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8. For example, which of the ancients can be found to have used vermilion otherwise than sparingly, like a drug? But today whole walls are commonly covered with it everywhere. Then, too, there is malachite green, purple, and Armenian blue. When these colours are laid on, they present a brilliant appearance to the eye even although they are inartistically applied, and as they are costly, they are made exceptions in contracts, to be furnished by the employer, not by the contractor.
I have now sufficiently explained all that I could suggest for the avoidance of mistakes in stucco work. Next, I shall speak of the components as they occur to me, and first I shall treat of marble, since I spoke of lime at the beginning.
CHAPTER VI
MARBLE FOR USE IN STUCCO
Marble is not produced everywhere of the same kind. In some places the lumps are found to contain transparent grains like salt, and this kind when crushed and ground is extremely serviceable in stucco work. In places where this is not found, the broken bits of marble or "chips," as they are called, which marble-workers throw down as they work, may be crushed and ground and used in stucco after being sifted. In still other places—for example, on the borderland of Magnesia and Ephesus—there are places where it can be dug out all ready to use, without the need of grinding or sifting, but as fine as any that is crushed and sifted by hand.
CHAPTER VII
NATURAL COLOURS
As for colours, some are natural products found in fixed places, and dug up there, while others are artificial compounds of different substances treated and mixed in proper proportions so as to be equally serviceable.
1. We shall first set forth the natural colours that are dug up as such, like yellow ochre, which is termed [Greek: ochra] in Greek. This is found in many places, including Italy, but Attic, which was the best, is not now to be had because in the times when there were slaves in the Athenian silver mines, they would dig galleries underground in order to find the silver. Whenever a vein of ochre was found there, they would follow it up like silver, and so the ancients had a fine supply of it to use in the polished finishings of their stucco work.
2. Red earths are found in abundance in many places, but the best in only a few, for instance at Sinope in Pontus, in Egypt, in the Balearic islands of Spain, as well as in Lemnos, an island the enjoyment of whose revenues the Senate and Roman people granted to the Athenians.
3. Paraetonium white gets its name from the place where it is dug up. The same is the case with Melian white, because there is said to be a mine of it in Melos, one of the islands of the Cyclades.
4. Green chalk is found in numerous places, but the best at Smyrna. The Greeks call it [Greek: theodoteion], because this kind of chalk was first found on the estate of a person named Theodotus.
5. Orpiment, which is termed [Greek: arsenikon] in Greek, is dug up in Pontus. Sandarach, in many places, but the best is mined in Pontus close by the river Hypanis.
CHAPTER VIII
CINNABAR AND QUICKSILVER
1. I shall now proceed to explain the nature of cinnabar. It is said that it was first found in the Cilbian country belonging to Ephesus, and both it and its properties are certainly very strange. First, before getting to the vermilion itself by methods of treatment, they dig out what is called the clod, an ore like iron, but rather of a reddish colour and covered with a red dust. During the digging it sheds, under the blows of the tools, tear after tear of quicksilver, which is at once gathered up by the diggers.
2. When these clods have been collected, they are so full of moisture that they are thrown into an oven in the laboratory to dry, and the fumes that are sent up from them by the heat of the fire settle down on the floor of the oven, and are found to be quicksilver. When the clods are taken out, the drops which remain are so small that they cannot be gathered up, but they are swept into a vessel of water, and there they run together and combine into one. Four pints of it, when measured and weighed, will be found to be one hundred pounds.
3. If the quicksilver is poured into a vessel, and a stone weighing one hundred pounds is laid upon it, the stone swims on the surface, and cannot depress the liquid, nor break through, nor separate it. If we remove the hundred pound weight, and put on a scruple of gold, it will not swim, but will sink to the bottom of its own accord. Hence, it is undeniable that the gravity of a substance depends not on the amount of its weight, but on its nature.
4. Quicksilver is a useful thing for many purposes. For instance, neither silver nor copper can be gilded properly without it. And when gold has been woven into a garment, and the garment becomes worn out with age so that it is no longer respectable to use, the pieces of cloth are put into earthen pots, and burned up over a fire. The ashes are then thrown into water and quicksilver added thereto. This attracts all the bits of gold, and makes them combine with itself. The water is then poured off, and the rest emptied into a cloth and squeezed in the hands, whereupon the quicksilver, being a liquid, escapes through the loose texture of the cloth, but the gold, which has been brought together by the squeezing, is found inside in a pure state.
CHAPTER IX
CINNABAR (continued)
1. I will now return to the preparation of vermilion. When the lumps of ore are dry, they are crushed in iron mortars, and repeatedly washed and heated until the impurities are gone, and the colours come. When the cinnabar has given up its quicksilver, and thus lost the natural virtues that it previously had, it becomes soft in quality and its powers are feeble.
2. Hence, though it keeps its colour perfectly when applied in the polished stucco finish of closed apartments, yet in open apartments, such as peristyles or exedrae or other places of the sort, where the bright rays of the sun and moon can penetrate, it is spoiled by contact with them, loses the strength of its colour, and turns black. Among many others, the secretary Faberius, who wished to have his house on the Aventine finished in elegant style, applied vermilion to all the walls of the peristyle; but after thirty days they turned to an ugly and mottled colour. He therefore made a contract to have other colours applied instead of vermilion.
3. But anybody who is more particular, and who wants a polished finish of vermilion that will keep its proper colour, should, after the wall has been polished and is dry, apply with a brush Pontic wax melted over a fire and mixed with a little oil; then after this he should bring the wax to a sweat by warming it and the wall at close quarters with charcoal enclosed in an iron vessel; and finally he should smooth it all off by rubbing it down with a wax candle and clean linen cloths, just as naked marble statues are treated.
