(6) We may now consider the question whether fire is the sole element existing in that celestial realm and whether there is any outgoing thence with the consequent need of renewal.

Timaeus pronounced the material frame of the All to consist primarily of earth and fire for visibility, earth for solidity- and deduced that the stars must be mainly composed of fire, but not solely since there is no doubt they are solid.

And this is probably a true account. Plato accepts it as indicated by all the appearances. And, in fact, to all our perception- as we see them and derive from them the impression of illumination- the stars appear to be mostly, if not exclusively, fire: but on reasoning into the matter we judge that since solidity cannot exist apart from earth-matter, they must contain earth as well.

But what place could there be for the other elements? It is impossible to imagine water amid so vast a conflagration; and if air were present it would be continually changing into fire.

Admitting that two self-contained entities, standing as extremes to each other need for their coherence two intermediaries; we may still question whether this holds good with regard to physical bodies. Certainly water and earth can be mixed without any such intermediate. It might seem valid to object that the intermediates are already present in the earth and the water; but a possible answer would be, "Yes, but not as agents whose meeting is necessary to the coherence of those extremes."

None the less we will take it that the coherence of extremes is produced by virtue of each possessing all the intermediates. It is still not proven that fire is necessary to the visibility of earth and earth to the solidarity of fire.

On this principle, nothing possesses an essential-nature of its very own; every several thing is a blend, and its name is merely an indication of the dominant constituent.

Thus we are told that earth cannot have concrete existence without the help of some moist element- the moisture in water being the necessary adhesive- but admitting that we so find it, there is still a contradiction in pretending that any one element has a being of its own and in the same breath denying its self-coherence, making its subsistence depend upon others, and so, in reality, reducing the specific element to nothing. How can we talk of the existence of the definite Kind, earth- earth essential- if there exists no single particle of earth which actually is earth without any need of water to secure its self-cohesion? What has such an adhesive to act upon if there is absolutely no given magnitude of real earth to which it may bind particle after particle in its business of producing the continuous mass? If there is any such given magnitude, large or small, of pure earth, then earth can exist in its own nature, independently of water: if there is no such primary particle of pure earth, then there is nothing whatever for the water to bind. As for air- air unchanged, retaining its distinctive quality- how could it conduce to the subsistence of a dense material like earth?

Similarly with fire. No doubt Timaeus speaks of it as necessary not to the existence but to the visibility of earth and the other elements; and certainly light is essential to all visibility- we cannot say that we see darkness, which implies, precisely, that nothing is seen, as silence means nothing being heard.

But all this does not assure us that the earth to be visible must contain fire: light is sufficient: snow, for example, and other extremely cold substances gleam without the presence of fire- though of course it might be said that fire was once there and communicated colour before disappearing.

As to the composition of water, we must leave it an open question whether there can be such a thing as water without a certain proportion of earth.

But how can air, the yielding element, contain earth?

Fire, again: is earth perhaps necessary there since fire is by its own nature devoid of continuity and not a thing of three dimensions?

Supposing it does not possess the solidity of the three dimensions, it has that of its thrust; now, cannot this belong to it by the mere right and fact of its being one of the corporeal entities in nature? Hardness is another matter, a property confined to earth-stuff. Remember that gold- which is water- becomes dense by the accession not of earth but of denseness or consolidation: in the same way fire, with Soul present within it, may consolidate itself upon the power of the Soul; and there are living beings of fire among the Celestials.

But, in sum, do we abandon the teaching that all the elements enter into the composition of every living thing?

For this sphere, no; but to lift clay into the heavens is against nature, contrary to the laws of her ordaining: it is difficult, too, to think of that swiftest of circuits bearing along earthly bodies in its course nor could such material conduce to the splendour and white glint of the celestial fire.

