed the eighth, or starry, heaven, to be the outermost, but that Ptolemy assumed a ninth, “because he said that he had discovered a slow motion along the signs of the zodiac in the fixed stars.” Albertus Magnus, in his _De Cœlo et Mundo_, Book II., says also that the ancients, including Aristotle, believed that there were only eight heavens, but that Ptolemy, so far as he can understand, believed in ten, on philosophical not mathematical grounds (compare _Conv._ II. iii. 40, 41). Albertus accepted the theory of “trepidation,” and thought this was the only movement which ought to be assigned to the star sphere; there remained, therefore, two motions, which affect all the planetary spheres and the star sphere, for which two more spheres must be assumed, a ninth sphere for precession, and a tenth, the primum mobile, for the diurnal motion. Outside all was the Empyrean. Dante never mentions trepidation, and evidently did not believe in it: he needed only nine moving spheres, therefore, but counts the Empyrean as a tenth heaven. ------------------------------------------------------------------------

On the other hand Dante quotes twice quite correctly from the _Tetrabiblios_, which was more widely known.[94] He may, therefore, possibly have read it, and he alludes to it in the _Convivio_, though by a curious slip he does not give its name, thinking he has done so already: “Tolommeo dice nello allegato libro....”[95] This is in the fourteenth chapter of the second treatise, but so far from having just quoted any special work by Ptolemy he has said nothing at all about him since the third chapter, and then it was only his opinion and name that were mentioned. I have not been able to trace the quotation given in the _Quæstio de Aqua et Terra_ (xxi. 29-31), where Ptolemy is said to have asserted that things on earth resemble things in heaven, but this probably comes also (or was supposed to come), from the “judicial astronomy” of the _Tetrabiblios_. It is not taken from the _Almagest_.

------------------------------------------------------------------------ [94] _Conv._ II. xiv. 198-202. _Ibid._ 249-253.

[95] “Ptolemy says in the book above cited.” ------------------------------------------------------------------------

The elements of Ptolemy’s system, however, could be learned indirectly, and it seems that Dante had recourse to the excellent epitome of the Arab astronomer Alfraganus. It is true that his name is only mentioned once, and his book once; but nearly all Dante’s astronomical data appear to have been taken from him, and his very expressions are sometimes repeated.

One of the most striking examples of borrowing from the _Elementa Astronomica_ of Alfraganus occurs in the _Paradiso_, where Dante likens twenty-four spirits to as many brilliant stars.[96] He makes up the number by taking fifteen specially bright stars from different parts of the sky, and adding to them the stars of Ursa Major and two stars of Ursa Minor. The seven chief stars of Ursa Major are well known, but Beta and Gamma Ursæ Minoris are not conspicuous nor specially familiar; and why, if he takes fifteen unnamed, should he name any of the twenty-four? Turning to chapter 19 of Alfraganus’ book, we find that he follows Ptolemy in enumerating fifteen first-magnitude stars in different parts of the sky, and then he gives as examples of the second magnitude (_i.e._ next in brightness) Benet Naax and Alfarcatein, Arab constellations which correspond with the tail of Ursa Major, and Beta and Gamma of Ursa Minor.

------------------------------------------------------------------------ [96] _Par._ xiii. 1-13. ------------------------------------------------------------------------

There is no reason to suppose that Dante knew Arabic, but there were several versions of Alfraganus in Latin, and it is even possible to determine with some certainty which of them he used. Speaking of the movements of the planet Venus, he says that they may be found, summarized from the best demonstrations of the astrologers, in the _Book of the Collection of the Stars_:—

“Li quali, secondochè nel _Libro dell’ Aggregazione delle Stelle_ epilogato si trova, dalla migliore dimostrazione degli astrologi ....” (_Conv._ II. vi. 133-136).

Although the usual name for the book of Alfraganus in Latin was _Elementa Astronomica_, the version for which mediæval students were indebted to the indefatigable translator Gerard of Cremona bears in the MSS. the title _Alfragani liber de aggregationibus Scientiæ Stellarum et de principiis cœlestium motuum_. It is this book, therefore, that Dante means, though he has translated the title somewhat inaccurately.[97]

------------------------------------------------------------------------ [97] See Schiaparelli’s letter in Lubin’s _Dante e gli Astronomi Italiani_. The name is, however, also used as a sub-title in the printed edition of Christmann, Frankfort, 1590, which was based not on the translation of Gerard but of Johannes Hispalensis of Seville; and Toynbee thinks that this Frankfort edition represents most nearly the version of Alfraganus used by Dante. It is the only one of the five printed editions which gives the same figure for the diameter of Mercury as that quoted by Dante. See Toynbee, “Dante’s Obligations to Alfraganus” in _Romania_ xxiv. 95, and Moore, _Studies in Dante_ iii. p. 3, _note_. ------------------------------------------------------------------------

There were several other books known to Dante from which he must have gleaned information about Ptolemy’s system, but Alfraganus we may regard as his standard reference book. Many versions of Alfraganus are still extant, and it is pleasant to feel that we can hold in our own hands Dante’s text-book on astronomy. The best known is the printed edition of Golius, published in Amsterdam in 1669: it is in both Latin and Arabic, and opening in the middle we may turn the pages backwards to see the beautiful Arabic letters of Alfraganus’ own language, which is written from right to left, or forwards to look at the Latin in which he became known to Dante.

Next in importance to Alfraganus among Dante’s authorities on astronomy was Aristotle. We have seen how overwhelming his authority became in natural science in the second half of the thirteenth century, and how for some time scholars failed to distinguish between the system of spheres devised by Eudoxus, which was the scheme upheld by Aristotle, and the epicycles and eccentrics of Ptolemy. Among all Aristotle’s admirers none was more devoted than Dante: for him Aristotle is not only “Il Filosofo,” the Philosopher _par excellence_, as he was generally called in that age; he is “quello glorioso filosofo al quale la Natura più aperse li suoi segreti,” his intellect was “quasi divino,” and his words are of “somma e altissima autoritade.”[98] Throughout Dante’s own writings his references to Aristotle are so frequent that Dr. Moore observes: “The amount and variety of Dante’s knowledge of the contents of the various works of Aristotle is nothing less than astonishing.”[99]

------------------------------------------------------------------------ [98] “That glorious philosopher to whom Nature most fully revealed her secrets,” _Conv._ III. v. 54-56; “almost divine,” _Conv._ IV. vi. 133; “supreme and highest authority,” _Ibid._ 52.

[99] Moore, _Studies in Dante_ I. (Scripture and Classical Authors in Dante), from which much of the information in this chapter has been taken. ------------------------------------------------------------------------

He does not, however, consider Aristotle infallible as regards the details of astronomy, for in these the philosopher was only following the observers and mathematicians;[100] but in all matters which depend upon first principles, in which Dante would include the form of the earth, Aristotle’s authority may not be called in question.[101] In cosmical physics, such as the doctrine of the four elements, and in meteorology, Dante follows “il mio Maestro”[102] implicitly, and it is also largely from the _De Cælo_ that he gained his knowledge of early Greek speculations regarding the universe.

------------------------------------------------------------------------ [100] _Conv._ II. iii. 19-21.

[101] _Conv._ III. v. 62-65.

[102] “My master.” ------------------------------------------------------------------------

Dante knew little more of Greek than of Arabic. His occasional use of Greek words is enough to prove this—for example when he discusses the Pythagorean theory of “Antictona,” using the accusative as if it were a nominative.[103] In several passages he implies that the language was not known to him, and he distinctly states that he used translations of Aristotle’s works. Here again we are able to identify the versions he used. In _Conv._ II. xv. 59-73 he complains that it is impossible to know what Aristotle believed about the Milky Way, because in the “old translation” he is made to say one thing, and in the “new translation” quite another. From his quotations of these two conflicting opinions, we are able to deduce that the “old translation” was that which Michael Scot made from the Arabic, and the “new translation” that of Aquinas, which was made direct from the Greek.

------------------------------------------------------------------------ [103] _Conv._ III. v. 32. ------------------------------------------------------------------------

He had access, therefore, to more than one Latin translation of Aristotle; and beside this, his quotations seem to have been often taken from commentators and compilers of his own times, especially Aquinas and Albertus Magnus. This was frequently the case with the _Meteorologica_ of Aristotle, for the _De Meteoris_ of Albertus Magnus seems to have been much used by Dante in place of Aristotle’s own work. Dante quotes it by name as _Meteora_ in _Conv._ II. xiv. 169, and also in _Conv._ IV. xxiii. 125-126, where he mentions “Alberto” as the author.

These two, then, the Arab Alfraganus and the Greek Aristotle, were Dante’s chief authorities in astronomy, both in Latin translations.

Besides these, there is evidence in his writings that he was familiar with several classical authors who treated of astronomy. He quotes frequently from many of Cicero’s works, and we find echoes, in two passages, of the _Dream of Scipio_,[104] which he is almost certain to have read, since it was a favourite book in his time. There are several references to Seneca, but the only time that an astronomical phenomenon recorded by him is mentioned[105] Dante is evidently quoting at second-hand from Albertus Magnus. With all the works of Virgil, and with the _Metamorphoses_ of Ovid (from which he took his astronomical myths)[106] he was evidently very familiar; and Lucan is one of his authorities for the position of the earth’s equator. In this case the name of the author and the number of the book are precisely stated.[107]

------------------------------------------------------------------------ [104] _Inf._ ii. 76-78; _Par._ xxii. 134-138.

[105] _Conv._ ii. xiv. 174-176.

[106] Phaëthon, _Conv._ II. xv. 53-55, _Purg._ xxix. 118-120; Latona, _Purg._ xx. 130-132; the Horses of the Sun, _Conv._ IV. xxiii. 134-139, etc., etc.

[107] _Conv._ III. v. 115-117. ------------------------------------------------------------------------

Dante had a great reverence for Plato, whom he calls “uomo eccellentissimo,”[108] and of whom he repeats the mediæval legend that he was a prince who gave up all for the sake of acquiring wisdom.[109] Of his writings he only knew the _Timaeus_, probably the Latin translation and commentary of Chalcidius, which was widely known. Or he may have been acquainted with Aquinas’ commentary, which has since been lost. He also knew something of Plato’s teachings through Aristotle and Cicero, Albertus Magnus, and Aquinas, and perhaps St. Augustine. When he feels obliged to dissent from the great philosopher’s doctrine that the souls of men come from the stars, he does so with reluctance and great gentleness.[110]

------------------------------------------------------------------------ [108] “A man of supreme excellence.” _Conv._ II. v. 21, 22.

[109] _Conv._ III. xiv. 76-79.

[110] _Par._ iv. 22-24, 49-60. ------------------------------------------------------------------------

Among other Greek philosophers who speculated on astronomy, Dante mentions Thales[111] and Pythagoras. The date when the latter flourished he takes (he tells us) from Livy, and his theory that the Universe is governed by the principle of number from Aristotle’s first book of Metaphysics. The astronomical theories of his school are also doubtless taken from Aristotle. Dante tells the story of Pythagoras that he was the first man to be called “philosopher,” because when asked if he considered himself a wise man, he replied, “No, but only a lover of wisdom.”[112] Dionysius the Academician and Socrates are referred to for their opinions on the influence of the stars upon human souls;[113] and Anaxagoras and Democritus for their galactic theories,[114] which Dante obtained from Albertus Magnus.

------------------------------------------------------------------------ [111] _Conv._ III. xi. 39; _Inf._ iv. 137.

[112] _Conv._ III. xi. 22-33; II. xiv. 144-147; III. v. 29-44; III. xi. 41-47.

[113] _Conv._ II. xiv. 34, 35.

[114] _Conv._ II. xv. 56. ------------------------------------------------------------------------

Except for Alfraganus, Dante refers but seldom to Arab astronomers. He does not seem to have known Albategnius. The _De Substantia Orbis_ of Averroës is quoted in the _Quæstio de Aqua et Terra_,[115] and it is possible that from this book Dante derived a theory about the moon which he expounds in the _Convivio_. He quotes Alpetragius on circular existence (dependent on the spheres),[116] Avicenna on the Galaxy, and again with Algazel on the influence of the spheres,[117] and Albumassar on meteors.[118] The quotation from the latter, however, is second-hand from Albertus Magnus, and is a mistake, for the passage is not to be found in that astronomer’s works. He was born in Turkestan, in 805.

------------------------------------------------------------------------ [115] _Qu._ xviii. 38, 39.

[116] _Conv._ III. ii. 37.

[117] _Conv._ II. xv. 77, II. xiv. 32.

[118] _Conv._ II. xiv. 170-174. ------------------------------------------------------------------------

We may here remind our readers that the three Latin poets, Virgil, Ovid, and Lucan, were among the world’s five greatest poets met by Dante in Limbo; that next to Aristotle among the philosophers stood Socrates and Plato, and near these were Democritus, Anaxagoras, and Thales, Cicero and Seneca, Ptolemy, Avicenna and Averroës.[119]

------------------------------------------------------------------------ [119] _Inf._ iv. 80, 81, 90, 131-144. ------------------------------------------------------------------------

Among Christian writers, Dante may have gathered some information about ancient Greek speculations from St. Augustine and Peter Lombard; and Orosius, the Spanish friend of Augustine, was his chief authority for that geographical system which, in connection with astronomy, plays an important part in the time-indications of the _Divina Commedia_. Orosius had a great reputation among geographers and map-makers. He had travelled much between Spain, Africa, and Palestine, and he devotes a chapter to describing the different parts of the earth in his history _Adversus Paganos_, which he wrote to prove that Christianity had not injured but benefitted the countries in which it had been accepted. This fifth century geography seems to have been largely based on the first-century geography of Strabo, who quotes Eratosthenes, Posidonius, and Hipparchus among his authorities. Orosius states that the land is entirely surrounded by Ocean, and is divided into three continents—Asia, with the mouths of Ganges in the middle of its eastern coast, Europe stretching vaguely very far to the north-east, and Africa a narrow and long strip from east to west between the Mediterranean and the southern ocean. This chapter is quoted in _De Mon._ II. iii. 87-90 and _Qu._ xix. 43; and Orosius is almost certainly “quell’ avocato dei tempi cristiani,”[120] seen by Dante among the learned doctors in the Heaven of the Sun.