4. This process is termed [Greek: ganosis] in Greek. The protecting coat of Pontic wax prevents the light of the moon and the rays of the sun from licking up and drawing the colour out of such polished finishing.
The manufactories which were once at the mines of the Ephesians have now been transferred to Rome, because this kind of ore was later discovered in Spain. The clods are brought from the mines there, and treated in Rome by public contractors. These manufactories are between the temples of Flora and Quirinus.
5. Cinnabar is adulterated by mixing lime with it. Hence, one will have to proceed as follows, if one wishes to prove that it is unadulterated. Take an iron plate, put the cinnabar upon it, and lay it on the fire until the plate gets red hot. When the glowing heat makes the colour change and turn black, remove the plate from the fire, and if the cinnabar when cooled returns to its former colour, it will be proved to be unadulterated; but if it keeps the black colour, it will show that it has been adulterated.
6. I have now said all that I could think of about cinnabar. Malachite green is brought from Macedonia, and is dug up in the neighbourhood of copper mines. The names Armenian blue and India ink show in what places these substances are found.
CHAPTER X
ARTIFICIAL COLOURS. BLACK
1. I shall now pass to those substances which by artificial treatment are made to change their composition, and to take on the properties of colours; and first I shall treat of black, the use of which is indispensable in many works, in order that the fixed technical methods for the preparation of that compound may be known.
2. A place is built like a Laconicum, and nicely finished in marble, smoothly polished. In front of it, a small furnace is constructed with vents into the Laconicum, and with a stokehole that can be very carefully closed to prevent the flames from escaping and being wasted. Resin is placed in the furnace. The force of the fire in burning it compels it to give out soot into the Laconicum through the vents, and the soot sticks to the walls and the curved vaulting. It is gathered from them, and some of it is mixed and worked with gum for use as writing ink, while the rest is mixed with size, and used on walls by fresco painters.
3. But if these facilities are not at hand, we must meet the exigency as follows, so that the work may not be hindered by tedious delay. Burn shavings and splinters of pitch pine, and when they turn to charcoal, put them out, and pound them in a mortar with size. This will make a pretty black for fresco painting.
4. Again, if the lees of wine are dried and roasted in an oven, and then ground up with size and applied to a wall, the result will be a colour even more delightful than ordinary black; and the better the wine of which it is made, the better imitation it will give, not only of the colour of ordinary black, but even of that of India ink.
CHAPTER XI
BLUE. BURNT OCHRE
1. Methods of making blue were first discovered in Alexandria, and afterwards Vestorius set up the making of it at Puzzuoli. The method of obtaining it from the substances of which it has been found to consist, is strange enough. Sand and the flowers of natron are brayed together so finely that the product is like meal, and copper is grated by means of coarse files over the mixture, like sawdust, to form a conglomerate. Then it is made into balls by rolling it in the hands and thus bound together for drying. The dry balls are put in an earthern jar, and the jars in an oven. As soon as the copper and the sand grow hot and unite under the intensity of the fire, they mutually receive each other's sweat, relinquishing their peculiar qualities, and having lost their properties through the intensity of the fire, they are reduced to a blue colour.
2. Burnt ochre, which is very serviceable in stucco work, is made as follows. A clod of good yellow ochre is heated to a glow on a fire. It is then quenched in vinegar, and the result is a purple colour.
CHAPTER XII
WHITE LEAD, VERDIGRIS, AND ARTIFICIAL SANDARACH
1. It is now in place to describe the preparation of white lead and of verdigris, which with us is called "aeruca." In Rhodes they put shavings in jars, pour vinegar over them, and lay pieces of lead on the shavings; then they cover the jars with lids to prevent evaporation. After a definite time they open them, and find that the pieces of lead have become white lead. In the same way they put in plates of copper and make verdigris, which is called "aeruca."
2. White lead on being heated in an oven changes its colour on the fire, and becomes sandarach. This was discovered as the result of an accidental fire. It is much more serviceable than the natural sandarach dug up in mines.
CHAPTER XIII
PURPLE
1. I shall now begin to speak of purple, which exceeds all the colours that have so far been mentioned both in costliness and in the superiority of its delightful effect. It is obtained from a marine shellfish, from which is made the purple dye, which is as wonderful to the careful observer as anything else in nature; for it has not the same shade in all the places where it is found, but is naturally qualified by the course of the sun.
2. That which is found in Pontus and Gaul is black, because those countries are nearest to the north. As one passes on from north to west, it is found of a bluish shade. Due east and west, what is found is of a violet shade. That which is obtained in southern countries is naturally red in quality, and therefore this is found in the island of Rhodes and in other such countries that are nearest to the course of the sun.
3. After the shellfish have been gathered, they are broken up with iron tools, the blows of which drive out the purple fluid like a flood of tears, and then it is prepared by braying it in mortars. It is called "ostrum" because it is taken from the shells of marine shellfish. On account of its saltness, it soon dries up unless it has honey poured over it.
CHAPTER XIV
SUBSTITUTES FOR PURPLE, YELLOW OCHRE, MALACHITE GREEN, AND INDIGO
1. Purple colours are also manufactured by dyeing chalk with madder root and with hysginum. Other colours are made from flowers. Thus, when fresco painters wish to imitate Attic yellow ochre, they put dried violets into a vessel of water, and heat them over a fire; then, when the mixture is ready, they pour it onto a linen cloth, and squeeze it out with the hands, catching the water which is now coloured by the violets, in a mortar. Into this they pour chalk and bray it, obtaining the colour of Attic yellow ochre.
2. They make a fine purple colour by treating bilberry in the same way and mixing it with milk. Those who cannot use malachite green on account of its dearness, dye blue with the plant called dyer's weed, and thus obtain a most vivid green. This is called dyer's malachite green. Again, for want of indigo, they dye Selinusian or anularian chalk with woad, which the Greeks call [Greek: isatis], and make an imitation of indigo.
