alone! some of which we may learn from Plutarch. The Milky Way, he says, is a nebulous circle, which constantly appears in the sky, and which owes its name to its white appearance. Certain Pythagoreans a.s.sert that when Phaeton lit up the universe, one star, which escaped from its proper place, set light to the whole s.p.a.ce it pa.s.sed over in its circular course, and so formed the Milky Way. Others thought that this circle was where the sun had been moving at the beginning of the world.

According to others it is but an optical phenomenon produced by the reflection of the sun's rays from the vault of the sky as from a mirror, and comparable with the effects seen in the rainbow and illuminated clouds. Metrodorus says it is the mark of the sun's pa.s.sage which moves along this circle. Parmenidas pretends that the milky colour arises from a mixture of dense and rare air. Anaxagoras thinks it an effect of the earth's shadow projected on this part of the heavens, when the sun is below. Democritus says that it is the l.u.s.tre of several little stars which are very near together, and which reciprocally illuminate each other. Aristotle believes it to be a vast ma.s.s of arid vapours, which takes fire from a glowing tress, above the region of the ether, and far below that of the planets. Posidonius says that the circle is a compound of fire less dense than that of the stars, but more luminous.

All such opinions, except that of Democritus, are of little value, because founded on nothing; perhaps the worst is that of Theophrastus, who said it was the junction between the two hemispheres, which together formed the vault of heaven: and that it was so badly made that it let through some of the light that he supposed to exist everywhere behind the solid sky.

We now know that the Milky Way, like many of the nebulae, is an immense agglomeration of suns. The Milky Way is itself a nebula, a ma.s.s of sidereal systems, with our own among them, since our sun is a single star in this vast archipelago of eighteen million orbs. The Greeks called it the Galaxy. The Chinese and Arabians call it the River of Heaven. It is the Path of Souls among the North American Indians, and the Road of S. Jacques de Compostelle among French peasants.

In tracing the history of ideas concerning the structure of the heavens among the Greek philosophers, we meet with other modifications which it will be interesting to recount. Thus Eudoxus, who paid greater attention than others to the variations of the motions of the planets, gave more than one sphere to each of them to represent these observed changes.

Each planet, according to him, has a separate part of the heaven to itself, which is composed of several concentric spheres, whose movements, modifying each other, produce that of the planet. He gave three spheres to the sun: one which turned from east to west in twenty-four hours, to represent the diurnal rotation; a second, which turned about the pole of the ecliptic in 365-1/4 days, and produced its annual movement; and a third was added to account for a certain supposed motion, by which the sun was drawn out of the ecliptic, and turned about an axis, making such an angle with that of the ecliptic, as represented the supposed aberration. The moon also had three spheres to produce its motions in longitude and lat.i.tude, and its diurnal motion. Each of the other planets had four, the extra one being added to account for their stations and retrogressions. It should be added that these concentric spheres were supposed to fit each other, so that the different planets were only separated by the thicknesses of these crystal zones.

Polemarch, the disciple of Eudoxus, who went to Athens with his pupil Calippus for the express purpose of consulting Aristotle on these subjects, was not satisfied with the exactness with which these spheres represented the planetary motions, and made changes in the direction of still greater complication. Instead of the twenty-six spheres which represented Eudoxus' system, Calippus established thirty-three, and by adding also intermediary spheres to prevent the motion of one planet interfering with that of the adjacent ones, the number was increased to fifty-six.

There is extant a small work, ascribed to Aristotle, ent.i.tled "Letter of Aristotle to Alexander on the system of the world," which gives so clear an account of the ideas entertained in his epoch that we shall venture to give a somewhat long extract from it. The work, it should be said, is not by all considered genuine, but is ascribed by some to Nicolas of Damas, by others to Anaximenas of Lampsacus, a contemporary of Alexander's, and by others to the Stoic Posidonius. It is certain, however, that Aristotle paid some attention to astronomy, for he records the rare phenomena of an eclipse of Mars by the moon, and the occultation of one of the Gemini by the planet Jupiter, and the work may well be genuine. It contains the following:--

"There is a fixed and immovable centre to the universe. This is occupied by the earth, the fruitful mother, the common focus of every kind of living thing. Immediately surrounding it on all sides is the air. Above this in the highest region is the dwelling-place of the G.o.ds, which is called the heavens. The heavens and the universe being spherical and in continual motion, there must be two points on opposite sides, as in a globe which turns about an axis, and these points must be immovable, and have the sphere between them, since the universe turns about them. They are called the poles. If a line be drawn from one of these points to the other it will be the diameter of the universe, having the earth in the centre and the two poles at the extremities; of these two poles the northern one is always visible above our horizon, and is called the Arctic pole; the other, to the south, is always invisible to us--it is called the Antarctic pole.