------------------------------------------------------------------------ [120] “The advocate of the Christian centuries.” (_Par._ x. 199). Orosius is also mentioned by name in _Conv._ III. xi. 27; _V. E._ II. vi. 84; and _De Mon._ II. ix. 26. ------------------------------------------------------------------------

The speaker who points him out in these words also mentions his own name and that of the spirit nearest to him:—

“Questi che m’è a destro più vicino Frate e maestro fummi, ed esso Alberto È di Cologna, ed io Thomas d’Aquino.”[121]

------------------------------------------------------------------------ [121] “He who is nearest to me on the right My brother and master was, and he Albertus Is of Cologne, I Thomas of Aquinum.” (_Par._ x. 97-99). ------------------------------------------------------------------------

These two, so near in heaven, had been close companions on earth. The youthful Thomas, son of Count d’Aquino in southern Italy, after six years’ study at the University of Naples joined the Dominican Order, and went to Cologne to learn from Albert, who was also of noble family but born in Suabia on the Danube. Together they went to Paris, together returned to Cologne, but after six more years there their paths separated: Albert rose to be Bishop of Ratisbon; Aquinas, after lecturing in Paris, Rome, and Bologna, became a professor at Naples, and died in Italy in 1274. His master survived him by six years, dying at Cologne at the advanced age of eighty-seven in 1280.[122]

------------------------------------------------------------------------ [122] Toynbee, _Dante Dictionary_; the source also of many other details given in this chapter. ------------------------------------------------------------------------

These two are in the foremost rank among authors of his own time who influenced Dante. He quotes both writers and several of their books by name,[123] and though he never mentions it he was very familiar with the _Summa Theologica_ of Aquinas. To the works of these famous authors he was frequently indebted for astronomical facts, theories, and history, as already noted. Besides this, his reverence for Aristotle, his belief in the essential harmony between religion and science, and his whole attitude towards knowledge, are greatly due to the influence of St. Thomas and his “brother and master,” Albert of Cologne.

------------------------------------------------------------------------ [123] Albert in _Conv._ III. v. 113-115, vii. 26-28; IV. xxiii. 125-6; Aquinas in _Conv._ II. xv. 125-6; IV. viii. 3-6, xv. 125-130, xxx. 26-30; _De Mon._ II. iv. 5-8; and see _Purg._ xx. 69. ------------------------------------------------------------------------

There are also three of Dante’s own fellow-countrymen and contemporaries whose books he is most likely to have read, although he does not mention them:—Brunetto Latini the Florentine, Cecco d’ Ascoli, professor at Bologna, and Ristoro the monk of Arezzo.

Brunetto Latini is only mentioned once in Dante’s works, besides the passage in the _Inferno_ already referred to. In the _De Vulgari Eloquentia_ Brunetus Florentinus is mentioned with admiration as a distinguished man of letters, but blamed with other Tuscans for writing in his own local dialect.[124] Brunetto, who was born in Florence about 1210, was sent on an embassy in 1260 to Alfonso X. of Castile, the learned king under whose guidance the famous astronomical Tables had been drawn up. But on his way back to Florence he was met by the news that the Florentine Guelphs had been defeated at the disastrous battle of Montaperti,[125] and expelled from Florence; and as he belonged to this party he took refuge in France, first at Montpellier and afterwards in Paris. When the Guelphs had regained the ascendancy through their victory at Benevento in 1266 (where Manfred lost his life),[126] Brunetto returned to Florence, and his name subsequently appears in no less than thirty-five public documents as having been consulted by the government of his native city on various important matters. For the most part, moreover, it is recorded that his advice was followed. He died at a venerable old age in Florence in 1294, and was buried in the church of Santa Maria Maggiore.

------------------------------------------------------------------------ [124] _V. E._, I. xiii. 1-11.

[125] _Inf._, xxxii. 81, and x. 85, 86.

[126] _Purg._, iii. 112-129. ------------------------------------------------------------------------

It was while exiled in France that Brunetto wrote the Italian poem _Il Tesoretto_, in which he represents himself as a pilgrim on an allegorical journey; and from this Dante perhaps derived some suggestions for his Vision. The poem is incomplete, and breaks off at a tantalizing point, for Brunetto has just met Ptolemy on Mount Olympus, and has put a question to him: Ptolemy “rispose in questa guisa”[127]—and here the poem ends!

------------------------------------------------------------------------ [127] “Replied after this fashion.” ------------------------------------------------------------------------

In France also he wrote _Li Louvres dou Trésor_, a great compendium of learning, in French prose. The first part treats of the Creation and Biblical history, and of the natural sciences; the second of ethics, rhetoric, and politics. In the section on astronomy which is included in the first part, Brunetto gives a very brief account of Ptolemy’s system, and the sizes and distances of the heavenly bodies as estimated by the Arabs: it seems to be based chiefly on Alfraganus. But beside the periods of the planets he adds in each case their astrological properties, as for instance:—

“Saturnus, qui est le souverain sor tous, est cruex et felons et de froide nature ... Jupiter ... ast dous et piteus et plains de biens.... Mars et chaus et bataillereus, et mauvais, et est apelez Diex de batailles.”[128]

------------------------------------------------------------------------ [128] _Li Louvres dou Trésor_, Chabaille, Paris 1863. ------------------------------------------------------------------------

When speaking of the two principal movements of the skies, he quotes a curious old idea which had been mentioned by Isidore of Seville, that they are in contrary directions because the tremendous speed of the diurnal motion would shake the whole universe to pieces if it were not that the seven planets go as it were to meet it, and soften its vehemence:—

“Li firmamenz court de orient en occident entre jor et nuit une fois, si roidement et si fort que sa pesanteur et so grandor la feroient tout tressaillir, se ne fussent les VII. planetes qui vont aussi comme a l’encontre dou firmament, et atemprent son cours selonc son erre.”[129]

------------------------------------------------------------------------ [129] _Ibid._ ------------------------------------------------------------------------

The _Acerba_ of Cecco d’Ascoli was another encyclopædic work, but in Italian verse. It was very much the fashion in those days to undertake a compilation of all kinds of knowledge, and this was doubtless very useful when few books could be owned by any single reader. Cecco had a considerable knowledge of natural science, and astrology was of great importance in his eyes. Though Dante never mentions him or his work, he can hardly have been ignorant of it, especially as he himself is mentioned in it.

Nor does he mention Ristoro of Arezzo, yet we find many ideas and expressions in Dante’s writings which are also in the _Composizione del Mondo_. Even if he did not borrow from it, the book is worth study by anyone interested in the popular astronomy of the thirteenth century. We learn from the author that he wrote his book in Arezzo, finishing it in the year 1282, that is about thirty years before Dante’s _Convivio_ appeared. The opening words run:—

“Incominiciasi il libro della Composizione del Mondo colle sue cagioni: composto da Ristoro di Arezzo in quella nobilissima città ... etc.”[130]

------------------------------------------------------------------------ [130] “Here beginneth the book of the _Composition of the World together with its Causes_: written by Ristoro of Arezzo in that most noble city.” ------------------------------------------------------------------------

and the closing words are:—

“Compiuto e questo libro sotto li anni di Cristo nel mille dugento ottantadue. Ridolfo imperadore aletto. Martino quarto papa residente. Amen.”[131]

------------------------------------------------------------------------ [131] “Here endeth this book, in the year of our Lord one thousand two hundred and eighty-two. Rudolph Emperor at this date. Martin IV. resident Pope.” Amen. ------------------------------------------------------------------------

We learn further that he was a monk and a native of Arezzo in an interesting passage where he describes a total eclipse of the sun seen by himself from his monastery: the sky was very clear, and it must have been a specially dark eclipse, for besides Mercury he saw many stars; totality lasted for as long as a man could easily walk 250 steps; there was a feeling of chill, and birds and wild animals were so frightened that they allowed themselves to be caught. Fra Ristoro made a calculation and found that on that day sun and moon were in the same position in the sky. It was perhaps this event which induced him to study astronomy.

The extent and depth of Ristoro’s reading evidently bore no comparison to Dante’s, but he was able to sit writing in his quiet cell, day after day, and had such books as he wanted at hand. The monastery seems to have been furnished with astronomical tables, a celestial globe, and the books of Alfraganus and other Arab writers. All these he had studied, and he was something of an observer too. Alfraganus must have been always at his elbow when writing, for he turns to it constantly, quoting (unlike Dante) the chapter referred to:—

“Alfragano pose nell’ ottavo capitolo;” “è testimonio l’Alfragano nelli venti e due capitoli del suo libro;”[132]

------------------------------------------------------------------------ [132] “Alfraganus said in the 8th chapter”; “Alfraganus bears witness in the 22nd chapter of his book.” ------------------------------------------------------------------------

one chapter is avowedly taken whole from Alfraganus, and where the opinions of “il grande Tolommeo”[133] are quoted they are evidently copied from the same source. Other Arab writers are quoted once or twice, for instance, Albumassar,

------------------------------------------------------------------------ [133] “The famous Ptolemy.”

“il quale fu altissimo maestro d’astrologia,”[134]

[134] “Who was a very great teacher of astrology.” ------------------------------------------------------------------------

and several lines are copied from a Latin translation of Algazel,[135] giving some astrological jargon about the twelve zodiacal signs.

------------------------------------------------------------------------ [135] “An Arabian philosopher of Baghdad, 1058-1111.” ------------------------------------------------------------------------

We have already quoted from Ristoro’s preface, showing the high opinion he held of astronomy. But it is disappointing to find that the greatest part of his book is devoted to the “cagioni,” that is, to purely fanciful “reasons,” for all the facts and fallacies concerning nature which he has here brought together.

He gravely argues about the constellation figures as if they were real pictures of animals and things pricked out by nature in stars on the vault of heaven, and not a human convention. He notes their paucity in the southern hemisphere, and that nearly all have their heads towards the north, and from this he draws the conclusion that the northern part of the sky is the nobler, for we can see it is the upper side, just as we know the top side of a book by the position of its letters.

It is for this reason, he thinks, that only the northern hemisphere of the earth contains land and is inhabited. Some, especially the great Averroës, had indeed held that there is inhabited land south of the equator, because the sun goes there. But this is because his movements of recession and approach are necessary to produce the seasons, and hence the growth of plant life, in the north. The constellations are upside down for the south, so they can have no effect there, therefore, there are no animals there (since every race of animals is under the protection of a constellation); therefore no plants, since they exist for animals, and therefore, Ristoro concludes his chain of argument triumphantly, there are no men, and no lands, for land without life would be useless.

Ristoro reproduces Alfraganus’ description of the sun’s movements as seen in different latitudes, quotes him as saying that the equatoral regions are inhabited, and Avicenna that the temperature there is equable because days and nights are always equal. The city Arym which is exactly on the equator has a perfect climate, and as it has two summers and two winters there are two harvests; moreover, all the stars in the sky are visible at the equator; therefore, the best astronomers, and the wisest and richest men, ought to live there, says Ristoro. When writing thus, he seems to have had before him one of the “climate maps” which were common in Europe in the eleventh and following centuries, having been introduced by Arab cartographers, who adopted the idea from Greek maps. For he goes on to point out that the first “climate” is much the longest, and that the others diminish gradually towards the pole, all the “terra scoperta”[136] being thus contained in one quarter of the earth, and having the shape of the moon when we see it half full.[137]

------------------------------------------------------------------------ [136] “The uncovered earth,” _i.e._ not hidden under the ocean.

[137] Bk. VI. cap. xi. ------------------------------------------------------------------------

[Illustration: Fig. 38. The half-moon shape of the habitable earth. (Ristoro).

There is nothing but sea south of the equator, and the habitable earth lies wholly in one half of the northern hemisphere, the other half being sea. The habitable earth, therefore, is the same shape as the half-moon, _i.e._ a quarter sphere.]

The accompanying climate map shows all these features, the famous city Arym—occupying nearly half the space, although it is supposed to be merely on the equator—the seven climates, and the region beyond the seventh, near the north pole, marked as uninhabitable through the cold. The half-moon shape of Earth’s habitable quarter is obvious. The map betrays Arab influence in the orientation, the south being at the top; and Arym, or Aren, was an Arab myth, perhaps derived from the Mount Meru of the Hindus, which is said in the Vedas to be “in the middle of the earth.”

According to Ristoro, the positions of the constellation figures do not only explain why one hemisphere of earth has land and the other none; they also explain the movements of the skies. For the figures of the zodiac face west (those that have faces), and this is why the diurnal movement of the whole heaven is towards the west, so that the constellations may move straightforward, in the natural way. On the other hand, the planets move in the opposite direction because it would not be seemly for them to pass each figure of the zodiac arriving first at the back and moving on to the head. This is the true reason of the contrary direction of the two principal celestial movements. Ristoro does not approve of the solution quoted by Brunetto Latini. He adds that the width of the zodiac was designed to contain the figures of the animals!

After this, we are not surprised to hear that the red colour of the planet Mars is the cause of its martial nature (not the reason for which such a nature is attributed to it). The markings on the moon Ristoro explains by saying that some body must exist in the World which is neither polished and shining all over, like the stars, nor altogether rugged and dark, as the earth was supposed to be, but partaking of both natures; and this body must be the moon, because of her intermediate position between the earth and the nearest of the other planets (Mercury).