3. In this book I have written down, so far as I could recall them, the methods and means of attaining durability in polished finishings, how pictures that are appropriate should be made, and also the natural qualities of all the colours. And so, having prescribed in seven books the suitable principles which should govern the construction of all kinds of buildings, I shall treat in the next of water, showing how it may be found in places where it is wanting, by what method it may be conducted, and by what means its wholesomeness and fitness may be tested.
BOOK VIII
INTRODUCTION
1. Among the Seven Sages, Thales of Miletus pronounced for water as the primordial element in all things; Heraclitus, for fire; the priests of the Magi, for water and fire; Euripides, a pupil of Anaxagoras, and called by the Athenians "the philosopher of the stage," for air and earth. Earth, he held, was impregnated by the rains of heaven and, thus conceiving, brought forth the young of mankind and of all the living creatures in the world; whatever is sprung from her goes back to her again when the compelling force of time brings about a dissolution; and whatever is born of the air returns in the same way to the regions of the sky; nothing suffers annihilation, but at dissolution there is a change, and things fall back to the essential element in which they were before. But Pythagoras, Empedocles, Epicharmus, and other physicists and philosophers have set forth that the primordial elements are four in number: air, fire, earth, and water; and that it is from their coherence to one another under the moulding power of nature that the qualities of things are produced according to different classes.
2. And, in fact, we see not only that all which comes to birth is produced by them, but also that nothing can be nourished without their influence, nor grow, nor be preserved. The body, for example, can have no life without the flow of the breath to and fro, that is, unless an abundance of air flows in, causing dilations and contractions in regular succession. Without the right proportion of heat, the body will lack vitality, will not be well set up, and will not properly digest strong food. Again, without the fruits of the earth to nourish the bodily frame, it will be enfeebled, and so lose its admixture of the earthy element.
3. Finally, without the influence of moisture, living creatures will be bloodless and, having the liquid element sucked out of them, will wither away. Accordingly the divine intelligence has not made what is really indispensable for man either hard to get or costly, like pearls, gold, silver, and so forth, the lack of which neither our body nor our nature feels, but has spread abroad, ready to hand through all the world, the things without which the life of mortals cannot be maintained. Thus, to take examples, suppose there is a deficiency of breath in the body, the air, to which is assigned the function of making up the deficiency, performs that service. To supply heat, the mighty sun is ready, and the invention of fire makes life more secure. Then again, the fruits of the earth, satisfying our desires with a more than sufficient store of food stuffs, support and maintain living beings with regular nourishment. Finally, water, not merely supplying drink but filling an infinite number of practical needs, does us services which make us grateful because it is gratis.
4. Hence, too, those who are clothed in priesthoods of the Egyptian orders declare that all things depend upon the power of the liquid element. So, when the waterpot is brought back to precinct and temple with water, in accordance with the holy rite, they throw themselves upon the ground and, raising their hands to heaven, thank the divine benevolence for its invention.
Therefore, since it is held by physicists and philosophers and priests that all things depend upon the power of water, I have thought that, as in the former seven books the rules for buildings have been set forth, in this I ought to write on the methods of finding water, on those special merits which are due to the qualities of localities, on the ways of conducting it, and how it may be tested in advance. For it is the chief requisite for life, for happiness, and for everyday use.
CHAPTER I
HOW TO FIND WATER
1. This will be easier if there are open springs of running water. But if there are no springs which gush forth, we must search for them underground, and conduct them together. The following test should be applied. Before sunrise, lie down flat in the place where the search is to be made, and placing the chin on the earth and supporting it there, take a look out over the country. In this way the sight will not range higher than it ought, the chin being immovable, but will range over a definitely limited height on the same level through the country. Then, dig in places where vapours are seen curling and rising up into the air. This sign cannot show itself in a dry spot.
2. Searchers for water must also study the nature of different localities; for those in which it is found are well defined. In clay the supply is poor, meagre, and at no great depth. It will not have the best taste. In fine gravel the supply is also poor, but it will be found at a greater depth. It will be muddy and not sweet. In black earth some slight drippings and drops are found that gather from the storms of winter and settle down in compact, hard places. They have the best taste. Among pebbles the veins found are moderate, and not to be depended upon. These, too, are extremely sweet. In coarse grained gravel and carbuncular sand the supply is surer and more lasting, and it has a good taste. In red tufa it is copious and good, if it does not run down through the fissures and escape. At the foot of mountains and in lava it is more plentiful and abundant, and here it is also colder and more wholesome. In flat countries the springs are salt, heavy-bodied, tepid, and ill-flavoured, excepting those which run underground from mountains, and burst forth in the middle of a plain, where, if protected by the shade of trees, their taste is equal to that of mountain springs.
3. In the kinds of soil described above, signs will be found growing, such as slender rushes, wild willows, alders, agnus castus trees, reeds, ivy, and other plants of the same sort that cannot spring up of themselves without moisture. But they are also accustomed to grow in depressions which, being lower than the rest of the country, receive water from the rains and the surrounding fields during the winter, and keep it for a comparatively long time on account of their holding power. These must not be trusted, but the search must be made in districts and soils, yet not in depressions, where those signs are found growing not from seed, but springing up naturally of themselves.
4. If the indications mentioned appear in such places, the following test should be applied. Dig out a place not less than three feet square and five feet deep, and put into it about sunset a bronze or leaden bowl or basin, whichever is at hand. Smear the inside with oil, lay it upside down, and cover the top of the excavation with reeds or green boughs, throwing earth upon them. Next day uncover it, and if there are drops and drippings in the vessel, the place will contain water.
