Mi384 + ⅛ = 432Re432 + ⅛ = 486Ut486 : 512 : : 243 : 256Si512 + ⅛ = 576La576 + ⅛ = 648Sol648 + ⅛ = 729Fa729 : 768 : : 243 : 256Mi768 + ⅛ = 864Re864 + ⅛ = 972Ut972 : 1024 : : 243 : 256Si1024 + ⅛ = 1152La1152 + ⅛ = 1296Sol1296 + ⅛ = 1458Fa1458 : 1536 : : 243 : 256Mi1536 + ⅛ = 1728Re1728 + ⅛ = 1944Ut1944 : 2048 : 243 : 256Si2048 + 139 = 2187Si 22187 : 2304 : : 243 : 256La2304 + ⅛ = 2592Sol2592 + ⅛ = 2916Fa2916 : 3072 : : 243 : 256Mi3072 + ⅛ = 3456Re3457 + ⅛ = 3888Ut3888 + ⅛ = 4374Si4374 : 4608 : : 243 : 256La4608 + ⅛ = 5184Sol5184 + ⅛ = 5832Fa5832 : 6144 : : 243 : 256Mi6144 + 417 = 6561Mi 26561 : 6912 : : 243 : 256Re6912 + ⅛ = 7776Ut7776 + ⅛ = 8748Si8748 : 9216 : : 243 : 256La9216 + ⅛ = 10368Sol10368 = 384 + 27
The empyreal heaven.Sum of all the terms, 114,695.
This series they considered a complete one, because by taking the terms in their proper intervals, the last becomes 27 times the original number, and in the school of Pythagoras this 27 had a mystic signification, and was considered as the perfect number.
The reason for considering 27 a perfect number was curious.It is the sum of the first linear, square, and cubic numbers added to unity. First there is 1, which represents the point, then 2 and 3, the first linear numbers, even and uneven, then 4 and 9, the first square or surface numbers, even and uneven, and the last 8 and 27, the first solid or cubic numbers, even and uneven, and 27 is the sum of all the former. Whence, taking the number 27 as the symbol of the universe, and the numbers which compose it as the elements, it appeared right that the soul of the universe should be composed of the same elements.
On this scale of distances, with corresponding velocities, they arranged the various planets, and the universe comprehended all these spheres, from that of the fixed stars (which was excluded) to the centre of the earth. The sphere of the fixed stars was the common envelope, or circumference of the universe, and Saturn, immediately below it, corresponded to the thirty-sixth tone, and the earth to the first, and the other planets with the sun and moon at the various harmonic distances.
They reckoned one tone from the earth to the moon, half a tone from the moon to Mercury, another half-tone to Venus, one tone and a half from Venus to the sun, one from the sun to Mars, a semitone from Mars to Jupiter, half a tone from Jupiter to Saturn, and a tone and a half from Saturn to the fixed stars; but these distances were not, as we shall see, universally agreed upon.
According to Timæus, the sphere of the fixed stars, whichcontains within it no principle of contrariety, being entirely divine and pure, always moves with an equal motion in the same direction from east to west. But the stars which are within it, being animated by the mixed principle, whose composition has been just explained, and thus containing two contrary forces, yield on account of one of these forces to the motion of the sphere of fixed stars from east to west, and by the other they resist it, and move in a contrary direction, in proportion to the degree with which they are endowed with each; that is to say, that the greater the proportion of the material to the divine force that they possess, the greater is their motion from west to east, and the sooner they accomplish their periodic course. Now the amount of this force depends on the matter they contain. Thus, according to this system, the planets turn each day by the common motion with all the heavens about the earth from east to west, but they also retrograde towards the east, and accomplish their periods according to their component parts.
The additions which Plato made to this theory have always been a proverb of obscurity, and none of his commentators have been able to make anything of them, and very possibly they were never intended to.
So far the harmony of the heavenly bodies has been explained with reference to numbers only, and we may add to this that they reckoned 126,000 stadia, or 14,286 miles, to represent a tone, which was thus the distance of the earth tothe moon, and the same measurement made it 500,000 from the earth to the sun, and the same distance from the sun to the fixed stars.
But Plato teaches in hisRepublicthat there is actual musical, harmony between the planets. Each of the spheres, he said, carried with it a Siren, and each of these sounding a different note, they formed by their union a perfect concert, and being themselves delighted with their own harmony, they sang divine songs, and accompanied them by a sacred dance. The ancients said there were nine Muses, eight of whom, according to Plato, presided over celestial, and the ninth over terrestrial things, to protect them from disorder and irregularity.
Cicero and Macrobius also express opinions on this harmonious concert. Such great motions, says Cicero, cannot take place in silence, and it is natural that the two extremes should have related sounds as in the octave. The fixed stars must execute the upper note, and the moon the base. Kepler has improved on this, and says Jupiter and Saturn sing bass, Mars takes the tenor, the earth and Venus are contralto, and Mercury is soprano! True, no one has ever heard these sounds, but Pythagoras himself may answer this objection. We are always surrounded, he says, by this melody, and our ears are accustomed to it from our birth, so that, having nothing different to compare it with, we cannot perceive it.