[Illustration: CLIMATE MAP, OF ABOUT A.D. 1110. [_To face p. 248._

_Reproduced by permission from Beazley’s “Dawn of Modern Geography.”_]

Of the influence of the heavens on the earth Ristoro has very much to say, from general statements such as that the spheres impress their influence on things of Earth, just as a seal impresses wax, down to details about the births of horses. If the moon is strong in Aries, and Aries is powerful, then, because the moon signifies white among the colours and Aries signifies the head, the horse will be born with a white mark on its head, and if the influence is very strong it will be a beautifully-shaped mark. Again and again he tells us about the various properties and “virtues” of the seven planets, but he does not omit to mention that the powers which move the planets and cause them to influence Earth are spirits, which we call Angels, and the philosophers call Intelligences. These have their several dwelling-places in the spheres, and the nobler their nature the higher is the sphere which they inhabit.

From these quotations the reader may judge of the general trend of the eight books comprised in _La Composizione del Mondo colle sue Cagioni_: we shall have occasion to refer to it again, by way of comparison and contrast, when dealing with Dante’s works in detail.

It is rather curious that there is no trace in Dante’s writings of acquaintance with the great Roger Bacon, or with Sacrobosco, especially as Brunetto Latini knew the former personally, and Cecco d’Ascoli wrote a commentary on the latter, but Dante may have known them, and also the works of Isidore and Bede, who are both mentioned in _Par._, x. 131, as well as other books which are now completely lost. Those we have described above would, however, be enough to supply him with all the astronomical data, except one, which we find in his writings. It is now time to examine these, and see what use he made in literature of the knowledge he possessed.

_IV. ASTRONOMY IN DANTE’S WRITINGS._

ASTRONOMY IN DANTE’S WRITINGS.

If we except the seven _Penitential Psalms_ and the _Profession of Faith_, which are only paraphrases, and are very doubtfully ascribed to Dante, no work of his can be mentioned which does not contain some reference to the heavenly bodies.

When writing the _Vita Nuova_, that story of his love for Beatrice which he calls the work of his boyhood,[138] he was haunted by the sublime idea of the rolling spheres. Beatrice at her first appearance as a little girl of eight, and Beatrice when she died, suggested thoughts of the nine heavens;[139] almost the first words of the book allude to the circling spheres of the sun and of the stars:[140] and the last sonnet soars beyond them all to the Empyrean.[141] Already he seems to have read Alfraganus, for he takes a suggestion which occurs in the first chapter of the _Elementa Astronomica et Chronologica_. Alfraganus there describes the different methods of reckoning days, months, and years, in use among different nations, and gives a special list of the Syrian months with their corresponding Roman months; and Dante, by using the Arabian system of days and the Syrian months, is able to prove to himself that the day and the month when Beatrice died were both at the sacred number of nine.[142] According to our method of reckoning, the time was sunset on the eighth of June, but this was the first hour of the ninth day according to Arabian usage, and our sixth month corresponds with the ninth of the Syrians.

------------------------------------------------------------------------ [138] _Conv._ I. i. 125, 126. Compare _Conv._ IV. xxiv. 1-13.

[139] _V. N._ ii. 9-12, xxx. 13-24.

[140] _V. N._ ii. 1-12.

[141] _V. N._ xlii. 47.

[142] _V. N._ xxx. 1-6. ------------------------------------------------------------------------

Dante had also read at this time Aristotle’s doctrines about the spheres and their Movers, for he quotes from the _Metaphysics_,[143] and this is the work in which they are found.

------------------------------------------------------------------------ [143] _V. N._ xlii. 30. ------------------------------------------------------------------------

Yet a familiarity with Alfraganus and Aristotle so early as this is hardly consistent with the difficulty he says he found in understanding Latin books of philosophy some time after the death of Beatrice.[144] Perhaps the latter part of the _Vita Nuova_ was written a good deal later; or it may be not altogether frivolous to suggest that in his youth Dante had read the first chapters of Alfraganus, which are easy, but did not master the rest of the book till later.

------------------------------------------------------------------------ [144] _Conv._ II. xiii. 22-26. ------------------------------------------------------------------------

Out of his fifty-three short poems (including all in Moore’s Oxford Edition, except those which form part of the _Vita Nuova_ or _Convivio_), twelve, or nearly a quarter, contain some reference to sun, moon, or stars, planets, or spheres; and from these alone we could form some idea of Dante’s acquaintance with astronomy. He speaks of the sun as measuring time,[145] and giving light to the stars[146] (according to the general belief); the moon[147] and each of the planets[148] is mentioned, some of the constellations also,[149] especially with reference to the seasons; the theory of the several heavens and their First Mover,[150] and the supposed influences of the stars and planets are alluded to.[151] These poems were written at different times, and some belong to a much later period than the _Vita Nuova_.

------------------------------------------------------------------------ [145] _Son._ xxxvi. 2; _Canz._ xx. 89.

[146] _Canz._ xix. 117; _Canz._ ix. 16, 17.

[147] _Canz._ xx. 89; _Son._ xxviii. 11.

[148] _Son._ xxviii.; _Canz._ xv. 4, 7.

[149] _Canz._ xv. 3, 29, 41.

[150] _Son._ xxviii. 2.

[151] _Son._ xxviii. _Canz._ xix. 77, _Ball._ vi. 11, 12, _Canz._ xv. 41., _Son._ xxvi. 14. ------------------------------------------------------------------------

It is when we come to examine the _Convivio_, the work of his manhood,[152] that we find the clearest evidence of Dante’s careful study of astronomy. This book was written with the professed intention (as one of its aims) of sharing with others the learning he had been happy enough to acquire—not indeed as one of the guests at the Table of Wisdom, but as one sitting at their feet and gathering up the crumbs.[153] The thread which connects his discourse is a collection of his own Odes, on each of which he had intended to write a treatise or commentary, but the book never advanced beyond the fourth treatise. These Odes were nearly all love-poems, but the poet explains that they are a figurative expression of his devotion to Philosophy, and the whole book is a glorification of the pursuit of knowledge. In the opening sentences, with the reference to Aristotle, the manner of reasoning, the assumptions of our innate desire for absolute knowledge and the bliss brought by its attainment, Dante is the spokesman of his period.

------------------------------------------------------------------------ [152] _Conv._ I. i. 111-113 and 125-127.

[153] _Conv._ I. i. 67-86.

“Siccome dice il Filosofo nel principio della _Prima Filosofia_, Tutti gli uomini naturalmente desideranno di sapere: La ragione di che puote essere, che ciascuna cosa, da providenza di propria natura impinta, è inclinabile alla sua perfezione. Onde, acciochè la scienza è l’ultima perfezione della nostra anima, nella quale sta la nostra ultima felicità, tutti naturalmente al suo desiderio siamo soggetti.”[154]

[154] “As the Philosopher says at the beginning of the _First Philosophy_, ‘All men naturally desire to have knowledge.’ The reason of this may be that everything, being impelled by foresight belonging to its own nature, tends to seek its own perfection. Wherefore inasmuch as knowledge is the final perfection of our soul in which our final happiness consists, all men are naturally subject to the desire for it.” _Conv._ I. i. 1-11. ------------------------------------------------------------------------

And from a study of the _Convivio_ we may learn much of the authors most esteemed, the methods of study pursued, and the results obtained, by thirteenth-century scholars seeking to gain the ultimate perfection of the soul.

Astronomy is frequently introduced, especially in the second and third treatises. The Ode which forms the text of the second treatise is that which is quoted by Charles of Hungary in _Par._ viii. 37—“Voi che intendendo il terzo ciel movete,”[155] and it gives Dante the occasion to speak first of the heaven of Venus, explaining Ptolemy’s system of epicycles, and later of all the heavens in their order, and the celestial bodies contained in them. The ode of the third treatise contains the line “Non vede il Sol, che tutto il mondo gira ...”[156] and upon this he hangs a complete little essay describing the movements of the sun, and how they appear from different parts of the earth, as well as a short dissertation on the question whether it is Sun or Earth which actually moves.

------------------------------------------------------------------------ [155] “Oh ye whose intellectual ministry Moves the third heaven.”—_Carey._

[156] “The sun sees not, though circling all the world.” ------------------------------------------------------------------------

The Latin works, _De Monarchia_, _De Vulgari Eloquentia_, the _Eclogues_, and the _Letters_, do not give much scope for astronomical references; yet there are many similes drawn especially from the sun and moon, and the thought of the spheres as instruments of God’s Will in bringing about events on earth is constantly recurring. In the curious work _Quæstio de Aqua et Terra_, Dante argues learnedly about the spheres, the orbit of the moon, and her effect on the tides, and the influences of the stars. The book purports to have been written at Verona in 1320 as the outcome of a discussion in which Dante had taken part as to the respective heights of land and ocean, a problem which had been dealt with by Ristoro d’ Arezzo some forty years earlier. Its authenticity has been questioned, partly under the mistaken idea that facts such as gravity, the spherical form of Earth, and the connection of tides with the moon were not known until much later; but as a matter of fact the discussion is quite in the manner of Dante’s day, and no facts or theories are put forward which he could not have learned from books with which we believe he was acquainted.[157] The internal evidence of his authorship is strong, and belief in it seems to be gaining ground among experts.[158]

------------------------------------------------------------------------ [157] The spherical form of Earth, and the action of gravity at the earth’s surface, were commonplaces with the Greeks, as we have seen in Part I. of this book. Posidonius, Strabo, and other classical writers speak of the tides as following the revolution of the heavens, and having periods similar to those of the moon; Albertus Magnus and Aquinas ascribe them to the influence of the moon, and so does Dante himself in _Par._ xvi. 83.

[158] See Moore, _Studies in Dante_, II. “The Genuineness of the _Quæstio de Aqua et Terra_,” for a complete discussion of the question. ------------------------------------------------------------------------

Finally, the _Divine Comedy_, the work of Dante’s maturity, which took him so many years to write, and for which he had studied ever since he closed the _Vita Nuova_ with the resolve to write more worthily one day of Beatrice,[159] focuses in one unique and finished work the thoughts and ideals, the knowledge and fancies, of the poet and his age. The subject of the poem, taken in its literal sense, is cosmical, for it describes a journey in which the author penetrates to the centre of the universe, and passes from planet to planet until he reaches the outermost sphere. Moreover, the journey is assumed to take a definite space of time, and the passing of the hours by day and by night is indicated by the successive positions of sun or stars, and the phases and movements of the moon. The _Divine Comedy_ contains more than twice as many allusions to the heavenly bodies as all the other works of Dante put together.

------------------------------------------------------------------------ [159] _V. N._ xliii. 3-7. ------------------------------------------------------------------------

But we must discriminate in drawing conclusions from these astronomical references so freely distributed in all Dante’s writings. If he wrote the _Quæstio_, it is his only professedly scientific work, written for scientific men, and astronomy is only brought in incidentally. The _Convivio_, in which astronomical facts and theories are set forth in much greater detail and fulness than elsewhere, was a popular work meant for those who had no inclination, or else no opportunity, for prolonged serious studies. We expect, therefore, that technical details will be avoided. Still more will they be omitted in the _Divine Comedy_ and other poetical works, where difficult problems and pedantical accuracy would be most unsuitable. We can _infer_ the knowledge which lay in Dante’s mind, behind his popular use of it in literature; and we can often find an explanation in the prose of the _Convivio_ for a slight allusion in the poetical works; but we must not deal with any as if they were text-books, and set forth precisely and completely all that Dante knew of his favourite science. It is the poet’s artistic use of the astronomy of his day which merits our admiration quite as much as the scholar’s proficiency.

This being premised, we may now proceed to quote from his works, showing how he has dealt with first the facts, and secondly the theories, of astronomy. Finally we shall be able to form a clear mental picture of the universe as it was believed to exist by Dante, and not only by his contemporaries but by his successors for many generations.

_V. OBSERVATIONAL ASTRONOMY._

“The heavens declare the glory of God; and the firmament sheweth His handy-work. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language where their voice is not heard. Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun; which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race.”

1. MOVEMENTS OF THE MOON.

Of all the seven sciences of the Trivium and Quadrivium, Astronomy, Dante thought, was the noblest, and for two reasons. Aristotle had said that a science is noble in proportion to the nobility of its subject, and the certainty of its conclusions; and in both of these Astronomy excels. Its subject is the Movement of the Heavens, and its certainty is perfect. “E nobile e alta per nobile e alto suggetto, ch’è del movimento del cielo: è alta e nobile per la sua certezza, la quale è senza ogni difetto.”[160] If astronomers are sometimes mistaken, the fault lies in them, as Ptolemy said, and not in the science.

------------------------------------------------------------------------ [160] _Conv._ II. xiv. 244-217. “It is noble and lofty because of its noble and lofty subject, which is the movement of the heavens; it is lofty and noble because of its certainty, which is without flaw.” ------------------------------------------------------------------------

This quotation from Ptolemy is from his book on “judicial astronomy,”[161] and it may be that Dante was partly thinking of astrological predictions, as he almost certainly was in the passage that follows, where he adds that astronomy takes a long time to learn, not only because of its great range, but because experience is necessary to form a correct judgment. Nevertheless, it is probable that by its flawless certainty he meant that unchanging laws govern the celestial phenomena, so that they may always be predicted without error when the laws are known.

------------------------------------------------------------------------ [161] See p. 156. ------------------------------------------------------------------------

His definition of astronomy was accurate, for it was not until the middle of the nineteenth century that physical astronomy began to take its place beside the old “astronomy of position,” and in Dante’s day practically the only subject open to research concerning the heavenly bodies was their movements. Of these, and especially the “prime motion” of the diurnal revolution, he was vividly conscious. His favourite name for the heavens is “wheels”—“le ruote magne,” “eterne ruote,” “stellate ruote”;[162] and he often refers to them as a standard of motion. Thus when with Beatrice he was rapt from the summit of Mount Purgatory, to express the swiftness of their flight he says it was almost as rapid as the movement of the sky—“veloci, quasi come il ciel vedete.”[163] Constantine moving the capital of the Roman Empire eastwards is described as turning the Roman Eagle contrary to the course of the sky—“contra il corso del ciel,”[164] and the sky itself is described as a sphere which is ceaselessly at play like a lively child:—

------------------------------------------------------------------------ [162] “The great wheels,” “eternal wheels,” “starry wheels.”