5. Again, if a vessel made of unbaked clay be put in the hole, and covered in the same way, it will be wet when uncovered, and already beginning to go to pieces from dampness, if the place contains water. If a fleece of wool is placed in the excavation, and water can be wrung out of it on the following day, it will show that the place has a supply. Further, if a lamp be trimmed, filled with oil, lighted, and put in that place and covered up, and if on the next day it is not burnt out, but still contains some remains of oil and wick, and is itself found to be damp, it will indicate that the place contains water; for all heat attracts moisture. Again, if a fire is made in that place, and if the ground, when thoroughly warmed and burned, sends up a misty vapour from its surface, the place will contain water.
6. After applying these tests and finding the signs described above, a well must next be sunk in the place, and if a spring of water is found, more wells must be dug thereabouts, and all conducted by means of subterranean channels into one place.
The mountains and districts with a northern exposure are the best spots in which to search, for the reason that springs are sweeter, more wholesome, and more abundant when found there. Such places face away from the sun's course, and the trees are thick in them, and the mountains, being themselves full of woods, cast shadows of their own, preventing the rays of the sun from striking uninterruptedly upon the ground and drying up the moisture.
7. The valleys among the mountains receive the rains most abundantly, and on account of the thick woods the snow is kept in them longer by the shade of the trees and mountains. Afterwards, on melting, it filters through the fissures in the ground, and thus reaches the very foot of the mountains, from which gushing springs come belching out.
But in flat countries, on the contrary, a good supply cannot be had. For however great it is, it cannot be wholesome, because, as there is no shade in the way, the intense force of the sun draws up and carries off the moisture from the flat plains with its heat, and if any water shows itself there, the lightest and purest and the delicately wholesome part of it is summoned away by the air, and dispersed to the skies, while the heaviest and the hard and unpleasant parts are left in springs that are in flat places.
CHAPTER II
RAINWATER
1. Rainwater has, therefore, more wholesome qualities, because it is drawn from the lightest and most delicately pure parts of all the springs, and then, after being filtered through the agitated air, it is liquefied by storms and so returns to the earth. And rainfall is not abundant in the plains, but rather on the mountains or close to mountains, for the reason that the vapour which is set in motion at sunrise in the morning, leaves the earth, and drives the air before it through the heaven in whatever direction it inclines; then, when once in motion, it has currents of air rushing after it, on account of the void which it leaves behind.
2. This air, driving the vapour everywhere as it rushes along, produces gales and constantly increasing currents by its mighty blasts. Wherever the winds carry the vapour which rolls in masses from springs, rivers, marshes, and the sea, it is brought together by the heat of the sun, drawn off, and carried upward in the form of clouds; then these clouds are supported by the current of air until they come to mountains, where they are broken up from the shock of the collision and the gales, turn into water on account of their own fulness and weight, and in that form are dispersed upon the earth.
3. That vapour, mists, and humidity come forth from the earth, seems due to the reason that it contains burning heat, mighty currents of air, intense cold, and a great quantity of water. So, as soon as the earth, which has cooled off during the night, is struck by the rays of the rising sun, and the winds begin to blow while it is yet dark, mists begin to rise upward from damp places. That the air when thoroughly heated by the sun can make vapours rise rolling up from the earth, may be seen by means of an example drawn from baths.
4. Of course there can be no springs above the vaultings of hot bathrooms, but the atmosphere in such rooms, becoming well warmed by the hot air from the furnaces, seizes upon the water on the floors, and takes it up to the curved vaultings and holds it up there, for the reason that hot vapour always pushes upwards. At first it does not let the moisture go, for the quantity is small; but as soon as it has collected a considerable amount, it cannot hold it up, on account of the weight, but sprinkles it upon the heads of the bathers. In the same way, when the atmospheric air feels the heat of the sun, it draws the moisture from all about, causes it to rise, and gathers it into clouds. For the earth gives out moisture under the influence of heat just as a man's heated body emits sweat.
5. The winds are witnesses to this fact. Those that are produced and come from the coolest directions, the north and northeast winds, blow in blasts that are rarefied by the great dryness in the atmosphere, but the south wind and the others that assail us from the direction of the sun's course are very damp, and always bring rain, because they reach us from warm regions after being well heated there, and licking up and carrying off the moisture from the whole country, they pour it out on the regions in the north.
6. That this is the state of the case may be proved by the sources of rivers, the majority and the longest of which, as drawn and described in geographies of the world, are found to rise in the north. First in India, the Ganges and Indus spring from the Caucasus; in Syria, the Tigris and Euphrates; in Pontus in Asia, the Dnieper, Bug, and Don; in Colchis, the Phasis; in Gaul, the Rhone; in Celtica, the Rhine; on this side of the Alps, the Timavo and Po; in Italy, the Tiber; in Maurusia, which we call Mauretania, the Dyris, rising in the Atlas range and running westerly to Lake Heptagonus, where it changes its name and is called Agger; then from Lake Heptabolus it runs at the base of barren mountains, flowing southerly and emptying into the marsh called[10]... It surrounds Meroe, which is a kingdom in southern Ethiopia, and from the marsh grounds there, winding round by the rivers Astansoba and Astoboa and a great many others, it passes through the mountains to the Cataract, and from there it dashes down, and passes to the north between Elephantis and Syene and the plains of Thebes into Egypt, where it is called the Nile.
[Note 10: Here something is lost, as also in chapter III, sections 5 and 6.]
7. That the source of the Nile is in Mauretania is known principally from the fact that there are other springs on the other side of the Atlas range flowing into the ocean to the west, and that ichneumons, crocodiles, and other animals and fishes of like nature are found there, although there are no hippopotamuses.
8. Therefore, since in descriptions of the world it appears that all rivers of any size flow from the north, and since in the plains of Africa, which are exposed to the course of the sun in the south, the moisture is deeply hidden, springs not common, and rivers rare, it follows that the sources of springs which lie to the north or northeast are much better, unless they hit upon a place which is full of sulphur, alum, or asphalt. In this case they are completely changed, and flow in springs which have a bad smell and taste, whether the water is hot or cold.