"The substance of the heavens and of the stars is called ether; not that it is composed of flame, as pretended by some who have not considered its nature, which is very different from that of fire, but it is so called because it has an eternal circular motion, being a divine and incorruptible element, altogether different from the other four.

"Of the stars contained in the heavens some are fixed, and turn with the heavens, constantly maintaining their relative positions. In their middle portion is the circle called the _zooph.o.r.e_, which stretches obliquely from one tropic to the other, and is divided into twelve parts, which are the twelve signs (of the zodiac). The others are wandering stars, and move neither with the same velocity as the fixed stars, nor with a uniform velocity among themselves, but all in different circles, and with velocities depending on the distances of these circles from the earth.

"Although all the fixed stars move on the same surface of the heavens, their number cannot be determined. Of the movable stars there are seven, which circulate in as many concentric circles, so arranged that the lower circle is smaller than the higher, and that the seven so placed one within the other are all within the spheres of the fixed stars.

"On the nearer, that is inner, side of this ethereal, immovable, unalterable, impa.s.sible nature is placed our movable, corruptible, and mortal nature. Of this there are several kinds, the first of which is fire, a subtle inflammable essence, which is kindled by the great pressure and rapid motion of the ether. It is in this region of air, when any disturbance takes place in it, that we see kindled shooting-stars, streaks of light, and shining motes, and it is there that comets are lighted and extinguished.

"Below the fire comes the air, by nature cold and dark, but which is warmed and enflamed, and becomes luminous by its motion. It is in the region of the air, which is pa.s.sive and changeable in any manner, that the clouds condense, and rain, snow, frost, and hail are formed and fall to the earth. It is the abode of stormy winds, of whirlwinds, thunder, lightning, and many other phenomena.

"The cause of the heaven's motion is G.o.d. He is not in the centre, where the earth is a region of agitation and trouble, but he is above the outermost circ.u.mference, which is the purest of all regions, a place which we call rightly _ouranos_, because it is the highest part of the universe, and _olympos_, that is, perfectly bright, because it is altogether separated from everything like the shadow and disordered movements which occur in the lower regions."

We notice in this extract a curious etymology of the word ether, namely, as signifying perpetual motion ([Greek: aei teein]), though it is more probable that its true, as its more generally accepted derivation is from [Greek: aithein], to burn or shine, a meaning doubtless alluded to in a remarkable pa.s.sage of Hippocrates, [Greek: Peri Sarkon]. "It appears to me," he says, "that what we call the principle of heat is immortal, that it knows all, sees all, hears all, perceives all, both in the past and in the future. At the time when all was in confusion, the greater part of this principle rose to the circ.u.mference of the universe; it is this that the ancients have called _ether_."

The first Greek that can be called an astronomer was Thales, born at Miletus 641 B.C., who introduced into Greece the elements of astronomy.

His opinions were these: that the stars were of the same substance as the earth, but that they were on fire; that the moon borrowed its light from the sun, and caused the eclipses of the latter, while it was itself eclipsed when it entered the earth's shadow; that the earth was round, and divisible into five zones, by means of five circles, _i.e._ the Arctic and Antarctic, the two tropics, and the equator; that the latter circle is cut obliquely by the ecliptic, and perpendicularly by the meridian. Up to his time no division of the sphere had been made beyond the description of the constellations. These opinions do not appear to have been rapidly spread, since Herodotus, one of the finest intellects of Greece, who lived two centuries later, was still so ill-instructed as to say, in speaking of an eclipse, "The sun abandoned its place, and night took the place of day."

Anaxagoras, of whom we have spoken before, a.s.serted that the sun was a ma.s.s of fire larger than the Peloponnesus. Plutarch says he regarded it as a burning stone, and Diogenes Laertius looked upon it as hot iron.

For this bold idea he was persecuted. They considered it a crime that he taught the causes of the eclipses of the moon, and pretended that the sun is larger than it looks. He first taught the existence of one G.o.d, and he was taxed with impiety and treason against his country. When he was condemned to death, "Nature," he said, "has long ago condemned me to the same; and as to my children, when I gave them birth I had no doubt but they would have to die some day." His disciple Pericles, however, defended him so eloquently that his life was spared, and he was sent into exile.

Pythagoras, who belonged to the school of Thales, and who travelled in Phoenicia, Chaldea, Judaea, and Egypt, to learn their ideas, ventured, in spite of the warnings of the priests, to submit to the rites of initiation at Heliopolis, and thence returned to Samos, but meeting with poor reception there, he went to Italy to teach. From him arose the _Italian School_, and his disciples took the name of philosophers (lovers of wisdom) instead of that of sages. We shall learn more about him in the chapter on the Harmony of the Spheres.