We may here recall the further development of the idea of the soul of the universe, which was the source of this harmony, and endeavour to find a rational interpretation of their meaning. They said that nature had made the animals mortal and ephemeral, and had infused their souls into them, as they had been extracts from the sun or moon, or even from one of the planets. A portion of the unchangeable essence was added to the reasoning part of man, to form a germ of wisdom in privileged individuals. For the human soul there is one part which possesses intelligence and reason, and another part which has neither the one nor the other.
The various portions of the general soul of the universe resided, according to Timæus, in the different planets, and depended on their various characters. Some portions were in the moon, others in Mercury, Venus, or Mars, and so on, and thus they give rise to the various characters and dispositions that are seen among men. But to these parts of the human soul that are taken from the planets is joined a spark of the supreme Divinity, which is above them all, and this makes man a more holy animal than all the rest, and enables him to have immediate converse with the Deity himself. All the different substances in nature were supposed to be endowed with more or less of this soul, according to their material nature or subtilty, and were placed in the same order along the line, from the centre to the circumference, on which the planets were situated, as we have seenabove. In the centre was the earth, the heaviest and grossest of all, which had but little if any soul at all. Between the earth and the moon, Timæus placed first water, then the air, and lastly elementary fire, which he considered to be principles, which were less material in proportion as they were more remote and partook of a larger quantity of the soul of the universe. Beyond the moon came all the planets, and thus were filled up the greater number of the harmonic degrees, the motions of the various bodies being guided by the principle enunciated above.
When we carefully consider this theory we find that by a slight change of name we may bring it more into harmony with modern ideas. It would appear indeed that the ancients called that "soul" which we now call "force," and while we say that this force of attraction is in proportion to the masses and the inverse square of the distance, they put it that it was proportional to the matter, and to the divine substance on which the distance depended. So that we may interpret Timæus as stating this proposition:The distances of the stars and their forces are proportional among themselves to their periodic times."Some people," says Plutarch, "seek the proportions of the soul of the universe in the velocities (or periodic times), others in the distances from the centre; some in the masses of the heavenly bodies, and others more acute in the ratios of the diameters of their orbits. It is probable that the mass of each planet, theintervals between the spheres and the velocities of their motions, are like well-tuned musical instruments, all proportional harmonically with each other and with all other parts of the universe, and by necessary consequence that there are the same relative proportions in the soul of the universe by which they were formed by the Deity."
It is marvellous how deeply occupied were all the best minds in Greece and Italy on this subject, both poets and philosophers; Ocellus, Democritus, Timæus, Aristotle, and Lucretius have all left treatises on the same subject, and almost with the same title, "The Nature of the Universe."
Though somewhat similar to that of Timæus, it will be interesting to give an account of the ideas of one of these, Ocellus of Lucania.
Ocellus represents the universe as having a spherical form. This sphere is divided into concentric layers; above that of the moon they were called celestial spheres, while below it and inwards as far as the centre of the earth they were called the elementary spheres, and the earth was the centre of them all.
In the celestial spheres all the stars were situated, which were so many gods, and among them the sun, the largest and most powerful of all. In these spheres is never any disturbance, storm, or destruction, and consequently no reparation, no reproduction, no action of any kind was required on the part of the gods. Below the moon all is at war, all is destroyed and reconstructed, and here therefore it is thatgenerations are possible. But these take place under the influence of the stars, and particularly that of the sun, which in its course acts in different ways on the elementary spheres, and produces continual variations in them, from whence arises the replenishing and diversifying of nature. It is the sun that lights up the region of fire, that dilates the air, melts the water, and renders fertile the earth, in its daily course from east to west, as well as in this annual journey into the two tropics. But to what does the earth owe its germs and its species? According to some philosophers these germs were celestial ideas which both gods and demons scattered from above over every part of nature, but according to Ocellus they arise continually under the influence of the heavenly bodies. The divisions of the heavens were supposed to separate the portion that is unalterable from that which is in ceaseless change. The line dividing the mortal from the immortal is that described by the moon: all that lies above that, inclusive, is the habitation of the gods; all that lies below is the abode of nature and discord; the latter tending constantly to destruction, the former to the reconstruction of all created things.