(61) Timaeus: Thus earth when it is not forcibly condensed is dissolved only by water; and when it is condensed it is dissolved by fire only, since no entrance is left for anything save fire. Water, again, when most forcibly massed together is dissolved by fire only, but when massed less forcibly both by fire and air, the latter acting by way of the interstices, and the former by way of the triangles; but air when forcibly condensed is dissolved by nothing save by way of its elemental triangles, and when unforced it is melted down by fire only. As regards the classes of bodies which are compounds of earth and water,

(56) Timaeus: since it is in all ways the sharpest and most acute of all; and it must also be the lightest, since it is composed of the fewest identical parts; and the second comes second in point of these same qualities, and the third third. Thus, in accordance with the right account and the probable, that solid which has taken the form of a pyramid shall be the element and seed of fire; the second in order of generation we shall affirm to be air, and the third water. Now one must conceive all these to be so small that none of them,

(56) Timaeus: and the fractions of air which come from the dissolving of one particle will form two corpuscles of fire. And again, when a small quantity of fire is enclosed by a large quantity of air and water, or of earth, and moves within them as they rush along, and is defeated in its struggle and broken up, then two corpuscles of fire unite to make one form of air. And when air is defeated and disintegrated, from two whole forms of air and a half, one whole form of water will be compounded.

(3) Anaxacoras saith:—I make known that the beginning of all those things which God hath created is weight and proportion,* for weight rules all things, and the weight and spissitude of the earth is manifest in proportion; but weight is not found except in body. And know, all ye Turba, that the spissitude of the four elements reposes in the earth; for the spissitude of fire falls into air, the spissitude of air, together with the spissitude received from the fire, falls into water; the spissitude also of water, increased by the spissitude of fire and air, reposes in earth. Have you not observed how the spissitude of the four elements is conjoined in earth? The same, therefore, is more inspissated than all.

Then saith the Turba: —Thou hast well spoken. Verily the earth is more inspissated than are the rest. Which, therefore, is the most rare of the four elements and is most worthy to possess the rarity of these four?

He answereth:—Fire is the most rare among all, and thereunto cometh what is rare of these four. But air is less rare than fire, because it is warm and moist, while fire is warm and dry; now that which is warm and dry is more rare than the warm and moist. They say unto him: —Which element is of less rarity than air?

He answereth:—Water, since cold and moisture inhere therein, and every cold humid is of less rarity than a warm humid.

Then do they say unto him:—Thou hast spoken truly. What, therefore, is of less rarity than water?

He answereth:-—Earth, because it is cold and dry, and that which is cold and dry is of less rarity than that which is cold and moist.

PyTHAGoRAS saith:—Well have ye provided, O Sons of the Doctrine, the description of these four natures,* out of which God hath created all things. Blessed, therefore, is he who comprehends what ye have declared, for from the apex of the world he shall not find an intention greater than his own! Let us, therefore, make perfect our discourse.

They reply:—Direct every one to take up our speech in turn. Speak thou, O Pandolfus!

To

(56) Timaeus: Wherefore, we are preserving the probable account when we assign this figure to earth, and of the remaining figures the least mobile to water, and the most mobile to fire, and the intermediate figure to air; and, further, when we assign the smallest body to fire, and the greatest to water, and the intermediate to air; and again, the first in point of sharpness to fire, the second to air, and the third to water. As regards all these forms, that which has the fewest bases must necessarily be the most mobile,

(32) As Fire, Air, Water, and Earth, lie in one Case, [or Chest,] and they four are but one Thing, and yet of four distinct Differences, and none of them can comprehend, nor retain the other, and something of one of the four being fixed in every Creature, that Creature cannot bind itself as to that, but is manifested therein, and according to that Spirit is comprehensible and perceptible, and yet is incomprehensible to the Spirits of the other Elements.

(54) Timaeus: the equilateral triangle is constructed as a third. The reason why is a longer story; but should anyone refute us and discover that it is not so, we begrudge him not the prize. Accordingly, let these two triangles be selected as those wherefrom are contrived the bodies of fire and of the other elements,— one being the isosceles, and the other that which always has the square on its greater side three times the square on the lesser side. Moreover, a point about which our previous statement was obscure must now be defined more clearly. It appeared as if the four Kinds,

(7) We can scarcely do better, in fine, than follow Plato.