9. The fact is, heat is not at all a property of water, but when a stream of cold water happens upon a hot place, it boils up, and issues through the fissures and out of the ground in a state of heat. This cannot last very long, but in a short time the water becomes cold. If it were naturally hot, it would not cool off and lose its heat. Its taste, however, and its smell and colour are not restored, because it has become saturated and compounded with these qualities on account of the rarity of its nature.
CHAPTER III
VARIOUS PROPERTIES OF DIFFERENT WATERS
1. There are, however, some hot springs that supply water of the best taste, which is so delightful to drink that one does not think with regret of the Fountain of the Muses or the Marcian aqueduct. These hot springs are produced naturally, in the following manner. When fire is kindled down beneath in alum or asphalt or sulphur, it makes the earth immediately over it very hot, and emits a glowing heat to the parts still farther above it, so that if there are any springs of sweet water found in the upper strata, they begin to boil in their fissures when they are met by this heat, and so they run out with their taste unimpaired.
2. And there are some cold springs that have a bad smell and taste. They rise deep down in the lower strata, cross places which are on fire, and then are cooled by running a long distance through the earth, coming out above ground with their taste, smell, and colour spoiled; as, for instance, the river Albula on the road to Tivoli and the cold springs of Ardea, which have the same smell and are called sulphur springs, and others in similar places. Although they are cold, yet at first sight they seem to be hot for the reason that when they happen upon a burning spot deep down below, the liquid and the fire meet, and with a great noise at the collision they take in strong currents of air, and thus, swollen by a quantity of compressed wind, they come out at the springs in a constant state of ebullition. When such springs are not open but confined by rocks, the force of the air in them drives them up through the narrow fissures to the summits of hills.
3. Consequently those who think that they have excavated sources of springs at the height of such hills find themselves mistaken when they open up their excavations. Suppose a bronze vase filled not to the very lips, but containing two thirds of the quantity of water which forms its capacity, and with a cover placed upon it. When it is subjected to a very hot fire, the water must become thoroughly heated, and from the rarity of its nature it greatly expands by taking in the heat, so that it not only fills the vase but raises its cover by means of the currents of air in it, and swells and runs over. But if you take the cover off, the expanding forces are released into the open air, and the water settles down again to its proper level. So it is with the sources of springs. As long as they are confined in narrow channels, the currents of air in the water rush up in bubbles to the top, but as soon as they are given a wider outlet, they lose their air on account of the rarity peculiar to water, and so settle down and resume their proper level.
4. Every hot spring has healing properties because it has been boiled with foreign substances, and thus acquires a new useful quality. For example, sulphur springs cure pains in the sinews, by warming up and burning out the corrupt humours of the body by their heat. Aluminous springs, used in the treatment of the limbs when enfeebled by paralysis or the stroke of any such malady, introduce warmth through the open pores, counter-acting the chill by the opposite effect of their heat, and thus equably restoring the limbs to their former condition. Asphaltic springs, taken as purges, cure internal maladies.
5. There is also a kind of cold water containing natron, found for instance at Penne in the Vestine country, at Cutiliae, and at other similar places. It is taken as a purge and in passing through the bowels reduces scrofulous tumours. Copious springs are found where there are mines of gold, silver, iron, copper, lead, and the like, but they are very harmful. For they contain, like hot springs, sulphur, alum, asphalt,... and when it passes into the body in the form of drink, and spreading through the veins reaches the sinews and joints, it expands and hardens them. Hence the sinews, swelling with this expansion, are contracted in length and so give men the cramp or the gout, for the reason that their veins are saturated with very hard, dense, and cold substances.
6. There is also a sort of water which, since it contains... that are not perfectly clear, and it floats like a flower on the surface, in colour like purple glass. This may be seen particularly in Athens, where there are aqueducts from places and springs of that sort leading to the city and the port of Piraeus, from which nobody drinks, for the reason mentioned, but they use them for bathing and so forth, and drink from wells, thus avoiding their unwholesomeness. At Troezen it cannot be avoided, because no other kind of water at all is found, except what the Cibdeli furnish, and so in that city all or most of the people have diseases of the feet. At the city of Tarsus in Cilicia is a river named Cydnus, in which gouty people soak their legs and find relief from pain.
7. There are also many other kinds of water which have peculiar properties; for example, the river Himera in Sicily, which, after leaving its source, is divided into two branches. One flows in the direction of Etruria and has an exceedingly sweet taste on account of a sweet juice in the soil through which it runs; the other runs through a country where there are salt pits, and so it has a salt taste. At Paraetonium, and on the road to Ammon, and at Casius in Egypt there are marshy lakes which are so salt that they have a crust of salt on the surface. In many other places there are springs and rivers and lakes which are necessarily rendered salt because they run through salt pits.
8. Others flow through such greasy veins of soil that they are overspread with oil when they burst out as springs: for example, at Soli, a town in Cilicia, the river named Liparis, in which swimmers or bathers get anointed merely by the water. Likewise there is a lake in Ethiopia which anoints people who swim in it, and one in India which emits a great quantity of oil when the sky is clear. At Carthage is a spring that has oil swimming on its surface and smelling like sawdust from citrus wood, with which oil sheep are anointed. In Zacynthus and about Dyrrachium and Apollonia are springs which discharge a great quantity of pitch with their water. In Babylon, a lake of very great extent, called Lake Asphaltitis, has liquid asphalt swimming on its surface, with which asphalt and with burnt brick Semiramis built the wall surrounding Babylon. At Jaffa in Syria and among the Nomads in Arabia, are lakes of enormous size that yield very large masses of asphalt, which are carried off by the inhabitants thereabouts.