[163] “Swift, almost as the heaven ye behold.” _Par._ ii. 21.

[164] “Against the course of the sky.” _Par._ vi. 2.

... “la spera, Che sempre a guisa di fanciullo scherza.”[165]

[165] ... “That sphere, Which aye in fashion of a child is playing.” _Purg._ xv. 2, 3. (_Longfellow_). ------------------------------------------------------------------------

To Dante, as to the Greeks, it is not the unusual or startling that appeals, but the unfailing harmony of the regular celestial movements. Comets he mentions only twice, and shooting stars twice, eclipses seven times; but there are scores of allusions to the rhythmical progression of Sun and stars, Moon and planets. The skies were familiar to him in all their daily aspects—sunset and dawn and radiant noons; cloudy nights “sotto pover cielo,”[166] brilliant starlit nights, nights of clear moonlight. He had seen the stars fade one by one, till at last even the brightest vanished in the glow of dawn:—

------------------------------------------------------------------------ [166] “Under a poor sky.” _Purg._ xvi. 2.

“E come vien la chiarissima ancella Del sol più oltre, così il ciel sì chiude Di vista in vista, infino alla più bella.”[167]

[167] “And as advances, bright exceedingly, The handmaid of the sun, the heaven is closed, Light after light, to the most beautiful.” _Par._ xxx. 7-9. (_Longfellow_). ------------------------------------------------------------------------

he had watched for their first appearance in the evening twilight:—

“E sì come al salir di prima sera Comincian per lo ciel nuove parvenze, Sì che la vista pare e non par vera....”[168]

------------------------------------------------------------------------ [168] “As at evening hour Of twilight, new appearances through heaven Peer with faint glimmer, doubtfully descried.” _Par._ xiv. 70-72. (_Carey_). ------------------------------------------------------------------------

Numberless other passages and expressions will occur to every Dante reader, proving how keenly he felt the beauty of the skies.

But they prove more than this. Other authors have felt and have described poetically the beauties of the skies, but they often remember imperfectly what they saw, or draw upon their imagination without any knowledge of the celestial movements, and so fall into absurd mistakes. The moon especially is a stumbling-block, and it is quite a rare thing for a modern novelist to introduce one without making it do something impossible. A new moon will rise at midnight, or a waning moon at sunset; she has even been known to rise and then to set in the dark hours of one short midsummer night;[169] and a well known author sees her in two phases at the same moment: “the full moon rose, yellow _and gibbous_!”[170]

------------------------------------------------------------------------ [169] In Kenneth Grahame’s delightful book, full of sympathy with Nature, _The Wind in the Willows_. The moon rose when it was “past ten o’clock,” and “sank earthwards reluctantly and left them” before dawn.

[170] H. G. Wells, _The Time Machine_. ------------------------------------------------------------------------

Dante’s moon does indeed give us a little trouble once or twice, but he never makes flagrant mistakes of this kind. His consistency and truth of description prove his knowledge of astronomy, and also imply intelligent thoughtful watching of the celestial movements; for it is notorious that book-knowledge, if unassisted by acquaintance at first-hand with the facts of a subject like astronomy, will not save a writer from glaring inaccuracies.

His allusions to the motions of the moon, both diurnal and monthly, show plainly that he understood them well. His new moon appears in the evening, his waning moon rises late at night and sets in morning sunshine,[171] and his full moon comes on the meridian at midnight, for when he wishes to describe her at her brightest, as a comparison with a very brilliant light, he places her in a clear sky at midnight in her mid-month.[172] In the middle of a lunar month the moon is full, and being exactly opposite the sun will reach the meridian at midnight: this therefore is the time when she gives all the light she possibly can. In the _Quæstio_[173] Dante mentions that the moon does not move in the celestial equator, but sometimes north of it, and sometimes an equal amount south; in the _Convivio_ he indicates the length of her period, and briefly describes her phases and their cause—“Ora luce da un lato, e ora luce dall’ altro, secondo che ’l sole la vede.”[174]

------------------------------------------------------------------------ [171] _Inf._ xv. 18, 19; _Purg._ xviii. 76-81; _Purg._ x. 14, 15, _Cf._ ix. 44.

[172] _Purg._ xxix. 53, 54.

[173] _Qu._ xx. 61-63.

[174] “Now she shines on one side, and now on the other, according to the way the sun looks upon her.” _Conv._ II. xiv. 77-79. ------------------------------------------------------------------------

Her position in the zodiac is mentioned several times. In one passage he indicates a very brief space of time in the following curious way:—

“Quando ambo e due i figli di Latona, Coperti del Montone e della Libra, Fanno dell’ orizzonte insieme zona, Quant’ è dal punto che il zenit inlibra. Infin che l’uno e l’altro da quel cinto, Cambiando l’emisperio, si dilibra, Tanto, col volto di riso dipinto, Si tacque Beatrice.”[175]

------------------------------------------------------------------------ [175] “At what times both the children of Latona, Surmounted by the Ram and by the Scales, Together make a zone of the horizon, As long as from the time the zenith holds them In equipoise, till from that girdle both Changing their hemisphere disturb the balance, So long, her face depicted with a smile, Did Beatrice keep silence.” _Par._ xxix. 1-8. ------------------------------------------------------------------------

That is to say, when Sun and Moon (the children of Latona) are both on the horizon, but one being in Aries and the other in Libra they are opposite one another, the zenith for a moment holds them, as it were, in balance; but the next moment one will drop below the horizon while the other rises above it, thus changing from the visible to the invisible hemisphere and _vice versa_, as each frees itself (“si dilibra”) of the common horizon that girdled them. The pause of Beatrice was as brief as the time during which sun and moon would thus hang in the balance.

Yet, though Dante shows that he was familiar with the movements and appearances of the moon, his allusions to her are cold and comparatively rare. Unlike modern poets, moonlight does not seem to have had any great fascination for him. In all his works there are only fifty-one references to the moon, and far the greater number of these are remarks about the measurement of time, or else her phases, her markings, her share in causing eclipses etc. In all his short poems (including those of the _Vita Nuova_ and _Convivio_) there are but two references, and those as dry as possible. “Più lune”[176] is once used, meaning several months, and in a sonnet which describes the influences of each heaven on his lady, all he can find to say of the moon’s is “E ’l primo ciel di sè già non l’è duro.”[177]

------------------------------------------------------------------------ [176] “Many moons.” _Canz._ xx. 89.

[177] “And the first heaven is not grudging to her.”—_Sonetto_ xxviii. ------------------------------------------------------------------------

The chill of moonlight is spoken of as with a shudder on the hill of Purgatory;[178] and its usefulness is recognized rather grudgingly when Virgil remarks that yesternight the moon was full, and adds that Dante must remember it, since it did him no harm in the depths of the Forest.[179] It is true there is some beauty in the description of the aurora which preceded moonrise[180] on the first night in Purgatory, but Dante gives it an ugly name, and the waning moon when seen on the following night, four days after full, is oddly compared to a bucket in shape. Dante did not admire this gibbous form, for he instances the outline of the moon when not quite full as an ignoble curve, contrasting it with the beauty of a perfect circle.[181]

------------------------------------------------------------------------ [178] _Purg._ xix. 1, 2.

[179] _Inf._ xx. 127-129.

[180] _Purg._ ix. 1-9.

[181] _Conv._ IV. xvi. 89-93. ------------------------------------------------------------------------

[Illustration: Fig. 39. Sun, moon, and zenith.

To illustrate _Par._ xxix. 1-6. (_See p. 265_).

In the first figure the sun and moon are balanced, as it were, being at equal distances from the zenith: in the second, a few minutes later, by the rising of the sun and the setting of the moon, the balance is disturbed, and each changes its hemisphere.]

Hardly ever does he find a beautiful epithet for her: she is ruler of Hell,[182] Cain and the Thorns[183] (in reference to the legend which sees this figure in her dark markings); or she is simply Delia,[184] Trivia,[185] the daughter of Latona,[186] or with a little warmth the sister of the sun,[187] and with the sun one of the two Eyes of Heaven.[188] One exception to this harsh treatment is in the beautiful description of reaching the heaven of the moon,[189] for there she is the first star, the eternal pearl; and the sudden burst of eloquence in the midst of a grave argument in _De Monarchia_ startles us doubly when we find that Justice is compared to the moon—not, as one might expect, resplendent in a dark sky, but Phœbe gazing at her brother opposite, in the purple of the morning calm.[190] The passage from _Par._ xxix. quoted above helps us to understand why the moon in this position should symbolize Justice, for here again is suggested the perfect balancing of the two great orbs, as the sun rises and the full moon sets.

------------------------------------------------------------------------ [182] _Inf._ x. 80.

[183] _Inf._ xx. 126.

[184] _Purg._ xxix. 78; _Ep._ vi. 54.

[185] _Par._ xxiii. 26.

[186] _Par._ x. 67; xxii. 139; xxix. 1.

[187] _Purg._ xxiii. 120.

[188] _Purg._ xx. 132.

[189] _Par._ ii. 25-36.

[190] _De Mon._ I. xi. 35-37. ------------------------------------------------------------------------

Add to these passages two similes drawn not indeed from the moon itself but from the halo surrounding her,[191] and two descriptions of brilliant moonlight nights,[192] and we have all that Dante has written in praise of the moon. It is true that throughout the _Inferno_ and _Purgatorio_ the sun typifies Divine Grace, and the moon is his opposite, but this cannot altogether explain the difference in their treatment, even in the _Divine Comedy_. A deeper reason seems to be Dante’s true southerner’s love of the sun; and he doubtless had the astronomer’s feeling that moonlight always means loss of starlight, which he dearly loved (see _Purg._ xviii. 76, 77). Perhaps too the astrological views of the moon influenced him, consciously or not. According to Ristoro, the moon represents the poorest and lowest classes of people, who are servants and messengers to the rest; and as all the planets were supposed to be either masculine or feminine, he ungallantly adds—“E questa Luna, a cagione di sua viltà, potemo dire per ragione ch’ella sia femmina.”[193] Her only house, too, which is Cancer, is also poor and base. The moon, moreover, is nearer Earth than any other planet, and shows by her dark markings that she is less pure than the rest.

------------------------------------------------------------------------ [191] _Par._ x. 67-69; and _Purg._ xxix. 78.

[192] _Purg._ xxix. 53, 54; and _Par._ xxiii. 26.

[193] “And this moon, because of her inferiority, is rightly called feminine.” ------------------------------------------------------------------------

2. MOVEMENTS OF THE SUN.

Whatever the reason, Dante’s fifty-one references to the moon are in strong contrast to his allusions to the sun. These are four times as many, and they include warm expressions of admiration and delight, and beautiful epithets and similes. The sun is Titan with his chariot and horses,[194] he is a Mirror, a Car of Light, the Lantern of the World, the Prince of the Stars, the Father of all mortal life.[195] His beautiful form is admired, “la perfetta sua bella figura,”[196] and his intense brilliance often noted.[197] He is the guide that leads all aright,[198] to whom Virgil appeals:—

------------------------------------------------------------------------ [194] _Ecl._ ii. 1-4.

[195] _Purg._ iv. 62, 63; _Purg._ iv. 59; and xxix. 117, 118; _Par._ i. 38; _Canz._ xix. 114; _Par._ xxii. 116.

[196] “The perfection and beauty of his shape.” _Canz._ xix. 76.

[197] _V. N._ xlii. 29; _Canz._ ix. 2; _Conv._ II. xiv. 126, 127; _Purg._ xvii. 52, 53; _Par._ i. 54; and x. 48, etc.

[198] _Inf._ i. 17, 18.

“O dolce Lume, a cui fidanza i’ entro Per lo nuovo cammin, tu ne conduci.”[199]

[199] “O pleasant light, my confidence and hope! Conduct us thou,” he cried, “on this new way.” _Purg._ xiii. 16, 17. (_Carey_). ------------------------------------------------------------------------

Under his rays the rose expands, the air is gladdened, mists are dispelled, snow melts, and all things are quickened into life.[200] Unlike the moon, the sun is the bringer of warmth and comfort, chasing away cold and darkness,[201] sunrise is the hour of renewed hope and confidence,[202] it strengthens our limbs, paralysed by the cold of night,[203] it is eagerly awaited through the darkness by the little bird on her nest;[204] and delicate flowers, bowed and closed during the cold night, rise upright on their stems and open as soon as the sun shines once more upon them.[205] The exquisite sunsets and sunrises of the _Purgatorio_ are favourite passages with all readers.

------------------------------------------------------------------------ [200] _Par._ xxii. 55, 56; _Inf._ vii. 122; _De Mon._ II. i. 37-39; and _Par._ ii. 106-108; _Canz._ xi. 37; _Conv._ III. xii. 59, 60, etc. etc.

[201] _Canz._ ix. 5.

[202] _Inf._ i. 41-43.

[203] _Purg._ xix. 10, 11.

[204] _Par._ xxiii. 1-9.

[205] _Inf._ ii. 127-129. ------------------------------------------------------------------------

Love is compared with the summer sun,[206] the generosity of a noble nature resembles “the great planet.”[207] The Emperor Henry VII., from whom Dante expected the regeneration of Italy and the whole Christian world, is likened to the rising sun;[208] the birth of St. Francis is described as “nacque al mondo un sole,”[209] and his birthplace ought rightly to be called not Assisi but Orient.[210] Virgil is addressed as “O Sol che sani ogni vista turbata;”[211] Beatrice is “Il sol degli occhi miei.”[212] Finally the sun is the best symbol of God,[213] and so it is used many times in the _Divine Comedy_: “Il Sol degli angeli,”[214] “Il Sol che raggia tutto nostro stuolo;”[215] a spirit turns to “il Sol che la riempie,”[216] and when Virgil laments that he is shut out of heaven it is in these words: “Ho i’ perduto Di veder l’ alto Sol che tu disiri.”[217]

------------------------------------------------------------------------ [206] _De Mon._ II. i. 36-41.; _Canz._ ix.