Ideas such as these, of which we could give other examples more remotely connected with harmony, whatever amount of truth we may discover in them, prove themselves to have been made before the sciences of observation had enabled men to make anything better than empty theories, and tosupport them with false logic. No better example of the latter can perhaps be mentioned here than the way in which Ocellus pretends to prove that the world is eternal. "The universe," he says, "havingalways existed, it follows that everything in it and every arrangement of it must always have been as it is now. The several parts of the universehavingalways existed with it, we may say the same of the parts of these parts; thus the sun, the moon, the fixed stars, and the planets have always existed with the heavens; animals, vegetables, gold, and silver with the earth; the currents of air, winds, and changes from hot to cold, from cold to hot, with the air.Thereforethe heaven, with all that it now contains; the earth, with all that it produces and supports; and lastly, the whole aërial region, with all its phenomena, have always existed." When this system of argument passed away, and exact observation took its place, it was soon found that so far from what the ancients had arguedmust bereally being the case, no such relation as they indicated between the distances or velocities of the planets could be traced, and therefore no harmony in the heavens in this sense. It is not indeed that we can say no sounds exist because we hear none; but considering harmony really to consist of the relations of numbers, no such relations exist between the planets' distances, as measured now of course from the sun, instead of being, as then, imagined from the earth.
The gamut is nothing else than the series of numbers:—
doremifasollasido19/85/44/33/25/315/82
and is independent of our perception of the corresponding notes. A concert played before a deaf assembly would be a concert still. If one note is made by 10,000 vibrations per second, and another by 20,000, we should hear them as an octave, but if one had only 10 and the other 20, they would still be an octave, though inaudible as notes to us; so too we may speak even of the harmony of luminous vibrations of ether, though they do not affect our ears.
The velocities of the planets do not coincide with the terms of this series. The nearer they are to the sun the faster is their motion, Mercury travelling at the mean rate of 55,000 metres a second, Venus, 36,800, the earth 30,550, Mars 24,448, Jupiter 13,000, Saturn 9,840, Uranus 6,800, and Neptune 5,500, numbers which are in the proportion roundly of 100, 67, 55, 44, 24, 16, 12, 10, which have no sufficient relation to the terms of an harmonic series, to make any harmony obvious.
Returning, however, to the ancient philosophers, we are led by their ideas about the soul of the universe to discover the origin of their gods and natural religion. They were persuaded that only living things could move, and consequently that the moving stars must be endowed with superiorintelligence. It may very well be that from the number seven of the planets, including the sun and moon, which were their earliest gods, arose the respect and superstition with which all nations, and especially the Orientals, regarded that number. From these arose the seven superior angels that are found in the theologies of the Chaldeans, Persians, and Arabians; the seven gates of Mithra, through which all souls must pass to reach the abode of bliss; the seven worlds of purification of the Indians, and all the other applications of the number seven which so largely figure in Judaism, and have descended from it to our own time. On the other hand, as we have seen, this number seven may have been derived from the number of the stars in the Pleiades.
We have noticed in our chapter on the History of the Zodiac how the various signs as they came round and were thought to influence the weather and other natural phenomena, came at last to be worshipped. Not less, of course, were the sun and moon deified, and that by nations who had no zodiac. Among the Egyptians the sun was painted in different forms according to the time of year, very much as he is represented in our own days in pictures of the old and new years. At the winter solstice with them he was an infant, at the spring equinox he was a young man, in summer a man in full age with flowing beard, and in the autumn an old man. Their fable of Osiris was founded on the same idea. They represented the sun by thehawk, and the moon by the Ibis, and to these two, worshipped under the names of Osiris and Isis they attributed the government of the world, and built a city, Heliopolis, to the former, in the temple of which they placed his statue.
The Phenicians in the same way, who were much influenced by ideas of religion, attributed divinity to the sun, moon, and stars, and regarded them as the sole causes of the production and destruction of all things. The sun, under the name of Hercules, was their great divinity.
The Ethiopians worshipped the same, and erected the famous table of the sun. Those who lived above Meroë, admitted the existence of eternal and incorruptible gods, among which they included the sun, moon, and the universe. Like the Incas of Peru, they called themselves the children of the sun, whom they regarded as their common father.
The moon was the great divinity of the Arabs. The Saracens called it Cabar, or the great, and its crescent still adorns the religious monuments of the Turks. Each of their tribes was under the protection of some particular star. Sabeism was the principal religion of the east. The heavens and the stars were its first object.
In reading the sacred books of the ancient Persians contained in theZendavesta, we find on every page invocations addressed to Mithra, to the moon, the stars, the elements, the mountains, the trees, and every part of nature.The ethereal fire circulating through all the universe, and of which the sun is the principal focus, was represented among the fire-worshippers by the sacred and perpetual fire of their priests. Each planet had its own particular temple, where incense was burnt in its honour. These ancient peoples embodied in their religious systems the ideas which, as we have seen, led among the Greeks to the representation of the harmony of heaven. All the world seemed to them animated by a principle of life which circulated through all parts, and which preserved it in an eternal activity. They thought that the universe lived like man and the other animals, or rather that these latter only lived because the universe was essentially alive, and communicated to them for an instant an infinitely small portion of its own immortality. They were not wise, it may be, in this, but they appear to have caught some of the ideas that lie at the basis of religious thought, and to have traced harmony where we have almost lost the perception of it.