9. There is nothing marvellous in this, for quarries of hard asphalt are numerous there. So, when a quantity of water bursts its way through the asphaltic soil, it carries asphalt out with it, and after passing out of the ground, the water is separated and so rejects the asphalt from itself. Again, in Cappadocia on the road from Mazaca to Tyana, there is an extensive lake into which if a part of a reed or of some other thing be plunged, and withdrawn the next day, it will be found that the part thus withdrawn has turned into stone, while the part which remained above water retains its original nature.
10. In the same way, at Hierapolis in Phrygia there is a multitude of boiling hot springs from which water is let into ditches surrounding gardens and vineyards, and this water becomes an incrustation of stone at the end of a year. Hence, every year they construct banks of earth to the right and left, let in the water, and thus out of these incrustations make walls for their fields. This seems due to natural causes, since there is a juice having a coagulating potency like rennet underground in those spots and in that country. When this potency appears above ground mingled with spring water, the mixture cannot but be hardened by the heat of the sun and air, as appears in salt pits.
11. There are also springs which issue exceedingly bitter, owing to a bitter juice in the soil, such as the river Hypanis in Pontus. For about forty miles from its source its taste is very sweet; then it reaches a point about one hundred and sixty miles from its mouth, where it is joined by a very small brook. This runs into it, and at once makes that vast river bitter, for the reason that the water of the brook becomes bitter by flowing through the kind of soil and the veins in which there are sandarach mines.
12. These waters are given their different flavours by the properties of the soil, as is also seen in the case of fruits. If the roots of trees, vines, or other plants did not produce their fruits by drawing juices from soil of different properties, the flowers of all would be of the same kind in all places and districts. But we find in the island of Lesbos the protropum wine, in Maeonia, the catacecaumenites, in Lydia, the Tmolian, in Sicily, the Mamertine, in Campania, the Falernian, between Terracina and Fondi, the Caecuban, and wines of countless varieties and qualities produced in many other places. This could not be the case, were it not that the juice of the soil, introduced with its proper flavours into the roots, feeds the stem, and, mounting along it to the top, imparts a flavour to the fruit which is peculiar to its situation and kind.
13. If soils were not different and unlike in their kinds of juices, Syria and Arabia would not be the only places in which the reeds, rushes, and all the plants are aromatic, and in which there are trees bearing frankincense or yielding pepper berries and lumps of myrrh, nor would assafoetida be found only in the stalks growing in Cyrene, but everything would be of the same sort, and produced in the soil of all countries. It is the inclination of the firmament and the force of the sun, as it draws nearer or recedes in its course, that make these diversities such as we find them in different countries and places, through the nature of the soil and it's juices. And not only in the case of the things mentioned, but also in that of sheep and cattle. These diversities would not exist if the different properties of soils and their juices were not qualified by the power of the sun.
14. For instance, there are in Boeotia the rivers Cephisus and Melas, in Lucania, the Crathis, in Troy, the Xanthus, and certain springs in the country of the Clazomenians, the Erythraeans, and the Laodiceans. When sheep are ready for breeding at the proper season of the year, they are driven every day during that season to those rivers to drink, and the result is that, however white they may be, they beget in some places whity-brown lambs, in other places gray, and in others black as a raven. Thus, the peculiar character of the liquid, entering their body, produces in each case the quality with which it is imbued. Hence, it is said that the people of Ilium gave the river Xanthus its name because reddish cattle and whity-brown sheep are found in the plains of Troy near that river.
15. Deadly kinds of water are also found, which run through soil containing a noxious juice, and take in its poisonous quality: for instance, there is said to have been a spring at Terracina, called the spring of Neptune, which caused the death of those who thoughtlessly drank from it. In consequence, it is said that the ancients stopped it up. At Chrobs in Thrace there is a lake which causes the death not only of those who drink of it, but also of those who bathe in it. In Thessaly there is a gushing fount of which sheep never taste, nor does any sort of creature draw near to it, and close by this fount there is a tree with crimson flowers.
16. In Macedonia, at the place where Euripides is buried, two streams approach from the right and left of his tomb, and unite. By one of these, travellers are in the habit of lying down and taking luncheon, because its water is good; but nobody goes near the stream on the other side of the tomb, because its water is said to be death-dealing. In Arcadia there is a tract of land called Nonacris, which has extremely cold water trickling from a rock in the mountains. This water is called "Water of the Styx," and no vessel, whether of silver, bronze, or iron, can stand it without flying to pieces and breaking up. Nothing but a mule's hoof can keep it together and hold it, and tradition says that it was thus conveyed by Antipater through his son Iollas into the province where Alexander was staying, and that the king was killed by him with this water.
17. Among the Alps in the kingdom of Cottius there is a water those who taste of which immediately fall lifeless. In the Faliscan country on the Via Campana in the Campus Cornetus is a grove in which rises a spring, and there the bones of birds and of lizards and other reptiles are seen lying.
Some springs are acid, as at Lyncestus and in Italy in the Velian country, at Teano in Campania, and in many other places. These when used as drinks have the power of breaking up stones in the bladder, which form in the human body.
18. This seems to be due to natural causes, as there is a sharp and acid juice contained in the soil there, which imparts a sharpness to these springs as they issue from it; and so, on entering the body, they disperse all the deposits and concretions, due to the use of other waters, which they find in the body. Why such things are broken up by acid waters we can see from the following experiments. If an egg is left for some time in vinegar, its shell will soften and dissolve. Again, if a piece of lead, which is very flexible and heavy, is put in a vase and vinegar poured over it, and the vase covered and sealed up, the lead will be dissolved and turn into white lead.