[207] _Canz._ xix. 96-114.

[208] _Ep._ v. 10; and vii. 19, 20, 25.

[209] “A sun rose upon the world.” _Par._ xi. 50.

[210] _Par._ xi. 52-54.

[211] “O sun that healest all imperfect vision,” _Inf._ xi. 91.

[212] “The sun of my eyes.” _Par._ xxx. 75 (See also _Par._ iii. 1-3).

[213] _Conv._ III. xii. 52-63.

[214] “The Sun of the angels.” _Par._ x. 53.

[215] “That Sun which enlightens all our company.” _Par._ xxv. 54.

[216] “The Sun which satisfies it.” _Par._ ix. 8.

[217] “I have lost the sight of that high Sun whom thou desirest.” _Purg._ vii. 25, 26. Compare _Par._ xxx. 126; xv. 76; xviii. 105. ------------------------------------------------------------------------

But we may not dwell on those thoughts of the sun as the typical giver of light and life; we must ask what Dante says about his movements, since this was the chief subject-matter of mediæval astronomy.

His daily course, “il cammin del Sole,”[218] is often spoken of, and is indicated both by his position in the sky, and the length and direction of shadows. The second _Eclogue_ begins with a description of a breathlessly hot midday, when objects, which are usually shorter than their own shadows, now surpassed them in length.

------------------------------------------------------------------------ [218] “The path of the sun.” _Purg._ xii. 74.

“Resque refulgentes, solitae superarier umbris, Vincebant umbras.” _Ecl._ ii. 5, 6. ------------------------------------------------------------------------

At this time the sun appears most brilliant, and seems to move most slowly, since he is scarcely changing his position with regard to the horizon.

“E più corrusco, e con più lenti passi, Teneva il sole il cerchio di merigge.”[219]

------------------------------------------------------------------------ [219] “Shining more brightly and with slower steps, the sun had gained the circle of midday.” _Purg._ xxxiii. 103, 104. ------------------------------------------------------------------------

The greatest number of references to the sun’s daily journey occur in the _Purgatory_, and we shall quote them in a later chapter.

His yearly journey through the zodiac is also very often referred to. When relating his first meeting with Beatrice, Dante names his age, not by simply saying that he was nearly nine years old, but by counting the number of the times that the “heaven of light,” that is, of the sun, had returned to the same point since his birth:—

“Nove fiate già, appresso al mio nascimento, era tornato lo cielo della luce quasi ad un medesimo punto, quanto alla sua proprio girazione.”[220]

------------------------------------------------------------------------ [220] “Nine times already since my birth had the heaven of light returned to the selfsame point almost, as concerns its own revolution.”

_V. N._ ii. 1-4. (_Rossetti_). ------------------------------------------------------------------------

The sun’s “own revolution” is of course its apparent yearly movement, as distinct from the diurnal movement which it shares with all the heavenly bodies.

The same thought is expressed in a sonnet:

“Io sono stato con Amore insieme Dalla circolazion del Sol mia nona.”[221]

We know further that Dante was born in either May or June, because he says, when he finds himself among the stars of Gemini, that the sun was rising and setting in this sign at the time of his birth.[222]

------------------------------------------------------------------------ [221] “I have dwelt with Love since my ninth revolution of the sun.” _Son._ xxxvi. 1, 2.

[222] See diagram on p. 276.

“O gloriose stelle Con voi nasceva e s’ascondeva vosco Quegli ch’è padre d’ogni mortal vita, Quand’ io senti’ da prima l’ aer tosco.”[223]

[223]

“O glorious stars ... With you was born, and hid himself with you, He who is father of all mortal life, When first I tasted of the Tuscan air.” _Par._ xxii. 112-117. (_Longfellow_).

At this date the sun entered the _constellation_ of Gemini on June 1 (Old Style), but was in the _sign_ from May 11 to June 11, and it is always to the signs that Dante refers in the _Divine Comedy_. The anonymous fourteenth century commentator known as “l’Ottimo” interprets this passage as indicating the time “between the middle of May and the middle of June.” ------------------------------------------------------------------------

Boccaccio tells us that a Mayday feast, given by the father of Beatrice, was the occasion of Dante’s first meeting with her, and also that not long before his death in Ravenna he told a friend that he had completed his fifty-sixth year in the preceding May, so we may conclude that May was the month of his birth.

Dante seems to have taken some trouble to find out the exact period of the sun’s revolution. His text-book, the _Elementa_ of Alfraganus, only gives it as 365¼ days nearly:—“Sol ... orbem confecit diebus 365 et propè ¼.” Ristoro d’Arezzo and Brunetto Latini were content to repeat this rough estimate, and call the year 365 days 6 hours, but Dante wished to be more exact, and somehow contrived to obtain a value which was much nearer the modern estimate of 365 days, 5 hours, 48 minutes, 46 seconds. We know this from two passages. In the _Convivio_ he gives the half period as less than 182 days 15 hours; and in the _Paradiso_ Beatrice says that January will in time cease to be a winter month, because of a neglected fraction of time.

“Prima che gennaio tutto si sverni Per la centesma ch’ è laggiù negletta.”[224]

------------------------------------------------------------------------ [224] “Ere January be unwintered wholly By the centesimal on Earth neglected.” _Par._ xxvii. 142-143. (_Longfellow_). ------------------------------------------------------------------------

January was in fact receding from the winter, and steadily though slowly advancing towards the spring, because the Julian year (as we saw, p. 171) was 11 minutes 14 seconds longer than the true solar tropical year. When Julius Cæsar reformed the Calendar, March 25 was made (as of old) to coincide with the spring equinox, but by Dante’s time this date was 13 days late, and the true equinox fell on March 12. Consequently though the day called January 1 still came 84 days before March 25, it was only 71 days before the spring equinox.

If Beatrice meant to speak with scientific precision, and was correct in her hundredth part of a day per annum, that is, if the difference between the astronomical and the Julian year was one day in a hundred years, it would be 7100 years before the first of January came to coincide with the spring equinox, and January became a spring month. But the error quoted is really rather too large, for a hundredth part of a day is 14 minutes 24 seconds, and it was in fact only 11 minutes 14 seconds.

It would be interesting to know where Dante found this value, which is practically the only astronomical datum not given in Alfraganus. Ptolemy, following Hipparchus, had given the tropical year as ¹/₃₀₀ part of a day less than 365¼; Albategnius gave a more accurate figure, and one which agrees well with the “centesma,” for his tropical year differs from the Julian by a little less than ¹/₁₀₆ of a day; but he also improved the value of precession, and Dante does not seem to have known this, so he was probably not acquainted with this astronomer’s work. The Alfonsine Tables gave a value which was very close indeed to the correct one, making the tropical year only 30 seconds longer than the modern value, and the difference between the Julian and true year ¹/₁₃₄ of a day. (The correct value is ¹/₁₂₈). Either of these figures may have been known to Dante indirectly: perhaps he had obtained the Alfonsine value in conversation with Brunetto Latini, who had visited Alfonso’s court. His fraction was evidently only approximate, but it is interesting to know that he had found out more than popular books could tell him about the period of the sun’s revolution, and that he had been sufficiently struck by the small difference between the calendar and astronomical years to mention it in a picturesque way in his poem. It is possible that he had heard of Roger Bacon’s appeal to the Pope in 1267 to correct the calendar because the date of the spring equinox was of importance in connection with the observation of Easter.

It is hardly necessary to remind my readers that this was done by another Pope three hundred years later, before January had made much more advance towards becoming a spring month. The hundredth part of a day, of which Beatrice complained, is now subtracted from the year by omitting to make century years leap years; but as the error was really not quite so great as she said, an exception is made for century years divisible by 400. Thus 1600 was a leap year, but not 1700, 1800, or 1900.

[Illustration: Fig. 40. The Zodiac and the Months.]

Dante seems to have connected any season of the year with the sun’s path in the zodiac as readily as with the name of a month. The sun’s yearly course through the signs is shown diagrammatically in figure 40, and a glance at this will make clear a number of allusions without any explanation.

Starting from the first point of Aries at the spring equinox, which in Dante’s time fell in the middle of March, and taking one-twelfth of the year to traverse each sign, it is evident that during the end of March and beginning of April the sun was in Aries; he entered Cancer and reached the summer solstice in June, the autumnal equinox in Libra in September, and the winter solstice when he entered Capricornus in December. The six signs above the horizontal line are northern, the six below are southern.

The following are a few typical examples.

When Dante wishes to express the transition of his feelings from despondency to courage, at seeing the stern and troubled face of his guide melt suddenly to a smile, he compares himself to a poor shepherd who wakes early and sees the fields covered, as he thinks, with snow, but in a short time finds that it is only hoar-frost which has put on the semblance of her white sister, and seeing the face of the world changed he gladly leads out his sheep to pasture. The time at which this may happen is

“Quella parte del giovinetto anno, Che il sole i crin sotto l’Aquario tempra, E già le notti al mezzodì sen vanno.”[225]

------------------------------------------------------------------------ [225] “In that part of the youthful year wherein The sun his locks beneath Aquarius tempers, And now the nights draw near to half the day.” _Inf._ xxiv. 1-3. (_Longfellow_). ------------------------------------------------------------------------

That part of the youthful year when the sun cools his locks beneath Aquarius is clearly the end of January or beginning of February, but the last line may bear one of two meanings. If we translate “mezzodì” as “half the day” it means that the nights are growing shorter, and very soon (in March) when the sun will have reached the equinox, they will be just twelve hours long. If we take “mezzodì” as meaning “the south,” we must interpret the passage in the light of others in the _Divine Comedy_ where Night is personified, and considered as circling in the zodiac always opposite to the sun. For instance in _Purg._ ii. 1-6 (a passage which will be more fully explained later) Night is described as circling opposite to the sun, “La notte, che opposita a lui cerchia,”[226] and as the sun at that time was in Aries, Night was in Libra, “le Bilance.” Henceforth for six months the sun will be in the northern signs, and the days longer than the nights, but as soon as Night begins to assert her supremacy, and the nights begin to be longer than the days, the sun enters Libra and then it is not visible all night. This is the meaning of

------------------------------------------------------------------------ [226] “Night that opposite to him revolves.” (_Longfellow_).

“le Bilance, Che le caggion di man quando soverchia.”[227]

[227] “The Scales, that from her hands are dropped When she reigns highest.” _Purg._ ii. 5, 6. (_Carey_). ------------------------------------------------------------------------

When Night becomes dominant, the Scales fall from her hand, for the sun is in that sign.

Applying this idea to the passage quoted above, it will mean “The nights are going southward,” for the sun in Aquarius is not far from the point where he crosses the equator to the north, therefore Night circling opposite to him is nearing the point where she goes south. Either interpretation is faithful to fact, but perhaps the circumstance that the plural noun is used favours the first.

[Illustration: Fig. 41. The Ram on the Ecliptic. [_To face p. 279._

_From the “Cosmi Historia” of Robert Flud, a.d. 1612._

(_Reproduced from Brown’s Phainomena of Aratos._)]

Conrad Malaspina prophesied to Dante that his favourable opinion of the Malaspina family would be justified “before the sun had come to rest again seven times in the bed which the Ram covers and bestrides with his four feet.”

“Ed egli: Or va, che il Sol non si ricorca Sette volte nel letto che il Montone Con tutti e quattro i pie copre ed inforca Che cotesta cortese opinione ...”[228]

------------------------------------------------------------------------ [228] “And he: Now go, for the sun shall not lie Seven times upon the pillow which the Ram With all his four feet covers and bestrides. Before that such a courteous opinion ...” _Purg._ viii. 133-136. (_Longfellow_). ------------------------------------------------------------------------

The sun was at the time in the Ram, and Malaspina means that less than seven years would elapse, before his prophecy was fulfilled. The aptness of the description may be seen by the figure of Aries as portrayed in an old seventeenth century book in which the Ram is uncomfortably trying to sit on the ecliptic.

Another instance is in the beautiful midwinter Ode, “Io son venuto al punto della rota.”[229] Each stanza pictures a feature of a severe winter—snow and rain, the absence of summer birds, bare trees and dead flowers, the favourite walk become a torrent; but the first describes the position of stars and planets. When the sun sets, the Twins appear on the eastern horizon, hence we know at once that the sun is in Sagittarius and the time is November or December. To confirm his melancholy, the poet adds that the Star of Love (Venus) is hidden from us by the sun’s rays which now shine athwart her, and that the planet which strengthens the cold (Saturn, the “frigida stella” of Virgil) displays himself in that arc of the sky in which all the seven planets cast the shortest shadow;[230] that is, either he is on the meridian at sunset, or he is in the most northerly part of the zodiac, in Gemini or Cancer. A planet in this place, as for instance the sun at midsummer, is visible longer, describes a longer arc, and casts shorter shadows, than in any other part of the zodiac. And as this is the part which rises over the eastern horizon as the sun sets, Saturn would also rise at that time and remain visible all night.

------------------------------------------------------------------------ [229] “I have come to that part of the wheel.” _Canz._ xv.

[230] Like all mediæval writers, Dante includes the sun and moon among the seven planets. The others do not cast perceptible shadows, except Venus and Jupiter at their brightest.