In our former chapters we have gained some idea of the general structure of the heavens as represented by ancient philosophers, and we no longer require to know what was thought in the infancy of astronomy, when any ideas promulgated were more or less random ones; but in this chapter we hope to discuss those arrangements of the heavenly bodies which have been promulgated by men as complete systems, and were supposed to represent the totality of the facts.
The earliest thoroughly-established system is that of Ptolemy. It was not indeed invented by him. The main ideas had been entertained long before his time, but he gave it consistence and a name.
We obtain an excellent view of the general nature of this system from Cicero. He writes:—
"The universe is composed of nine circles, or rather of nine moving globes. The outermost sphere is that of the heavens which surrounds all the others, and on which arefixed the stars. Beneath this revolve seven other globes, carried round by a motion in a direction contrary to that of the heavens. On the first circle revolves the star which men call Saturn; on the second Jupiter shines, that beneficent and propitious star to human eyes; then follows Mars, ruddy and awful. Below, and occupying the middle region, revolves the Sun, the chief, prince, and moderator of the other stars, the soul of the world, whose immense globe spreads its light through space. After him come, like two companions, Venus and Mercury. Lastly, the lowest globe is occupied by the moon, which borrows its light from the star of day. Below this last celestial circle, there is nothing but what is mortal and corruptible, except the souls given by a beneficent Divinity to the race of men. Above the moon all is eternal. The earth, situated in the centre of the world, and separated from heaven on all sides, forms the ninth sphere; it remains immovable, and all heavy bodies are drawn to it by their own weight."
The earth, we should add, is surrounded by the sphere of air, and then by that of fire, and by that of ether and the meteors.
With respect to the motions of these spheres. The first circle described about the terrestrial system, namely, that of the moon, was accomplished in 27 days, 7 hours, and 43 minutes. Next to the moon, Mercury in the second, and Venus in the third, and the sun in the fourth circle, all turned about the earth in the same time, 365 days, 5 hours, and 49minutes. But these planets, in addition to the general movement, which carried them in 24 hours round from east to west and west to east, and the annual revolution, which made them run through the zodiacal circle, had a third motion by which they described a circle about each point of their orbit taken as a centre.
Fig. 14.Fig. 14.—Ptolemy's Astronomical System.
The fifth sphere, carrying Mars, accomplished its revolutionin two years. Jupiter took 11 years, 313 days, and 19 hours to complete his orbit, and Saturn in the seventh sphere took 29 years and 169 days. Above all the planets came the sphere of the fixed stars, or Firmament, turning from east to west in 24 hours with inconceivable rapidity, and endued also with a proper motion from west to east, which was measured by Hipparchus, and which we now call the precession of the equinoxes, and know that it has a period of 25,870 years. Above all these spheres, aprimum mobilegave motion to the whole machine, making it turn from east to west, but each planet and each fixed star made an effort against this motion, by means of which each of them accomplished their revolution about the earth in greater or less time, according to its distance, or the magnitude of the orbit it had to accomplish.
One immense difficulty attended this system. The apparent motions of the planets is not uniform, for sometimes they are seen to advance from west to east, when their motion is calleddirect, sometimes they are seen for several nights in succession at the same point in the heavens, when they are calledstationary, and sometimes they return from east to west, and then their motion is calledretrograde.
We know now that this apparent variation in the motion of the planets is simply due to the annual motion of the earth in its orbit round the sun. For example, Saturn describes its vast orbit in about thirty years, and the earthdescribes in one year a much smaller one inside. Now if the earth goes faster in the same direction as Saturn, it is plain that Saturn will be left behind and appear to go backwards, while if the earth is going in the same direction the velocity of Saturn will appear to be decreased, but his direction of motion will appear unaltered.
To explain these variations, however, according to his system, Ptolemy supposed that the planets did not move exactly in the circumference of their respective orbits, but about anideal centre, which itself moved along this circumference. Instead therefore of describing a circle, they described parts of a series of small circles, which would combine, as is easy to see, into a series of uninterrupted waves, and these he calledEpicycles.
Another objection, which even this arrangement did not overcome, was the variation of the size of the planets. To overcome this Hipparchus gave to the sphere of each planet a considerable thickness, and saw that the planet did not turn centrally round the earth, but round a centre of motion placed outside the earth. Its revolution took place in such a manner, that at one time it reached the inner boundary, at another time the outer boundary of its spherical heaven.
But this reply was not satisfactory, for the differences in the apparent sizes proved by the laws of optics such a prodigious difference between their distances from the earth at the times of conjunction and opposition, that it would beextremely difficult to imagine spheres thick enough to allow of it.