19. On the same principle, copper, which is naturally more solid, will disperse and turn into verdigris if similarly treated. So, also, a pearl. Even rocks of lava, which neither iron nor fire alone can dissolve, split into pieces and dissolve when heated with fire and then sprinkled with vinegar. Hence, since we see these things taking place before our very eyes, we can infer that on the same principle even patients with the stone may, in the nature of things, be cured in like manner by means of acid waters, on account of the sharpness of the potion.
20. Then there are springs in which wine seems to be mingled, like the one in Paphlagonia, the water of which intoxicates those who drink of the spring alone without wine. The Aequians in Italy and the tribe of the Medulli in the Alps have a kind of water which causes swellings in the throats of those who drink it.
21. In Arcadia is the well-known town of Clitor, in whose territory is a cave with running water which makes people who drink of it abstemious. At this spring, there is an epigram in Greek verses inscribed on stone to the effect that the water is unsuitable for bathing, and also injurious to vines, because it was at this spring that Melampus cleansed the daughters of Proetus of their madness by sacrificial rites, and restored those maidens to their former sound state of mind. The inscription runs as written below:
Swain, if by noontide thirst thou art opprest When with thy flocks to Cleitor's bounds thou'st hied, Take from this fount a draught, and grant a rest To all thy goats the water nymphs beside. But bathe not in't when full of drunken cheer, Lest the mere vapour may bring thee to bane; Shun my vine-hating spring—Melampus here From madness once washed Proetus' daughters sane, And all th' offscouring here did hide, when they From Argos came to rugged Arcady.
22. In the island of Zea is a spring of which those who thoughtlessly drink lose their understanding, and an epigram is cut there to the effect that a draught from the spring is delightful, but that he who drinks will become dull as a stone. These are the verses:
This stone sweet streams of cooling drink doth drip, But stone his wits become who doth it sip.
23. At Susa, the capital of the Persian kingdom, there is a little spring, those who drink of which lose their teeth. An epigram is written there, the significance of which is to this effect, that the water is excellent for bathing, but that taken as drink, it knocks out the teeth by the roots. The verses of this epigram are, in Greek, as follows:
Stranger, you see the waters of a spring In which 'tis safe for men their hands to lave; But if the weedy basin entering You drink of its unpalatable wave, Your grinders tumble out that self-same day From jaws that orphaned sockets will display.
24. There are also in some places springs which have the peculiarity of giving fine singing voices to the natives, as at Tarsus in Magnesia and in other countries of that kind. Then there is Zama, an African city, which King Juba fortified by enclosing it with a double wall, and he established his royal residence there. Twenty miles from it is the walled town of Ismuc, the lands belonging to which are marked off by a marvellous kind of boundary. For although Africa was the mother and nurse of wild animals, particularly serpents, yet not one is ever born in the lands of that town, and if ever one is imported and put there, it dies at once; and not only this, but if soil is taken from this spot to another place, the same is true there. It is said that this kind of soil is also found in the Balearic Islands. The above mentioned soil has a still more wonderful property, of which I have learned in the following way.
25. Caius Julius, Masinissa's son, who owned all the lands about that town, served with Caesar the father. He was once my guest. Hence, in our daily intercourse, we naturally talked of literary subjects. During a conversation between us on the efficacy of water and its qualities, he stated that there were springs in that country of a kind which caused people born there to have fine singing voices, and that consequently they always sent abroad and bought handsome lads and ripe girls, and mated them, so that their progeny might have not only fine voices but also beautiful forms.
26. This great variety in different things is a distribution due to nature, for even the human body, which consists in part of the earthy, contains many kinds of juices, such as blood, milk, sweat, urine, and tears. If all this variation of flavours is found in a small portion of the earthy, we should not be surprised to find in the great earth itself countless varieties of juices, through the veins of which the water runs, and becomes saturated with them before reaching the outlets of springs. In this way, different varieties of springs of peculiar kinds are produced, on account of diversity of situation, characteristics of country, and dissimilar properties of soils.
27. Some of these things I have seen for myself, others I have found written in Greek books, the authorities for these writings being Theophrastus, Timaeus, Posidonius, Hegesias, Herodotus, Aristides, and Metrodorus. These men with much attention and endless pains showed by their writings that the peculiarities of sites, the properties of waters, and the characteristics of countries are conditioned by the inclination of the heaven. Following their investigations, I have set down in this book what I thought sufficient about different kinds of water, to make it easier, by means of these directions, for people to pick out springs from which they can conduct the water in aqueducts for the use of cities and towns.
28. For it is obvious that nothing in the world is so necessary for use as water, seeing that any living creature can, if deprived of grain or fruit or meat or fish, or any one of them, support life by using other foodstuffs; but without water no animal nor any proper food can be produced, kept in good condition, or prepared. Consequently we must take great care and pains in searching for springs and selecting them, keeping in view the health of mankind.
CHAPTER IV
TESTS OF GOOD WATER
1. Springs should be tested and proved in advance in the following ways. If they run free and open, inspect and observe the physique of the people who dwell in the vicinity before beginning to conduct the water, and if their frames are strong, their complexions fresh, legs sound, and eyes clear, the springs deserve complete approval. If it is a spring just dug out, its water is excellent if it can be sprinkled into a Corinthian vase or into any other sort made of good bronze without leaving a spot on it. Again, if such water is boiled in a bronze cauldron, afterwards left for a time, and then poured off without sand or mud being found at the bottom of the cauldron, that water also will have proved its excellence.
2. And if green vegetables cook quickly when put into a vessel of such water and set over a fire, it will be a proof that the water is good and wholesome. Likewise if the water in the spring is itself limpid and clear, if there is no growth of moss or reeds where it spreads and flows, and if its bed is not polluted by filth of any sort but has a clean appearance, these signs indicate that the water is light and wholesome in the highest degree.