The opening lines of the Ode run thus:—

“Io son venuto al punto della rota, Che l’orizzonte, quando il Sol si corca, Ci parturisce il geminato cielo; E la stella d’amor ci sta rimota Per lo raggio lucente, che la ’nforca Sì di traverso, che le si fa velo; E quel pianeta che conforta il gelo Si mostra tutto a noi per lo grand’ arco, Nel qual ciascun de’ sette fa poca ombra.”[231]

[231] “I to that point in the great wheel have come, Wherein the horizon, when the sun doth set, Brings forth the twin-starred heaven to our sight; And Love’s fair star away from us doth roam, Through the bright rays obliquely on it met In such wise that they veil its tender light; That planet which makes keen the cold of night Shows himself to us in the circle great, Where each star of the seven casts little shade.” (_Plumptre_). ------------------------------------------------------------------------

It is astonishing that Giuliani should so completely miss the point of the “twinned sky,” that he substitutes “ingemmato” for “geminato,” and reads—

“ ... la rota, Ch’ all orizzonte, quando il Sol si corca, Ci parturisce l’ingemmato cielo.”[232]

------------------------------------------------------------------------ [232] “The Wheel which, when the sun sets, brings forth for us on the horizon the jewelled sky.” ------------------------------------------------------------------------

He understands the hour of evening to be meant, when the Wheel of Day and Night brings a jewelled, _i.e._ starry sky on the horizon as the sun sets. But it is not only on the horizon that stars appear at sunset; and the mention of Gemini to indicate the time of year is thoroughly characteristic of Dante. The Wheel is the revolving year which has carried the sun into Sagittarius.

Angelitti remarks that the whole description was literally true for December 1296, since Venus was then in conjunction with the sun, and Saturn in Cancer;[233] and as this poem is a complaint of the hardness of his lady, to whom the poet is nevertheless wholly devoted, it may well have been written in that time when the lady Philosophy refused to smile upon her lover.[234]

------------------------------------------------------------------------ [233] _Sulla Data del Viaggio Dantesco_ p. 90, note.

[234] Comparing _Conv._ II. ii. 12, xiii. 49-52, and IV. i. 60-62, we learn that in August 1293 (_vide infra_, p. 314), Dante first became acquainted with the Lady Philosophy; that in the early part of 1296 he was completely under her spell; and that some time afterwards she for a while estranged herself from him. ------------------------------------------------------------------------

Further on in the same poem the effects of the sun in spring, when he is in the sign of Aries, are alluded to as “the virtue of Aries”:—

“Passato hanno lor termine le fronde, Che trasse fuor la virtù d’Ariete, Per adornare il mondo, e morta è l’ erba.”[235]

------------------------------------------------------------------------ [235] “Scattered and faded now is all the foliage Which had burst forth, beneath the power of Aries, To beautify the world, the grass is withered.” _Canz._ xv. 40-42. ------------------------------------------------------------------------

Contrast with this the passage in the _Paradiso_ where “nocturnal Aries” is used as a synonym for autumn.

“Questa primavera sempiterna Che notturno Ariete non dispoglia.”[236]

------------------------------------------------------------------------ [236] “This everlasting spring Nocturnal Aries never can despoil.” _Par._ xxviii. 116-117. ------------------------------------------------------------------------

For although Aries may be seen during some part of the night in the greater part of the year, it is most emphatically a noctural sign when it rises as the sun sets, and remains above the horizon until he rises; this happens when the sun is in the opposite sign of Libra, which he enters at the autumnal equinox.

A rather curious passage in the _Paradiso_ is incomprehensible unless we think of the sun’s path in the zodiac, and realize that Dante is comparing the brightness of the spirit of St. John in an indirect way with the brightness of the sun.

“Poscia tra esse un lume si schiarì, Sì che, se il Cancro avesse un tal cristallo, L’inverno avrebbe un mese d’un sol dì.”[237]

------------------------------------------------------------------------ [237] “Thereafterward a light among them brightened So, that if Cancer one such crystal had Winter would have a month of one sole day.” _Par._ xxv. 100-102. (_Longfellow_). ------------------------------------------------------------------------

If a light as dazzling as this spirit were to shine forth in Cancer, there would be perpetual day for a whole month in winter. For when the sun entered Capricornus, which he does in December, he would be exactly opposite, so that as one light set the other would rise, and there would be no darkness until the sun passed into another sign.

To many similar instances the diagram (p. 276) will be found to supply a key, and some we shall have occasion to notice presently in another connection.

3. THE STARS.

If our poet did not love moonlight, there is no doubt that starlight was very dear to him. Never are stars spoken of as cold, or placed in antithesis to the sun. Rather are they classed together, as in the pathetic letter, written when he heard of the possibility that the Florentines might receive him again if he would consent to return as a disgraced but pardoned criminal. If this is the only path to Florence, never will he re-enter the beloved city. “What then?” he cries. “Can he not see the mirrors of the sun and of the stars, wherever he may be? can he not meditate on precious truths under any sky?”[238]

------------------------------------------------------------------------ [238] _Ep._ ix. 46-49. ------------------------------------------------------------------------

He describes the Inferno as bereft of stars as well as of sun;[239] he hopes to escape those dark abysses to see the beautiful stars again,[240] and the terror of the sounds of weeping and crying is heightened indescribably by the simple words:—“risonavan per l’aer senza stelle.”[241] When he does at length come forth to see “le cose belle che porta il ciel”[242] how eagerly he gazes, not only at Venus, but at the new stars in the south! how his “greedy eyes”[243] seek the same region as soon as dusk begins to fall! and how radiantly the stars look down upon him on that last night on the rocky slopes of the Mountain, near the summit![244]

------------------------------------------------------------------------ [239] _Inf._ iii. 23.

[240] _Inf._ xvi. 82, 83.

[241] “Resounded through the air without a star.” _Inf._ iii. 23.

[242] “The fair things that heaven holds.” _Inf._ xxxiv. 137, 138.

[243] _Purg._ viii. 85.

[244] _Purg._ xxvii. 89, 90. ------------------------------------------------------------------------

This is all allegorical, no doubt, but it is because of Dante’s feeling for the real “belle stelle”[245] that he uses them as symbols of truth and holiness, and concludes each Cantica of the _Divine Comedy_ with their name:—

------------------------------------------------------------------------ [245] “Beautiful stars,” _Inf._ xvi. 83.

“E quindi uscimmo a riveder le stelle.”[246] “Puro e disposto a salire alle stelle.”[247] “L’Amor che move il sole e l’altre stelle.”[248]

[246] “Thence issuing we beheld again the stars.”

[247] “Pure and disposed to mount unto the stars.”

[248] “The Love that moves the sun and the other stars.” ------------------------------------------------------------------------

Here “stelle” has the wider meaning of the French “astres,” for which we have no equivalent in English except the clumsy “heavenly bodies;” but most of Dante’s hundred references are to stars in the more special sense, and often to particular stars or constellations. Over eighty occur in the _Divine Comedy_.

Stars are jewels, torches, flames, immortal nymphs adorning every region of the sky.[249] Heaven is made beautiful by their light, and the joy of the angels is expressed in their shining, as mortal joy shines forth in human eyes.[250] If the spirits in the fourth heaven are described as glowing suns,[251] the “splendours” that descend upon the golden ladder in the seventh, make Dante think that all the stars in the sky are gathered together there.[252]

------------------------------------------------------------------------ [249] _Purg._ ix. 4; _Purg._ viii. 89; _Purg._ i. 25; _Par._ xxiii. 26.

[250] _Par._ ii. 130, 142-144.

[251] _Par._ x. 76.

[252] _Par._ xxi. 28-33. ------------------------------------------------------------------------

The eyes of Beatrice shone brighter than stars;[253] light comes as from many stars in reading the sacred books;[254] faith gleams like a star in the sky;[255] and truth appears in a mind cleared of falsehood and error like the radiance of stars in a sky which has been wholly swept of cloud and mist by a north wind.

------------------------------------------------------------------------ [253] _Inf._ ii. 55.

[254] _Par._ xxv. 70. See also _Conv._ II. xvi. 4-12, where the writings of Boëthius and Cicero, and all instructive books, are called stars full of light.

[255] _Par._ xxiv. 147.

“Come rimane splendido e sereno L’emisperio dell’ aer, quando soffia Borea da quella guancia ond’ è più leno, Perchè si purga e risolve la roffia Che pria turbava, sì che il ciel ne ride Con le bellezze d’ogni sua paroffia: Così fec’ io, poi che mi provvide La Donna mia del suo risponder chiaro, E come stella in cielo il ver si vide.”[256]

[256] “Even as remaineth splendid and serene The hemisphere of air, when Boreas Is blowing from that cheek where he is mildest, Because is purified and resolved the wrack That erst disturbed it, till the welkin laughs With all the beauties of its pageantry: Thus did I likewise, after that my Lady Had me provided with her clear response, And like a star in heaven the truth was seen.” _Par._ xxviii. 79-87. (_Longfellow_). ------------------------------------------------------------------------

Stars, as well as the sun, are used as symbols for the objects of Dante’s deepest reverence; for the Blessed Virgin is called “la viva stella,”[257] and the Final Vision in which the redeemed find their ultimate bliss is a Trinal Light seen as a single star:—

------------------------------------------------------------------------ [257] “The shining star.” _Par._ xxiii. 92.

“O trina Luce, che in unica stella Scintillando a lor vista sì gli appaga, Guarda quaggiù alla nostra procella.”[258]

[258] “O Trinal Light, that in a single star Sparkling upon their sight so satisfies them, Look down upon our tempest here below!” _Par._ xxxi. 28-30. (_Longfellow_). ------------------------------------------------------------------------

The diurnal motion of the stars is referred to many times. As Dante watched the mystical procession in the Earthly Paradise, and saw one group follow in the footsteps of another across the flowers and the grass, he thought of the stately procession of stars which we see here by night, star following star across the sky.[259] Their movement marks for him the passage of time, as we see in the first sonnet of the _Vita Nuova_:—

------------------------------------------------------------------------ [259] _Purg._ xxix. 91.

“Già eran quasi ch’ atterzate l’ ore Del tempo che ogni stella è piu lucente.”[260]

[260] “Of those long hours wherein the stars above Wake and keep watch, the third was almost nought.” _V. N._ iii. 81, 82. (_Rossetti_). ------------------------------------------------------------------------

and in the _Inferno_, where Virgil hastens Dante, saying that all the stars are sinking which were rising when he started on his long journey.[261]

------------------------------------------------------------------------ [261] _Inf._ vii. 98, 99. ------------------------------------------------------------------------

The motion of those stars which neither rise nor set, but are always seen circling round the pole, is clearly described. In the heaven of the sun, spirits gather round Dante and Beatrice, and circle round them, “Come stelle vicine ai fermi poli;”[262] and the motion of the stars near the pole is said to be slow, like the part of a wheel which is near the axle.[263] We may compare these descriptions with the statement of Alfraganus:—“Eæ stellæ (_i.e._ the northern circumpolar) vertuntur omnes circa idem punctum. Et quei ex iis puncto huic est vicinior, minorem conficit circulum: motusque ejus appâret lentior.”[264] Dante assumes that his readers understand this motion when he describes himself as seeing unknown stars near the South Pole. The Mount of Purgatory is supposed to be situated in the southern hemisphere, and at his first arrival, before dawn, he turns to the right, after looking at Venus in the east, therefore to the south, and sees near the pole four stars so brilliant that the whole sky seems to rejoice in their radiance, and he pities the “widowed” northern hemisphere because they are invisible there.[265] In the evening, as soon as it begins to grow dark, although he is engaged in an interesting discourse with a friend with whom he had exchanged warm greetings, he looks eagerly once more towards the pole (note the intensity expressed by the repeated “pure”)—

------------------------------------------------------------------------ [262]

“Like unto stars neighbouring the stedfast poles.” _Par._ x. 78.

[263] _Purg._ viii, 86, 87.

[264] “These stars all revolve round the same point, and the nearer a star is to this point, the smaller is the circle that it makes, and the slower its motion appears.” _El. Ast._ cap. ii.

[265] _Purg._ i. 22-27.

“Gli occhi miei ghiotti andavan pure al cielo, Pur là dove le stelle son più tarde, Sì come rota più presso allo stelo.”[266]

[266] “My insatiate eyes Meanwhile to heaven had travelled, even there Where the bright stars are slowest, as a wheel Nearest the axle.” _Purg._ viii. 85-87. (_Carey_).

He now sees three bright stars which make this pole glow with light, and Virgil says that the stars he saw in the morning are low, while those now visible have risen higher to take their place.

“Ed egli a me: Le quattro chiare stelle Che vedevi staman son di là basse, E queste son salite ov’ eran quelle.”[267]

[267] “And he to me: The four resplendent stars Thou sawest this morning are down yonder low, And these have mounted up to where those were.” _Purg._ viii. 91-93. (_Longfellow_). ------------------------------------------------------------------------

The diurnal movement of the starry heaven is also alluded to in the _Convivio_, and contrasted with that immensely slow movement which was discovered by Hipparchus, and is called by us Precession. The starry heaven, says Dante, displays one of its poles to us, and keeps the other hidden; and in like manner it displays only one movement to us, and keeps the other almost hidden. By the first, it revolves once in every day from east to west; the other is nearly insensible, being only one degree in a hundred years, and it is from west to east.[268] This is the value of precession as given by Alfraganus, following Ptolemy.

------------------------------------------------------------------------ [268] _Conv._ II. xv. 10-14, and 96-104. ------------------------------------------------------------------------

It was this stupendous and mysterious cycle which was used by Dante to measure the age of Beatrice, though for his own he used (as we saw) the ordinary measure of the sun’s period. When he first saw “la gloriosa donna”[269] she had only been in this life so long that the starry heaven had moved towards the east one-twelfth part of a degree. Therefore, she was one-twelfth of a hundred years old, or 8 years 4 months, “so that it was near the beginning of her ninth year that she appeared to me, and I saw her nearly at the end of my ninth.”[270]

------------------------------------------------------------------------ [269] “The glorious Lady.”