It was a gigantic and formidable piece of machinery to which it was necessary to be continually adding fresh pieces to make observation accord with theory. In the thirteenth century, in the times of the King-Astronomer, Alphonso X. of Castile, there were already seventy-five circles, one within the other. It is said that one day he exclaimed, in a full assemblage of bishops, that if the Deity had done him the honour to ask his advice before creating the world, he could have told Him how to make it a little better, or at all events more simply. He meant to express how unworthy this complication was of the dignity of nature.
Fig. 15.Fig. 15.—The Epicycles of Ptolemy.
Fracastor, in hisHomocentrics, says that nothing is more monstrous or absurd than all the excentrics and epicycles ofPtolemy, and proposes to explain the difference of velocity in the planets at different parts of their orbits by the medium offering greater or less resistance, and their alteration in apparent size by the effect of refraction.
The essential element of this system was that it took appearances for realities, and was founded on the assumption that the earth is fixed in the centre of the universe, and of course therefore neglected all the appearances produced by its motion, or had to explain them by some peculiarity in the other planets.
Although it was corrected from time to time to make it accord better with observation, it was the same essentially that was taught officially everywhere. It reigned supreme in Egypt, Greece, Italy, and Arabia, and in the great school of Alexandria, which consolidated it and enriched it by its own observations.
But though the same in essence, the details, and especially the means of overcoming the difficulties raised by increased observations, have much varied, and it will be interesting and instructive to record some of the chief of them.
One of the most important influences in modifying the astronomical systems taught to the world has been that of the Fathers of the Christian Church. When, after five centuries of patient toil, of hopes, ambitions, and discussions, the Christian Church took possession of the thrones and consciences of men, they founded their physical edifice onthe ancient system, which they adapted to their special wants. With them Aristotle and Ptolemy reigned supreme. They decreed that the earth constituted the universe, that the heavens were made for it, that God, the angels, and the saints inhabited an eternal abode of joy situated above the azure sphere of the fixed stars, and they embodied this gratifying illusion in all their illuminated manuscripts, their calendars, and their church windows.
The doctors of the Church all acknowledged a plurality of heavens, but they differed as to the number. St. Hilary of Poitiers would not fix it, and the same doubt held St. Basil back; but the rest, for the most part borrowing their ideas from paganism, said there were six or seven, or up to ten. They considered these heavens to be so many hemispheres supported on the earth, and gave to each a different name. In the system of Bede, which had many adherents, they were the Air, Ether, Fiery Space, Firmament, Heaven of the Angels, and Heaven of the Trinity.
The two chief varieties in the systems of the middle ages may be represented as follows:—
Those who wished to have everything as complete as possible combined the system of Ptolemy with that of the Fathers of the Church, and placed in the centre of the earth the infernal regions which they surrounded by a circle. Another circle marked the earth itself, and after that the surrounding ocean, marked as water, then the circle of air,and lastly that of fire. Enveloping these, and following one after the other, were the seven circles of the seven planets; the eighth represented the sphere of the fixed stars on the firmament, then came the ninth heaven, then a tenth, thecœlum cristallinum, and lastly an eleventh and outermost, which was the empyreal heaven, where dwelt the cherubim and seraphim, and above all the spheres was a throne on which sat the Father, as Jupiter Olympus.
The others who wished for more simplicity, represented the earth in the centre of the universe, with a circle to indicate the ocean, the second sphere was that of the moon; the third was that of the sun; on the fourth were placed the four planets, Jupiter, Mars, Venus and Mercury; there was a fifth for the space outside the planets, and the last outside one was the firmament; altogether seven spheres instead of eleven. As a specimen of the style of representation of the astronomical systems of the middle ages, we may take the figure on the following page:—
Fig. 16.Fig. 16.—Heavens of the Middle Ages.
Here we see the earth placed immovable in the centre of the universe, and represented by a disc traversed by the Mediterranean, and surrounded by the ocean. Round this are circumscribed the celestial spheres. That of the moon first, then that of Mercury, in which several constellations, as the Lyre, Cassiopeia, the Crown, and others, are roughly indicated, then comes the sphere of Venus with Sagittarius and the Swan. After this comes thecelestis paradisus, and the legend that, "the paradise to which Paul was raised is in this third locality; some of these must reach to us, since in them repose the souls of the prophets." Inthe other circles are yet other constellations: for example Pegasus, Andromeda, the Dog, Argo, the He-goat, Aquarius, the Fishes, and Canopus, figured by a star of the first magnitude. To the north is seen near the constellation of the Swan a large star with seven rays, meant to represent the brightest of those which compose the Great Bear. The stars of Cassiopeia are not only misplaced, but roughly represented. The Lyre is curiously drawn. The positions of the constellations just named are all wrong in this figure, just as we find those of towns in maps of the earth. The cartographers of the middle ages, with incredible ignorance, misplaced in general every locality. They did the same for the constellations in the celestial hemispheres. In the heaven of Jupiter, and in that of Saturn we read the words—Seraphim, Dominationes, Potestates, Archangeli, Virtutes cœlorum, Principatus, Throni, Cherubim, all derived from their theology. A veritable muddle! The angels placed with the heroes of mythology, the immortal virgins with Venus and Andromeda, and the Saints with the Great Bear, the Hydra, and the Scorpion!