His first disciple, Empedocles, famous for the curiosity which led him to his death in the crater of aetna, as the story goes, thought that the true sun, the fire that is in the centre of the universe, illuminated the other hemisphere, and that what we see is only the reflected image of that, which is invisible to us, and all of whose movements it follows.

His disciple, Philolaus, also taught that the sun was a ma.s.s of gla.s.s, which sent us by reflection all the light that it scattered through the universe. We must not, however, forget that these opinions are recorded by historians who probably did not understand them, and who took in the letter what was only intended for a comparison or figure.

If we are to believe Plutarch, Xenophanes, who flourished about 360 B.C., was very wild in his opinions. He thought the stars were lighted every night and extinguished every morning; that the sun is a fiery cloud; that eclipses take place by the sun being extinguished and afterwards rekindled; that the moon is inhabited, but is eighteen times larger than the earth; that there are several suns and several moons for giving light to different countries. This can only be matched by those who said the sun went every night through a hole in the earth round again to the east; or that it went above ground, and if we did not see it going back it was because it accomplished the journey in the night.

Parmenidas was the disciple of Xenophanes. He divided the earth, like Thales, into zones; and he added that it was suspended in the centre of the universe, and that it did not fall because there was no reason why it should move in one direction rather than another. This argument is perfectly philosophical, and ill.u.s.trates a principle employed since the time of Archimedes, and of which Leibnitz made so much use.

Such are some of the general ideas which were held by the Greeks and others on the nature of the heavens, omitting that of Ptolemy, of which we shall give a fuller account hereafter. We see that they were all affected by the dominant idea of the superiority of the earth over the rest of the universe, and were spoiled for want of the grand conception of the immensity of s.p.a.ce. The universe was for them a closed s.p.a.ce, outside of which there was _nothing_; and they busied themselves with metaphysical questions as to the possibility of s.p.a.ce being infinite. In the meantime their conceptions of the distances separating us from other visible parts of the universe were excessively cramped. Hesiod, for instance, thinks to give a grand idea of the size of the universe by saying that Vulcan's anvil took seven days to fall from heaven to earth, when in reality, as now calculated, it would take no less than seventy-two years for the light, even travelling at a far greater rate, to reach us from one of the nearest of the fixed stars.

CHAPTER VII.

THE CELESTIAL HARMONY.

Nature presents herself to us under various aspects. At times, it may be, she presents to us the appearance of discord, and we fail to perceive the unity that pervades the whole of her actions. At others, however, and most often to an instructed mind, there is a concord between her various powers, a harmony even in her sounds, that will not escape us. Even the wild notes of the tempest and the ba.s.s roll of the thunder form themselves into part of the grand chorus which in the great opera are succeeded by the solos of the evening breeze, the songs of birds, or the ripple of the waves. These are ideas that would most naturally present themselves to contemplative minds, and such must have been the students of the silent, but to them harmonious and tuneful, star-lit sky, under the clear atmosphere of Greece. The various motions they observed became indissolubly connected in their minds with music, and they did not doubt that the heavenly spheres made harmony, if imperceptible to human ears. But their ideas were more precise than this. They discovered that harmony depended on number, and they attempted to prove that whether the music they might make were audible or not, the celestial spheres had motions which were connected together in the same way as the numbers belonging to a harmony. The study of their opinions on this point reveals some very curious as well as very interesting ideas. We may commence by referring to an ancient treatise by Timaeus of Locris on the soul of the universe. To him we owe the first serious exposition of the complete harmonic cosmography of Pythagoras.

We must premise that, according to this school, G.o.d employed all existing matter in the formation of the universe--so that it comprehends all things, and all is in it. "It is a unique, perfect, and spherical production, since the sphere is the most perfect of figures; animated and endowed with reason, since that which is animated and endowed with reason is better than that which is not."

So begins Timaeus, and then follows, as a quotation from Plato, a comparison of the earth to what would appear to us nowadays to be a very singular animal. Not only, says Plato, is the earth a sphere, but this sphere is perfect, and its maker took care that its surface should be perfectly uniform for many reasons. The universe in fact has no need of eyes, since there is nothing outside of it to see; nor yet of ears, since there is nothing but what is part of itself to make a sound; nor of breathing organs, as it is not surrounded by air: any organ that should serve to take in nourishment, or to reject the grosser parts, would be absolutely useless, for there being nothing outside it, it could not receive or reject anything. For the same reason it needs no hands with which to defend itself, nor yet of feet with which to walk.