[270] _V. N._ ii. 9-15. ------------------------------------------------------------------------

Dante tells us how many stars had been counted by “the sages of Egypt,” by whom he means Ptolemy and the other Alexandrians: he did not know that the star catalogue of the _Almagest_ was originally made by Hipparchus of Rhodes.

“Dico ch’ il cielo stellato ci mostra molto stelle; chè, secondochè li savi d’Egitto hanno veduto, infino all’ultima stella che appare loro in meridie, mille ventidue corpora di stelle pongono, di cui io parlo.”[271]

------------------------------------------------------------------------ [271] “I say that the starry heaven displays a multitude of stars to us, for as the Sages of Egypt have perceived, including the last star which appears to them in the south, they reckon one thousand and twenty-two starry bodies, of which I am now speaking.” _Conv._ II. xv. 18-22. (_Jackson_). ------------------------------------------------------------------------

It will be noted that he carefully avoids saying that this is the number of all the stars visible from the whole earth. Had he, like Ristoro, run away with the idea that a blank space on the globe meant a blank in the sky, his night sky seen from Purgatory would have been strangely bare and dull! Yet both writers used the same text-book. Dante is here following Alfraganus closely, for he had written in his nineteenth chapter:—

“Sciendum itaque sapientes inivisse mensuram stellarum fixarum omnium, quoad instrumentis observari eæ potuerunt, extremam usque meridiei partem, in tertio climate ipsis conspicuam.... Stellæ universae quarum agi mensura potuit sunt mille viginti duæ.”[272]

------------------------------------------------------------------------ [272] “You are to know that the Sages measured the places of all the fixed stars as accurately as possible with their instruments, as far south as they could see in the third climate.... The number of all the stars which he was able to measure is one thousand and twenty-two.” ------------------------------------------------------------------------

Both in the _Quæstio_ and the _Paradiso_ Dante notes how stars differ, not only in their brightness or “magnitude,” but also in the quality of their light, by which he probably means their colour:—

“Videmus in eo [_sc._ cœlum stellatum] differentiam in magnitudine stellarum et in luce.”[273]

------------------------------------------------------------------------ [273] “We see in it (the starry heaven) a difference in the magnitude of the stars and in their light.” _Qu._ xxi. 19-21.

“Lumi, li quali nel quale e nel quanto Notar si posson di diversi volti.”[274]

[274] “Lights many the eighth sphere displays to you Which in their quality and quantity May noted be of aspects different.” _Par._ ii. 65-66. (_Longfellow_). ------------------------------------------------------------------------

It seems as if it were the beauty and the movement of the starry sky as a whole which appealed to Dante, rather than the distinguishing of special stars and constellations. Those which he mentions are almost all either in the zodiac, and used to denote the hour, the season, or the position of one of the seven planets; or else they are near one of the poles and illustrate the circumpolar motion.

All the zodiacal constellations are mentioned except Virgo and Sagittarius. Besides the ordinary names of “Ariete,” “Libra,” etc., Aries is called “il Montone;”[275] Gemini “il segno che segue il Tauro,” “gli eterni Gemelli,” and “il bel nido di Leda,”[276] in reference to the mother of Castor and Pollux, its two brightest stars; Libra is “le Bilance”;[277] Scorpio “il freddo animale”;[278] Capricornus is “il Capra del ciel”;[279] and Pisces “la celeste Lasca.”[280]

------------------------------------------------------------------------ [275] “The Ram.” _Purg._ viii. 134; _Par._ xxix. 2.

[276] “The sign which follows Taurus,” _Par._ xxii. 110, 111; “The eternal Twins,” xxii. 152; “The fair nest of Leda,” xxvii. 98.

[277] “The Balance.” _Purg._ ii. 5.

[278] “The cold creature.” _Purg._ ix. 5.

[279] “The Goat of the sky.” _Par._ xxvii. 69.

[280] “The celestial Carp.” _Purg._ xxxii. 54. ------------------------------------------------------------------------

In one place Castor and Pollux are mentioned, but merely as a synonym for the whole constellation of Gemini.[281] “Il petto del Leone ardente”[282] is perhaps Cor Leonis, the Heart of the Lion, for this is the name given to Regulus by both Ptolemy and Alfraganus. The “Maggior Fortuna”[283] of _Purg._ xix. 4, is a group of stars belonging to the two constellations of Aquarius and Pisces, in which the geomancers, who told fortunes by means of certain points traced at random, thought they saw a special series of these points,-:::..

------------------------------------------------------------------------ [281] _Purg._ iv. 61.

[282] “The burning Lion’s breast.” _Par._ xxi. 14.

[283] “Greater Fortune.” ------------------------------------------------------------------------

It is generally agreed that the “gemme” of _Purg._ ix. 4, “poste in figura del freddo animale, Che con la coda percote la gente,”[284] are some stars of Scorpio which were shining on the eastern horizon just before the moon rose on the first night in the Island of Purgatory.

------------------------------------------------------------------------ [284] “Gems ... set in the shape of that cold animal Which with its tail doth smite amain the nations.” (_Longfellow_). ------------------------------------------------------------------------

The zodiacal constellations in general are spoken of as “all the lights of his [the sun’s] path:” “Tutti i lumi della sua strada.” (_Par._ xxvi. 121, 122).

The pole star is described as the point of the axle round which the first sphere revolves.[285] The first sphere (or wheel, as it is called, with reference to its circling motion) is here the Primum Mobile, which was thought to cause the diurnal motion. This unique position gains for the pole star the name of “the star,” as for instance in _Conv._ III. v. 84, 85, where Dante says that a man standing at the north pole would have “la stella” directly over his head. And in Paradise he hears a voice among the spirits which makes him turn in its direction as the needle turns to the star—

------------------------------------------------------------------------ [285] _Par._ xiii. 11, 12.

“Voce, che l’ago alla stella Parer mi fece in volgermi al suo dove.”[286]

[286] “A voice, That made me seem like needle to the star, In turning to its whereabout.” _Par._ xii. 29, 30. (_Carey_). ------------------------------------------------------------------------

This property of the magnet was known in Dante’s day, as well as its power of attracting iron, though only the latter had been known to Ptolemy and the classical world. Whether the discovery came from China, where it is said that some form of compass has been used since the second century A.D., or whether it had been discovered independently by Arab or Italian navigators, we do not know: but scholars and poets in the twelfth and early thirteenth centuries write of the “ugly brown stone” used by sailors to make an instrument that cannot lie. For a needle, rubbed by it and run through a straw, when floated on water turns so surely to “the star” that one need never doubt its guidance. Thus writes Guyot, the poet of Languedoc, about 1200:—

“Un art font qui mentir ne puet, Par la vertu de la manete, Une pierre laide et brunete, Ou le fers volentiers se joint, Ont: si esgardent le droit point, Puis c’une aiguile i ont touchie, Et en un festu l’ont couchie, En l’eve la metent sanz plus,

* * * * *

Puis se torne la pointe toute Contre l’estoile si sanz doute, Que ja nas hom n’en doutera.”

And thus Ristoro:—

“L’angola, che guidi li marinari, chè per la virtu del cielo è tratta e rivolta alla stella la quale è chiamata tramontana.”[287]

------------------------------------------------------------------------ [287] “The needle which guides mariners, for by the virtue of the heavens it is attracted and turned towards that star which is called the North Star.” _Composizione del Mondo_, Bk. VII. part iv. ch. 2. ------------------------------------------------------------------------

Albertus Magnus speaks of it in the same way, as something well known to mariners.

It seems strange to us how Dante and his contemporaries failed to see the importance of this discovery; Brunetto Latini, when the ugly stone was shown to him on his visit to Roger Bacon at Oxford, even professing to regard it as a mere toy, of no practical use. Dante discusses the number of the stars known to Ptolemy, and describes the last mad voyage of Ulysses, who saw all the stars of the other pole, while ours sank low on the ocean floor;[288] but he does not seem to guess that the new toy would make possible even longer voyages than these, and that in time the blank in his celestial globe would be filled.

------------------------------------------------------------------------ [288] _Inf._ xxvi. 127-129. ------------------------------------------------------------------------

Yet even in his own life-time plucky little Genoa fitted out two galleys which ventured through the forbidden Straits, with intent to circumnavigate Africa and find a new route to India. And meanwhile, travelling by old overland or coasting routes, Italian missionary monks, and Italian traders, were visiting southern countries and describing southern skies. Friar Giovanni de Monte Corvino, who was in South India with Nicolo of Pistoia, writes home in 1291, telling of his disappointment that he had never been able to see “the other pole star” (l’altra tramontana), though he saw new stars moving round and evidently near to it, close to the southern horizon. A few years later Marco Polo the Venetian was dictating the story of his travels to a Pisan in Genoa: he had been further south than the missionaries, for in a certain island (probably Sumatra) he had seen the south pole “a spear’s length” above the horizon; and in the land of Zinzi (Zanzibar?) he had seen a marvellous star as big as a sack (which was evidently the Greater Magellanic Cloud). This he drew a picture of with his own hand.

Dante’s silence, and probable incredulity, regarding these experiences of his own countrymen and contemporaries is characteristic of his age; for scholars were too eager to explore the precious classical lore lately recovered from oblivion, to realize that they were on the threshold of a new era in knowledge, of which these men were pioneers.

It is sometimes thought, however, that Dante made use of contemporary observations of southern skies in his description of the stars he feigned himself to have seen when the Wain disappeared under his northern horizon.[289] Quite correctly, he does not place any single bright star to mark the south pole; his two constellations, one of four bright stars seen above the pole in the morning,[290] one of three which takes its place after sunset,[291] are these real or fictitious?

------------------------------------------------------------------------ [289] _Purg._ i. 30.

[290] _Purg._ i. 26.

[291] _Purg._ viii. 89. ------------------------------------------------------------------------

It is a fact that there are four bright stars in the form of a cross, lying between 56° and 63° south: are these Dante’s “quattro chiare stelle,” “quattro luci sante?”[292] They were not recognized as a separate constellation until the beginning of the sixteenth century, when Amerigo Vespucci described them in his letters about his southern voyages, and the Florentine Andrea Corsali wrote about the marvellous Cross which was so beautiful that in his opinion no other constellation in the sky was worthy to be compared with it. This, he believed, was the very cross of which Dante had spoken in a prophecy.

------------------------------------------------------------------------ [292] “Four bright stars, four sacred lights.” ------------------------------------------------------------------------

Even among Dante’s most enthusiastic admirers, I suppose none will be found to-day to support this view; but many think that he must have heard of the Cross from travellers. True, these stars are visible during at least part of the year in all places south of 34° north, and therefore in North Africa, and they had been catalogued by Ptolemy as part of the Centaur, so that no astronomer could take them to be a newly-found constellation, but might not some unscientific traveller like Marco Polo have brought a vague report of their position?

[Illustration: MAP OF STARS VISIBLE BEFORE DAWN IN PURGATORY. _To face p. 295_]

To this we might reply that Dante never says his four stars were in the form of a Cross; that there had to be four to represent the four Pagan virtues, the other constellation of three representing the three Christian virtues (compare the group of four handmaidens who sing, “Noi siam qui ninfe, e nel ciel siamo stelle,”[293] and are followed by a group of three);[294] and that this other constellation was certainly imaginary, since there is no group of three bright stars anywhere near the south pole.

------------------------------------------------------------------------ [293] “We are nymphs here, and in heaven we are stars.” _Purg._ xxxi. 104-106.

[294] _Purg._ xxxi. 111. ------------------------------------------------------------------------

But the fact is that conjectures and arguments are unnecessary, since Dante has expressly said that his four stars had never been seen before by anyone except the first people—“non viste mai fuor che alla prima gente,” (_Purg._ i. 24)—that is, our first parents, in that Eden of his imagining which was in the southern hemisphere, and on the island where he was then standing in his vision.

As a matter of curiosity I have included a map showing what stars would have been really visible to Dante at the supposed latitude of Purgatory, when Pisces was on the eastern horizon, as described in _Purg._ i. It will be seen that the Southern Cross is low, and would have been hidden behind the Mountain of Purgatory at five o’clock in the morning.[295]

------------------------------------------------------------------------ [295] Antonelli thinks the four stars were α and β Crucis, α and β Centauri, all of which had been mentioned by Ptolemy, and all lie near the circle which marks the limit of circumpolar stars in the supposed latitude of Purgatory (32° south). The three stars he says were ζ Navis, Canopus, and Achernar:—Antonelli, _Accenni alle Dottrine Astronomiche nella Divina Commedia_. ------------------------------------------------------------------------

Among northern constellations, Ursa Major is frequently spoken of by Dante, under different names, but always with reference to its high northern latitude. As the Wain, “il Carro,” it is said to be lying in the north-west when Pisces is on the eastern horizon, and to have disappeared from view in the southern hemisphere.[296] The wain-pole or shaft is pictured as sweeping round in the diurnal revolution, but always remaining above our horizon day and night, throughout its turning:

------------------------------------------------------------------------ [296] _Inf._ xi. 113, 114; _Purg._ i. 30.

“Quel Carro, a cui il seno Basta del nostro cielo e notte e giorno, Sì ch’ al volger del temo non vien meno.”[297]

[297] “The Wain, that in the bosom of our sky Spins ever on its axle, night and day.” _Par._ xiii. 7-9. (_Carey_). ------------------------------------------------------------------------

The same idea is expressed in the Midwinter Ode, where the constellation is called the Seven Frosty Stars, never lost to sight in Europe:—

“Fuggito è ogni augel che ’l caldo segue Dal paese d’Europa, che non perde Le sette stelle gelide unquemai.”[298]

------------------------------------------------------------------------ [298] “Fled is every bird that seeks the warmth, From European lands which never lose The seven cold stars.” _Canz._ xv. 27-29. ------------------------------------------------------------------------

This is a reminiscence of some lines of Boëthius quoted by Dante in _De Monarchia_, in which the northern nations are described as under the sway of the “septem gelidi triones.”[299] The Septem Triones, the Seven Ploughing Oxen, was one of the Latin names for Ursa Major, whence comes “septentrional” for North. This name also is used by Dante in _Purg._ xxx. 1, where the Seven Candlesticks of the mystic procession seen in the Garden of Eden are likened to these seven stars, and are named the Septentrion of the First Heaven (the Empyrean). This divine Septentrion was guiding the Procession, as the starry Septentrion of a lower heaven guides the mariner into port:

------------------------------------------------------------------------ [299] “Seven cold oxen.” _De Mon._ II. ix. 96.