Another such richly illuminated manuscript in the library at Ghent, entitled Liber Floridus, contains a drawing similar to this under the titleAstrologia secundum Bedum. Only, instead of the earth, there is a serpent in the centre with the name Great Bear, and the twins are represented by a man and woman, Andromeda in a chasuble, and Venus as a nun!
Several similar ones might be quoted, varying more or less from this; one, executed in a geographical manuscript of the fifteenth century, has the tenth sphere, being that of the fixed stars, then the crystalline heaven, and then the immovable heaven, "which," it says, "according to sacred and certain theology, is the dwelling-place of the blessed, where may we live for ever and ever, Amen;" "this is also called the empyreal heaven." Near each planet the author marks the time of its revolution, but not at all correctly.
The constructors of these systems were not in the least doubt as to their reality, for they actually measured the distance between one sphere and another, though in every case their numbers were far from the truth as we now know it. We may cite as an example an Italian system whose spheres were as follows:—Terra, Aqua, Aria, Fuoco, Luna, Mercurio, Venus, Sol, Marte, Giove, Saturno, Stelle fixe, Sfera nona, Cielo empyreo. Attached to the design is the following table of dimensions which we may copy:—
Miles.From the centre of the Earth to the surface3,245" " " " inner side of the heaven of the Moon107,936Diameter of Moon1,896From the centre of the Earth to Mercury209,198Diameter of Mercury230From the centre of the Earth to Venus579,320Diameter of Venus2,884From the centre of the Earth to the Sun3,892,866Diameter of the Sun35,700From the centre of the Earth to Mars4,268,629Diameter of Mars7,572From the centre of the Earth to Jupiter8,323,520Diameter of Jupiter29,641From the centre of the Earth to outside of Saturn's heaven52,544,702Diameter of Saturn29,202From the centre of the Earth to the fixed stars73,387,747
Plate VII.Plate VII.—Heavens of the Fathers.
The author states that he cannot pursue his calculations further, and condescends to acknowledge that it is very difficult to know accurately what is the thickness of the ninth and of the crystalline heavens!
Perhaps, however, these reckonings are better than those of the Egyptians, who came to the conclusion that Saturn was only distant 492 miles, the sun only 369, and the moon 246.
These numerous variations and adaptations of the Ptolemaic system, prove what a firm hold it had taken, and how it reigned supreme over all minds. Nor are we merely left to gather this. They consciously looked to Ptolemy as their great light, if we may judge from an emblematic drawing taken from an authoritative astronomical work, theMargarita Philosophica, which we give on the opposite page.
In all the systems derived from Ptolemy, the order of the planets remained the same, and Mercury and Venus were placed nearer to the earth than the sun is. According to many authors, however, Plato made a variation in thisrespect, by putting them outside the sun, on the ground that they never were seen to pass across its surface. He had obviously never heard of the "Transit of Venus." This arrangement was adopted by Theon, in his commentary on theAlmagestaof Ptolemy, and afterwards by Geber, who alone among the Arabians departed from the strict Ptolemaic system.
Fig. 17.Fig. 17.
Fig. 18.Fig. 18.—Egyptian System.
The Egyptians improved upon this idea, and made the first step towards the true system, by representing these two planets, Mercury and Venus, as revolving round the sun instead of the earth. All the rest of their system was the same as that of Ptolemy, for the sun itself, and the other planets and the fixed stars all revolved round the earth in the centre. This system of course accounted accurately for the motions of the two inferior planets, whose nearness to the sun may have suggested their connection with it. This system was invogue at the same time as Ptolemy's, and numbers Vitruvius amongst its supporters.
Fig. 19.Fig. 19.—Capella's System.
In the fifth century of our era Martian Capella taught a variation on the Egyptian system, in which he made Mercury and Venus revolve in the same orbit round the sun. In the treatise entitledQuod Tellus non sit Centrum Omnibus Planetis, he explains that when Mercury is on this side of the orbit it is nearer to us than Venus, and farther offfrom us than that planet when it is on the other side. This hypothesis was also adopted in the middle ages.
We have here indicated the time of the revolution of the various planets, and notice that the firmament is said to move round from west to east in 7,000 years; the second heaven in 49,000, while theprimum mobileoutside moved in the contrary direction in twenty-four hours.
These Egyptian systems survived in some places the true one, as they were thought to overcome the chief difficulties of the Ptolemaic without interfering with the stability of the earth, and they were known as thecommon system,i.e.containing the elements of both.