Of the seven kinds of motion, its author has given it that which is most suitable for its figure in making it turn about its axis, and since for the execution of this rotatory motion no arms or legs are wanted, its maker gave it none.

With regard to the soul of the universe, Plato, according to Timaeus, says that G.o.d composed it "of a mixture of the divisible and indivisible essences, so that the two together might be united into one, uniting two forces, the principles of two kinds of motion, one that which is _always the same_, and the other that which is _always changing_. The mixture of these two essences was difficult, and was not accomplished without considerable skill and pains. The proportions of the mixture were according to harmonic numbers, so chosen that it is possible to know of what, and by what rule, the soul of the universe is compounded."

By harmonic numbers Timaeus means those that are proportional to those representing the consonances of the musical scale. The consonances known to the ancients were three in number: the diapason, or octave, in the proportion of 2 to 1, the diapent, or fifth, in that of 3 to 2, and the diatessaron, or fourth, in that of 4 to 3; when to these are joined the tones which fill the intervals of the consonances, and are in the proportion of 9 to 8, and the semitones in that of 256 to 243, all the degrees of the musical scale is complete.

The discovery of these harmonic numbers is due to Pythagoras. It is stated that when pa.s.sing one day near a forge, he noticed that the hammers gave out very accurate musical concords. He had them weighed, and found that of those which sounded the octave, one weighed twice as much as the other; that of those which made a perfect fifth, one weighed one third more than the other, and in the case of a fourth, one quarter more. After having tried the hammers, he took a musical string stretched with weights, and found that when he had applied a given weight in the first instance to make any particular note, he had to double the weight to obtain the octave, to add one third extra only to obtain a fifth, a quarter for the fourth, and eight for one tone, and about an eighteenth for a half-tone; or more simply still, he stretched a cord once for all, and then when the whole length sounded any note, when stopped in the middle it gave the octave, at the third it gave the fifth, at the quarter the fourth, at the eighth the tone, and at the eighteenth the semi-tone.

Since the ancients conceived of the soul by means of motion, the quant.i.ty of motion developed in anything was their measure of the quant.i.ty of its soul. Now the motion of the heavenly bodies seemed to them to depend on their distance from the centre of the universe, the fastest being those at the circ.u.mference of the whole. To determine the relative degrees of velocity, they imagined a straight line drawn outwards from the centre of the earth, as far as the empyreal heaven, and divided it according to the proportions of the musical scale, and these divisions they called the harmonic degrees of the soul of the universe. Taking the earth's radius for the first number, and calling it unity, or, in order to avoid fractions, denoting it by 384, the second degree, which is at the distance of an harmonic third, will be represented by 384 plus its eighth part, or 432. The third degree will be 432, plus its eighth part, or 486. The fourth, being a semitone, will be as 243 to 256, which will give 512; and so on. The eighth degree will in this way be the double of 384 or 768, and represents the first octave.

They continued this series to 36 degrees, as in the following table:--

The Earth.

Mi 384 + 1/8 = 432 Re 432 + 1/8 = 486 Ut 486 : 512 : : 243 : 256 Si 512 + 1/8 = 576 La 576 + 1/8 = 648 Sol 648 + 1/8 = 729 Fa 729 : 768 : : 243 : 256 Mi 768 + 1/8 = 864 Re 864 + 1/8 = 972 Ut 972 : 1024 : : 243 : 256 Si 1024 + 1/8 = 1152 La 1152 + 1/8 = 1296 Sol 1296 + 1/8 = 1458 Fa 1458 : 1536 : : 243 : 256 Mi 1536 + 1/8 = 1728 Re 1728 + 1/8 = 1944 Ut 1944 : 2048 : 243 : 256 Si 2048 + 139 = 2187 Si 2 2187 : 2304 : : 243 : 256 La 2304 + 1/8 = 2592 Sol 2592 + 1/8 = 2916 Fa 2916 : 3072 : : 243 : 256 Mi 3072 + 1/8 = 3456 Re 3457 + 1/8 = 3888 Ut 3888 + 1/8 = 4374 Si 4374 : 4608 : : 243 : 256 La 4608 + 1/8 = 5184 Sol 5184 + 1/8 = 5832 Fa 5832 : 6144 : : 243 : 256 Mi 6144 + 417 = 6561 Mi 2 6561 : 6912 : : 243 : 256 Re 6912 + 1/8 = 7776 Ut 7776 + 1/8 = 8748 Si 8748 : 9216 : : 243 : 256 La 9216 + 1/8 = 10368 Sol 10368 = 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 circ.u.mference 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 Timaeus, the sphere of the fixed stars, which contains 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 to the 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 his _Republic_ that 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 ba.s.s, 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.