“faceva lì ciascuno accorto Di suo dover, come il più basso face Qual timon gira per venire a porto.”[300]

[300] “To duty there Each one convoying, as that lower doth The steersman to his port.” _Purg._ xxx. 4-6. (_Carey_). ------------------------------------------------------------------------

Like the seven stars, also, the heavenly Septentrion is said figuratively to know neither setting nor rising, but unlike them it knows no cloud except of sin.[301] Because it is spoken of as guiding mariners, some commentators have taken the above to refer rather to Septentrio Minor (Ursa Minor), which also has seven chief stars, and is a better guide because nearer the Pole, as Thales taught; but the comparatively faint stars of the Little Bear would not be so apt a comparison with the celestial lights.

------------------------------------------------------------------------ [301] _Purg._ xxx. 1-3. ------------------------------------------------------------------------

By the name of the Bears, both Ursa Major and Minor are referred to as guides at sea in _Par._ ii. 9. In the strange new seas on which Dante warns his readers he is about to enter, Minerva will blow a favouring wind, Apollo will steer the barque, and the nine Muses will guide his course by the Bears. They are also spoken of together in _Purg._ iv. 65, to indicate the northern part of the sky.

A fifth name for Ursa Major is derived from the fable (known to Dante probably from Ovid’s _Metamorphoses_) of the nymph Helice, who was turned into a she-bear by Juno, and was hunted by her own son, Orcas. Jupiter transformed them into Ursa Major and Boötes.

“Se i barbari, venendo di tal plaga Che ciascun giorno d’Elice si copra, Rotante col suo figlio ond’ ell’ è vaga, Vedendo Rome e l’ ardua sua opra, Stupefaciensi....”[302]

------------------------------------------------------------------------ [302] “If the barbarians coming from some region That every day by Helice is covered, Revolving with her son whom she delights in, Beholding Rome and all her noble works Were wonder-struck....” _Par._ xxxi. 31-35. (_Longfellow_). ------------------------------------------------------------------------

Here we have the same idea as of the Wain wheeling round but never setting, with the addition of a neighbouring constellation describing a circle in the same time.

The Barbarians who lived in a region always dominated by Ursa Major, and came to marvel at the mighty buildings of ancient Rome, are probably the races of northern Europe in general; and this reminds us again of the lines of Boëthius quoted above, for it is among the peoples ruled by Rome that he mentions “quos premunt septem gelidi triones.”[303] If, however, Dante meant a country where the seven stars pass exactly overhead, the barbarians must have inhabited Scotland, or southern Scandinavia, or central Russia. If he means that Boötes also remained always above the horizon, they must have come from within the Arctic Circle, but this is not likely.

------------------------------------------------------------------------ [303] “Those under the sway of the seven cold oxen.” ------------------------------------------------------------------------

[Illustration: Fig. 42. Ursa Minor as a Horn. _Par._ xiii. 10.]

In one of the passages just quoted other constellations and stars are mentioned together with Ursa Major. In _Par._ xii. Dante has compared the two circles of spirits which surround Beatrice and himself to a double rainbow, and to two garlands of immortal roses. In the next canto he finds a new simile: in imagination he takes some of the brightest and most familiar stars from our sky, and makes of them two new constellations in the form of two crowns. The stars are these: fifteen from different parts of the sky, which are so brilliant that they shine through air dense enough to quench lesser orbs; the Wain, which never sets in our sky; and the mouth of the horn whose tip is the axis on which the Primum Mobile revolves. That is to say, as we have before remarked, Dante takes the fifteen first-magnitude stars and the stars instanced by Alfraganus as of second magnitude. Ursa Minor is aptly compared to a horn, the wide mouth of which is formed by its two bright stars Beta and Gamma,[304] while the narrow end is Alpha, the Pole Star. These twenty-four bright stars we must then imagine to group themselves into two constellations like that into which Ariadne, the daughter of Minos, was changed when she died; this is Corona Borealis or the Northern Crown, otherwise called Ariadne’s Crown, which suggests a circle, though it is not a perfect one. Dante uses the word “segni” for any constellations, a custom we find in Ristoro also, although the modern usage is to restrict “signs” to mean only divisions of the zodiac.

------------------------------------------------------------------------ [304] I do not know whether this comparison originated with Dante, but it was well known to Spanish sailors two centuries later. In the _Arte of Navigation_ which was “Englished out of the Spanyshe,” by Richard Eden in 1561, Beta and Gamma of Ursa Minor are referred to as “two starres called the Guardians, or the mouth of the horne.” ------------------------------------------------------------------------

The star-like spirits, thus grouped into a surpassingly brilliant double constellation, begin to sing their ineffable heavenly song, and to circle round the centre where Dante stands, in a marvellous dance, whose swiftness, when compared with anything known on earth, is as the movement of that swift heaven which carries with it all the rest, when compared with the flowing of the sluggish river Chiana.[305]

------------------------------------------------------------------------ [305] _Par._ xiii. 1-28. ------------------------------------------------------------------------

This passage helps us to understand expressions which often strike one as very strange, describing the circling movements of the spirits in Paradise. For the likeness to stars is clear throughout. Their brightness is an expression of their happiness,[306] and increases in each succeeding heaven. Only in the lowest can Dante see the forms and features of Piccarda and the other blessed spirits; in the next they clothe themselves in light, and although at first the radiant eyes of Justinian are seen, the first words addressed to him cause him to shine more brilliantly than before, and as the sun conceals himself by his own light, so the spirit conceals himself by the splendour which grows with his joy.[307] In the third heaven the spirits shine in the star of Venus like sparks seen in flame;[308] in the fourth they are called suns, and surpass the sun in brilliancy;[309] in the fifth they are compared with the Galaxy[310] and with shooting stars,[311] in the seventh and eighth with stars[312] and with spheres of light, turning on fixed poles and flaming like comets.[313]

------------------------------------------------------------------------ [306] _Par._ viii. 52, 53.

[307] _Par._ v. 136, 137.

[308] _Par._ viii. 16.

[309] _Par._ x. 76, 40-42.

[310] _Par._ xiv. 97-101.

[311] _Par._ xv. 13, 14.

[312] _Par._ xxi. 32, 33; xxiii. 26, 27.

[313] _Par._ xxii 23; xxiv. 11, 12. ------------------------------------------------------------------------

In like manner the swiftness of their motion increases in proportion to the clearness with which each beholds eternal truth.[314] The almost incredible speed with which Dante himself soars from sphere to sphere, and with which the spirits move—whether in coming towards him, impelled by Divine charity, in returning to the heaven of heavens, or in circling with one another in mystic dance—is frequently dwelt upon, and illustrated by many striking similes. The dance is always a circling or wheeling movement (“il giro,” “la rota,” _Par._ viii. 20 and 26; ix. 65). And besides this, individual spirits turn with a rapid motion, remaining on the same spot. Descending the celestial Ladder in the heaven of Saturn, step by step, they revolve:—

------------------------------------------------------------------------ [314] _Par._ viii. 20, 21; and xxviii. 100-102.

“Vid’ io più fiamelle Di grado in grado scendere e girarsi, Ed ogni giro le facea più belle.”[315]

[315] “Saw I many little flames From step to step descending and revolving, And every revolution made them fairer.” _Par._ xxi. 136-138. (_Longfellow_).

Compare 80, 81 and 39; and _Par._ xxiv. 10, 11. ------------------------------------------------------------------------

Now these two things, their light and their movements, were all the facts concerning the stars which mediæval astronomers could observe; and the movements were thought to be in circles and inconceivably rapid. Motion in circles, and especially the movement of rotation on an axis, remaining in the same place, had been said by Aristotle to be the most noble form of motion, and the fittest for celestial bodies. Therefore, when Dante represents the redeemed and the angels as expressing their bliss by radiance and marvellously rapid motion in circles, he makes them resemble the heavenly spheres and stars among which they manifest themselves to him. The motions are directly compared with those of stars in the passage already quoted:—

“Poi, sì cantando, quegli ardenti soli Si fur girati intorno a noi tre volte, Come stelle vicine ai fermi poli.”[316]

------------------------------------------------------------------------ [316] “As soon as singing thus those burning Suns Had round about us whirled themselves three times, Like unto stars neighbouring the steadfast poles.” _Par._ x. 76-78. (_Longfellow_). ------------------------------------------------------------------------

Remembering this significance of circular motion we shall feel a little less strange the similes of a mill and a top applied to the spirits of Paradise.[317]

A third way in which the spirits express their joy is by the sweetness of their song,[318] and here also they resemble the heavenly bodies, which make sweet music as they circle. This doctrine of Pythagoras was very popular throughout the Middle Ages.

------------------------------------------------------------------------ [317] _Par._ xxi. 80, 81; xii. 3; xviii. 41, 42.

[318] _Par._ xxiv. 22-24, x. 73, and many others. ------------------------------------------------------------------------

4. THE GALAXY.

The Galaxy or Milky Way is twice referred to in the _Divine Comedy_. In _Inf._ xvii. 106-108, it is in connection with the myth of Phaeton, who being allowed by his father Jove to drive the chariot of the sun for one day, lost control of his chargers, and going all astray, burned the sky in a part which still shows signs of this catastrophe, _i.e._ the Milky Way.

“Quando Fetòn abbandonò li freni, Per che il ciel, come pare ancor, si cosse.”[319]

------------------------------------------------------------------------ [319] “What time abandoned Phaëton the reins, Whereby the heavens, as still appears, were scorched.” _Inf._ xvii. 107-108. (_Longfellow_). ------------------------------------------------------------------------

This of course is only a poetical myth. But in the _Paradiso_, in three lines the appearance, colour, and approximate position of the Galaxy are described, and allusion is made to the difference of opinions between learned men with regard to the puzzling question of its nature. Dante is in the heaven of Mars. He sees the soldier saints, star-like and fiery red, some larger and some less, thronging thick in two great bands, which, crossing one another in the depths of the planet, form a marvellous Crucifix. The crowded lights make him think of the Galaxy, with its multitudinous points of light, differing in brightness, although that is white, and lies in a great circle between the celestial poles.

“Come, distinta da minori e maggi Lumi, biancheggia tra i poli del mondo Galassia sì che fa dubbiar ben saggi, Sì costellati facean nel profondo Marte quei rai il venerabil segno Che fan giunture di quadranti in tondo.”[320]

------------------------------------------------------------------------ [320] “Even as, distinct with less and greater lights, Glimmers between the two poles of the world The Galaxy that maketh wise men doubt, Thus constellated in the depths of Mars Those rays described the venerable sign That quadrants joining in a circle make.” _Par._ xiv. 97-102. (_Longfellow_). ------------------------------------------------------------------------

If we now turn to the fifteenth chapter of Treatise II. of the _Convivio_, we shall find the Phaeton myth and the various theories about the Milky Way set forth in due order, and shall learn which of these Dante considered to be true.

He is comparing the two sciences of Metaphysics and Physics with the Heaven of the Fixed Stars, and takes the opportunity to tell us some of the most important facts known about it. Here he calls the Galaxy a circle:—“La Galassia, cioè quello bianco cerchio che il vulgo chiama la Via de Santo Jacopo.”[321] This popular name perhaps arose through a confusion of Galaxy and Galicia, where was a famous shrine of St. James, and hence came the belief in Italy that the _Galassia_ was a sign by night to guide pilgrims on their way to this shrine at Compostella in _Galizia_.

------------------------------------------------------------------------ [321] “The Galaxy, that is, the white circle commonly called St. James’s Way.” ------------------------------------------------------------------------

Dante proceeds as follows with his comparison:—

“E per la Galassia, ha questo cielo grande similitudine colla Metafisica. Perchè è da sapere che di quella Galassia li filosofi hanno avuto diverse opinioni. Chè li Pittagorici dissero che ’l sole alcuna fiata errò nella sua via, e, passando per altre parti non convenienti al suo fervore, arse il luogo, per lo quale passò; e rimasevi quell’ apparenza dell’ arsura. E credo che si mossero dalla favola di Fetonte, la quale narra Ovidio nel principio del secondo di _Metamorfoseos_. Altri dissero (siccome fu Anassagora e Democrito) che ciò era lume del sole ripercosso in quella parte. E queste opinioni con ragioni dimostrative riprovarono. Quello che Aristotile si dicesse di ciò, non si può bene sapere, perchè la sua sentenza non si trova cotale nell’ una traslazione come nell’ altra. E credo che fosse l’errore de’ traslatori; che nella Nuova par dicere che ciò sia uno raunamento di vapori sotto le stelle di quelle parte, che sempre traggono quelli; e questa non pare avere ragione vera. Nella Vecchia dice, che la Galassia non è altro che multitudine di stelle fisse in quella parte, tanto picciole che distinguere di quaggiù non le potemo, ma di loro apparisce quello albore il quale noi chiamiamo Galassia. [E puote essere che il cielo in quella parte è più spesso, e però ritiene e ripresenta quello lume] e questa opinione pare avere, con Aristotile, Avicenna e Tolommeo. Onde conciossiacosachè la Galassia sia uno effetto di quelle stelle le quali non potemo vedere, se non per lo effetto loro intendiamo quelle cose, e la Metafisica tratta delle prime sustanze, le quali noi non potemo simigliantemente intendere se non per li loro effetti; manifesto è che ’l cielo stellato ha grande similitudine colla Metafisica.”[322]

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