Such were the astronomical systems in vogue before the time of Copernicus—all of them based upon the principle of the earth being the immovable centre of the universe. We must now turn to trace the history of the introduction of that system which has completely thrown over all these former ones, and which every one knows now to be the true one—the Copernican.
No revolution is accomplished, whether in science or politics, without having been long in preparation. The theory of the motion of the earth had been conceived, discussed, and even taught many ages before the birth of Copernicus. And the best proof of this is the acknowledgment of Copernicus himself in his great workDeRevolutionibus Orbium Cælestium, in which he laid down the principles of his system. We will quote the passage in which it is contained.
"I have been at the trouble," he writes, "to read over all the works of philosophers that I could procure, to see if I could find in them any different opinion to that which is now taught in the schools respecting the motions of the celestial spheres. And I saw first in Cicero that Mætas had put forth the opinion that the earth moves. (Mætam sensisse terram moveri.) Afterwards I found in Plutarch that others had entertained the same idea."
Here Copernicus quotes the original as far as it relates to the system of Philolaus, to the effect "that the earth turns round the region of fire (ethereal region), and runs through the zodiac like the sun and the moon." The principal Pythagoreans, such as Archytas of Tarentum, Heraclides of Pontium, taught also the same doctrine, saying that "the earth is not immovable in the centre of the universe, but revolves in a circle, and is far from occupying the chief place among the celestial bodies."
Pythagoras learnt this doctrine, it is said, from the Egyptians, who in their hieroglyphics represented the symbol of the sun by the stercoral beetle, because this insect forms a ball with the excrement of the oxen, and lying down on its back, turns it round and round with its legs.
Timæus of Locris was more precise than the other Pythagoreans in calling "the five planets the organs of time, on account of their revolutions," adding that we must conclude that the earth is not immovable in one place, but that it turns, on the contrary, about itself, and travels also through space.
Plutarch records that Plato, who had always taught that the sun turned round the earth, had changed his opinion towards the end of his life, regretting that he had not placed the sun in the centre of the universe, which was the only place, he then thought, that was suitable for that star.
Three centuries before Jesus Christ, Aristarchus of Samos is said by Aristotle to have composed a special work to defend the motion of the earth against the contrary opinions of philosophers. In this work, which is now lost, he laid down in the most positive manner that "the sun remains immovable, and that the Earth moves round it in a circular curve, of which that star is the centre." It would be impossible to state this in clearer terms; and what makes his meaning more clear, if possible, is that he was persecuted for it, being accused of irreligion and of troubling the repose of Vesta—"because," says Plutarch, "in order to explain the phenomena, he taught that the heavens were immovable, and that the earth accomplished a motion of translation in an oblique line, at the sametime that it turned round its own axis." This is exactly the opinion that Copernicus took up, after an interval of eighteen centuries—and he too was accused of irreligion.
In passing from the Greeks to the Romans, and from them to the middle ages, the doctrine of Aristarchus underwent a curious modification, assimilating it to the system of Tycho Brahe, which we shall hereafter consider, rather than to that of Copernicus. This consisted in making the planets move round the sun, while the sun itself revolved round the earth, and carried them with him, and the heavens revolved round all. Vitruvius and Macrobius both taught this doctrine. Although Cicero and Seneca, with Aristotle and the Stoics, taught the immobility of the earth in the centre of the universe, the question seemed undecided, to Seneca at least, who writes:—"It would be well to examine whether it is the universe that turns about the immovable earth, or the earth that moves, while the universe remains at rest. Indeed some men have taught that the earth is carried along, unknown to ourselves, that it is not the motion of the heavens that produces the rising and setting of the stars, but that it is we who rise and set relatively to them. It is a matter worthy of contemplation, to know in what state we are—whether we are assigned an immovable or rapidly-moving home—whether God makes all things revolve round us, or we round them."
The double motion of the earth, then, is an idea revivedfrom the Grecian philosophers. The theory was known indeed to Ptolemy, who devotes a whole chapter in his celebratedAlmagestato combat it. From his point of view it seemed very absurd, and he did not hesitate to call it so; and it was in reality only when fresh discoveries had altered the method of examining the question that the absurdities disappeared, and were transferred to the other side. Not until it was discovered that the earth was no larger and no heavier than the other planets could the idea of its revolution and translation have appeared anything else than absurd. We are apt to laugh at the errors of former great men, while we forget the scantiness of the knowledge they then possessed. So it will be instructive to draw attention to Ptolemy's arguments, that we may see where it is that new knowledge and ideas have led us, as they would doubtless have led him, had he possessed them, to a different conclusion.