Thus:

In the universe as a whole there must necessarily be such a degree of solidity, that is to say, of resistance, as will ensure that the earth, set in the centre, be a sure footing and support to the living beings moving over it, and inevitably communicate something of its own density to them: the earth will possess coherence by its own unaided quality, but visibility by the presence of fire: it will contain water against the dryness which would prevent the cohesion of its particles; it will hold air to lighten its bulky matters; it will be in contact with the celestial fire- not as being a member of the sidereal system but by the simple fact that the fire there and our earth both belong to the ordered universe so that something of the earth is taken up by the fire as something of the fire by the earth and something of everything by everything else.

This borrowing, however, does not mean that the one thing taking-up from the other enters into a composition, becoming an element in a total of both: it is simply a consequence of the kosmic fellowship; the participant retains its own being and takes over not the thing itself but some property of the thing, not air but air's yielding softness, not fire but fire's incandescence: mixing is another process, a complete surrender with a resultant compound not, as in this case, earth- remaining earth, the solidity and density we know- with something of fire's qualities superadded.

We have authority for this where we read:

"At the second circuit from the earth, God kindled a light": he is speaking of the sun which, elsewhere, he calls the all-glowing and, again, the all-gleaming: thus he prevents us imagining it to be anything else but fire, though of a peculiar kind; in other words it is light, which he distinguishes from flame as being only modestly warm: this light is a corporeal substance but from it there shines forth that other "light" which, though it carries the same name, we pronounce incorporeal, given forth from the first as its flower and radiance, the veritable "incandescent body." Plato's word earthy is commonly taken in too depreciatory a sense: he is thinking of earth as the principle of solidity; we are apt to ignore his distinctions and think of the concrete clay.

Fire of this order, giving forth this purest light, belongs to the upper realm, and there its seat is fixed by nature; but we must not, on that account, suppose the flame of earth to be associated with the beings of that higher sphere.

No: the flame of this world, once it has attained a certain height, is extinguished by the currents of air opposed to it. Moreover, as it carries an earthy element on its upward path, it is weighed downwards and cannot reach those loftier regions. It comes to a stand somewhere below the moon- making the air at that point subtler- and its flame, if any flame can persist, is subdued and softened, and no longer retains its first intensity, but gives out only what radiance it reflects from the light above.

And it is that loftier light- falling variously upon the stars; to each in a certain proportion- that gives them their characteristic differences, as well in magnitude as in colour; just such light constitutes also the still higher heavenly bodies which, however, like clear air, are invisible because of the subtle texture and unresisting transparency of their material substance and also by their very distance.

(23) And there the holy Tincture is generated out of the Essences, which regards not the Fire, but sets the Essences (viz. the Soul) in its pleasant Joy. Then come the other three Elements out of their Regions, and fill themselves also by Force Or Dominion. therein, each of them would taste of the Virgin, receive her and qualify [or mingle] with her: viz. the Water, that fills itself by Force also therein, and it tastes the sweet Tincture of the Soul. And the Fire says; I would willingly keep the Water, for I can quench my Thirst therewith, and refresh myself therein. And the Air says; I am indeed the Spirit, I will blow up the Heat and Fire, that the Water do not choak thee. And the Fire says to the Air; I will keep thee, for thou upholdest my Quality for me, that I also go not out. And then comes the Element [of] (Earth) and says; What will you three do alone? You will starve and consume one another; for you depend all three on one another and devour yourselves, and when you shall have consumed the Water, then you extinguish; for the Air cannot move, unless it has some Water; for the Water is the Mother of the Air, which generates the Air: Moreover, the Fire becomes much too fierce [violent and eager] if the Water be consumed, and consumes the Body, and then our Region is out, and none of us can subsist.

(32) Timaeus: and out of these materials, such in kind and four in number, the body of the Cosmos was harmonized by proportion and brought into existence. These conditions secured for it Amity, so that being united in identity with itself it became indissoluble by any agent other than Him who had bound it together. Now of the four elements the construction of the Cosmos had taken up the whole of every one. For its Constructor had constructed it of all the fire and water and air and earth that existed, leaving over, outside it, no single particle or potency of any one of these elements. And these were his intentions:

(8) For this is very well to be apprehended and perceived in the Earth and Stones, that the four Elements are of one only Substance, and that the Earth and Stones were generated in the Fierceness from the Kindling of the Elements. For a Stone is but Water; and therefore we should do well to consider, what Kind of Fierceness there must have been, that has drawn the Water so hard together.

