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 seen above. 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, the intervals 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 that generations 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 to support 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, "having always 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 universe having always 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. Therefore the 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 argued must be really 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:—

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