His argument depends essentially on the observed effects of weight. "Light bodies," he says, "are carried towards the circumference, they appear to us to goup; because we so speak of the space that is over our heads, as far as the surface which appears to surround us. Heavy bodies tend, on the contrary, towards the middle, as towards a centre, and they appear to us to falldown, because we so speak of whatever is under our feet, in the direction of the centre of the earth. These bodies are piled up roundthe centre by the opposed forces of their impetus and friction. We can easily see that the whole mass of the earth, being so large compared with the bodies that fall upon it, can receive them without their weight or their velocity communicating to it any perceptible oscillation. Now if the earth had a motion in common with all the other heavy bodies, it would not be long, on account of its weight, in leaving the animals and other bodies behind it, and without support, and it would soon itself fall out of heaven. Such would be the consequences of its motion, which are most ridiculous even to imagine."
Against the idea of the earth's diurnal rotation he argued as follows:—"There are some who pretend that nothing prevents us from supposing that the heaven remains immovable, and the earth turns round upon its axis from west to east, accomplishing the rotation each day. It is true that, as far as the stars are concerned, there is nothing against our supposing this, if guided only by appearances, and for greater simplicity; but those who do so forget how thoroughly ridiculous it is when we consider what happens near us and in the air. For even if we admit, which is not the case, that the lighter bodies have no motion, or only move as bodies of a contrary nature, although we see that aërial bodies move with greater velocity than terrestrial—if we admit that very dense and heavy bodies have a rapid and constant motion of their own, whereasin reality they obey but with difficulty the impulses communicated to them—we should then be obliged to assert that the earth, by its rotation, has a more rapid motion than any of the bodies that are round it, as it makes so large a circuit in so short a time. In this case the bodies which are not supported by it would appear to have a motion contrary to it, and no cloud or any flying bird could ever appear to go to the east, since the earth would always move faster than it in that direction."
TheAlmagestawas for a long time the gospel of astronomers; to believe in the motion of the earth was to them more than an innovation, it was simply folly. Copernicus himself well expresses the state of opinion in which he found the question, and the process of his own change, in the following words:—"And I too, taking occasion by these testimonies, commenced to cogitate on the motion of the earth, and although that opinion appeared absurd, I thought that as others before me had invented an assemblage of circles to explain the motion of the stars, I might also try if, by supposing the earth to move, I could not find a better account of the motions of the heavenly bodies than that with which we are at present contented. After long researches, I am at last convinced that if we assign to the circulation of the earth the motions of the other planets, calculation and observation will agree better together. And I have no doubt that mathematicians will be of my opinion, if they willtake the trouble to consider carefully and not superficially the demonstrations I shall give in this work." Although the opinions of Copernicus had been held before, it is very just that his should be the name by which they are known; for during the time that elapsed before he wrote, the adherents of such views became fewer and fewer, until at last the very remembrance of them was almost forgotten, and it required research to know who had held them and taught them. It took him thirty years' work to establish them on a firm basis. We shall make no excuse for quoting further from his book, that we may know exactly the circumstances, as far as he tells us, of his giving this system to the world.
"I hesitated for a long time whether I should publish my commentaries on the motions of the heavenly bodies, or whether it would not be better to follow the example of certain Pythagoreans, who left no writings, but communicated the mysteries of their philosophy orally from man to man among their adepts and friends, as is proved by the letter of Lysidas to Hipparchus. They did not do this, as some suppose, from a spirit of jealousy, but in order that weighty questions, studied with great care by illustrious men, might not be disparaged by the idle, who do not care to undertake serious study, unless it be lucrative, or by shallow-minded men, who, though devoting themselves to science, are of so indolent a spirit that they only intrude among philosophers, like drones among bees.
"When I hesitated and held back, my friends pressed me on. The first was Nicolas Schonberg, Cardinal of Capua, a man of great learning. The other was my best friend, Tideman Gysius, Bishop of Culm, who was as well versed in the Holy Scriptures as in the sciences. The latter pressed me so much that he decided me at last to give to the public the work I had kept for more than twenty-seven years. Many illustrious men urged me, in the interest of mathematics, to overcome my repugnance and to let the fruit of my labours see the light. They assured me that the more my theory of the motion of the earth appeared absurd, the more it would be admired when the publication of my work had dissipated doubts by the clearest demonstrations. Yielding to these entreaties, and buoying myself with the same hope, I consented to the printing of my work."
He tried to guard himself against the attacks of dogmatists by saying, "If any evil-advised person should quote against me any texts of Scripture, I deprecate such a rash attempt. Mathematical truths can only be judged by mathematicians."
Notwithstanding this, however, his work, after his death, was condemned by the Index in 1616, under Paul V.
On examining the ancient systems, Copernicus was struck by the want of harmony in the arrangements proposed, and by the arbitrary manner in which new principles were introduced and old ones neglected, comparing the system to a collection of legs and arms not united to any trunk, and it was thesimplicity and harmony which the one idea of the motion of the earth introduced into the whole system that convinced him most thoroughly of its truth.
He knew well that new views and truths would appear as paradoxes, and be rejected by men who were wedded to old doctrines, and on this account he took such pains to show that these views had been held before, and thus to disarm them of their apparent novelty.