(37) And Athamas the Pythagorean having said, "Thus was produced the beginning of the universe; and there are four roots - fire, water, air, earth: for from these is the origination of what is produced," - Empedocles of Agrigentum wrote: "The four roots of all things first do thou hear- Fire, water, earth, and ether's boundless height:

(53) Timaeus: of each of these Kinds which I must endeavor to explain to you in an exposition of an unusual type; yet, inasmuch as you have some acquaintance with the technical method which I must necessarily employ in my exposition, you will follow me. In the first place, then, it is plain I presume to everyone that fire and earth and water and air are solid bodies; and the form of a body, in every case, possesses depth also. Further, it is absolutely necessary that depth should be bounded by a plane surface; and the rectilinear plane is composed of triangles.

(49) Timaeus: as we believe, stones and earth; and again, this same substance, by dissolving and dilating, becoming breath and air; and air through combustion becoming fire; and conversely, fire when contracted and quenched returning back to the form of air and air once more uniting and condensing into cloud and mist; and issuing from these, when still further compressed, flowing water; and from water earth and stones again: thus we see the elements passing on to one another, as it would seem,

(32) Timaeus: had had to come into existence as a plane surface, having no depth, one middle term would have sufficed to bind together both itself and its fellow-terms; but now it is otherwise: for it behoved it to be solid of shape, and what brings solids into unison is never one middle term alone but always two. Thus it was that in the midst between fire and earth God set water and air, and having bestowed upon them so far as possible a like ratio one towards another—air being to water as fire to air, and water being to earth as air to water, —he joined together and constructed a Heaven visible and tangible. For these reasons

(4) Panvotrus saith:—I signify to posterity that air is a tenuous matter of water, and that it is not separated from it. It remains above the dry earth, to wit, the air hidden in the water, which is under the earth. If this air did not exist, the earth would not remain above the humid water. They answer:—Thou hast said well; complete, therefore, thy speech. Sut he continueth: The air which is hidden in the water under the earth is that which sustains the earth, lest it should be plunged into the said water; and it, moreover, prevents the earth from being overflowed by that water. The province of the air is, therefore, to fill up and to make separation between diverse things, that is to say, water and earth, and it is constituted a peacemaker between hostile things, namely, water and fire, dividing these, lest they destroy one another.

The Turba saith:—If you gave an illustration hereof, it would be clearer to those who do not understand.

He answereth:—An egg is an illustration, for therein four things are conjoined; the visible cortex or shell represents the earth, and the albumen, or white part, is the water.* But a very thin inner cortex is joined to the outer cortex, representing, as I have signified to you, the separating medium between earth and water, namely, that air which divides the earth from the water. The yolk also of the egg represents fire; the cortex which contains the yolk corresponds to that other air which separates the water from the fire. But they are both one and the same air, namely, that which separates things frigid, the earth from the water, and that which separates the water from the fire. But the lower air is thicker than the upper air, and the upper air is more rare and subtle, being nearer to the fire than the lower air. In the egg, therefore, are four things—earth, water, air, and fire. But the point of the Sun, these four excepted, is in the centre of the yolk, and this is the chicken. Consequently, all philosophers in this most excellent art have described the egg as an example, which same thing they have set over their work.

(67) The three elements, fire, air and water, have a threefold moving or qualification, but proceed from one body; and consider, the fire or heat swells and flies aloft from the sun and stars; and from the heat the air swells [or expands itself] and flies aloft; and from the air comes the water.

(53) Timaeus: We must now declare what will be the four fairest bodies, dissimilar to one another, but capable in part of being produced out of one another by means of dissolution; for if we succeed herein we shall grasp the truth concerning the generation of earth and fire and the mean proportionals. For to no one will we concede that fairer bodies than these, each distinct of its kind, are anywhere to be seen. Wherefore we must earnestly endeavor to frame together these four kinds of bodies which excel in beauty, and to maintain that we have apprehended

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.