CHAPTER V
LEVELLING AND LEVELLING INSTRUMENTS
1. I shall now treat of the ways in which water should be conducted to dwellings and cities. First comes the method of taking the level. Levelling is done either with dioptrae, or with water levels, or with the chorobates, but it is done with greater accuracy by means of the chorobates, because dioptrae and levels are deceptive. The chorobates is a straightedge about twenty feet long. At the extremities it has legs, made exactly alike and jointed on perpendicularly to the extremities of the straightedge, and also crosspieces, fastened by tenons, connecting the straightedge and the legs. These crosspieces have vertical lines drawn upon them, and there are plumblines hanging from the straightedge over each of the lines. When the straightedge is in position, and the plumblines strike both the lines alike and at the same time, they show that the instrument stands level.
2. But if the wind interposes, and constant motion prevents any definite indication by the lines, then have a groove on the upper side, five feet long, one digit wide, and a digit and a half deep, and pour water into it. If the water comes up uniformly to the rims of the groove, it will be known that the instrument is level. When the level is thus found by means of the chorobates, the amount of fall will also be known.
3. Perhaps some reader of the works of Archimedes will say that there can be no true levelling by means of water, because he holds that water has not a level surface, but is of a spherical form, having its centre at the centre of the earth. Still, whether water is plane or spherical, it necessarily follows that when the straightedge is level, it will support the water evenly at its extremities on the right and left, but that if it slopes down at one end, the water at the higher end will not reach the rim of the groove in the straightedge. For though the water, wherever poured in, must have a swelling and curvature in the centre, yet the extremities on the right and left must be on a level with each other. A picture of the chorobates will be found drawn at the end of the book. If there is to be a considerable fall, the conducting of the water will be comparatively easy. But if the course is broken by depressions, we must have recourse to substructures.
CHAPTER VI
AQUEDUCTS, WELLS, AND CISTERNS
1. There are three methods of conducting water, in channels through masonry conduits, or in lead pipes, or in pipes of baked clay. If in conduits, let the masonry be as solid as possible, and let the bed of the channel have a gradient of not less than a quarter of an inch for every hundred feet, and let the masonry structure be arched over, so that the sun may not strike the water at all. When it has reached the city, build a reservoir with a distribution tank in three compartments connected with the reservoir to receive the water, and let the reservoir have three pipes, one for each of the connecting tanks, so that when the water runs over from the tanks at the ends, it may run into the one between them.
2. From this central tank, pipes will be laid to all the basins and fountains; from the second tank, to baths, so that they may yield an annual income to the state; and from the third, to private houses, so that water for public use will not run short; for people will be unable to divert it if they have only their own supplies from headquarters. This is the reason why I have made these divisions, and also in order that individuals who take water into their houses may by their taxes help to maintain the conducting of the water by the contractors.
3. If, however, there are hills between the city and the source of supply, subterranean channels must be dug, and brought to a level at the gradient mentioned above. If the bed is of tufa or other stone, let the channel be cut in it; but if it is of earth or sand, there must be vaulted masonry walls for the channel, and the water should thus be conducted, with shafts built at every two hundred and forty feet.
4. But if the water is to be conducted in lead pipes, first build a reservoir at the source; then, let the pipes have an interior area corresponding to the amount of water, and lay these pipes from this reservoir to the reservoir which is inside the city walls. The pipes should be cast in lengths of at least ten feet. If they are hundreds, they should weigh 1200 pounds each length; if eighties, 960 pounds; if fifties, 600 pounds; forties, 480 pounds; thirties, 360 pounds; twenties, 240 pounds; fifteens, 180 pounds; tens, 120 pounds; eights, 100 pounds; fives, 60 pounds. The pipes get the names of their sizes from the width of the plates, taken in digits, before they are rolled into tubes. Thus, when a pipe is made from a plate fifty digits in width, it will be called a "fifty," and so on with the rest.
5. The conducting of the water through lead pipes is to be managed as follows. If there is a regular fall from the source to the city, without any intervening hills that are high enough to interrupt it, but with depressions in it, then we must build substructures to bring it up to the level as in the case of channels and conduits. If the distance round such depressions is not great, the water may be carried round circuitously; but if the valleys are extensive, the course will be directed down their slope. On reaching the bottom, a low substructure is built so that the level there may continue as long as possible. This will form the "venter," termed [Greek: Koilia] by the Greeks. Then, on reaching the hill on the opposite side, the length of the venter makes the water slow in swelling up to rise to the top of the hill.
6. But if there is no such venter made in the valleys, nor any substructure built on a level, but merely an elbow, the water will break out, and burst the joints of the pipes. And in the venter, water cushions must be constructed to relieve the pressure of the air. Thus, those who have to conduct water through lead pipes will do it most successfully on these principles, because its descents, circuits, venters, and risings can be managed in this way, when the level of the fall from the sources to the city is once obtained.
7. It is also not ineffectual to build reservoirs at intervals of 24,000 feet, so that if a break occurs anywhere, it will not completely ruin the whole work, and the place where it has occurred can easily be found; but such reservoirs should not be built at a descent, nor in the plane of a venter, nor at risings, nor anywhere in valleys, but only where there is an unbroken level.
8. But if we wish to spend less money, we must proceed as follows. Clay pipes with a skin at least two digits thick should be made, but these pipes should be tongued at one end so that they can fit into and join one another. Their joints must be coated with quicklime mixed with oil, and at the angles of the level of the venter a piece of red tufa stone, with a hole bored through it, must be placed right at the elbow, so that the last length of pipe used in the descent is jointed into the stone, and also the first length of the level of the venter; similarly at the hill on the opposite side the last length of the level of the venter should stick into the hole in the red tufa, and the first of the rise should be similarly jointed into it.
9. The level of the pipes being thus adjusted, they will not be sprung out of place by the force generated at the descent and at the rising. For a strong current of air is generated in an aqueduct which bursts its way even through stones unless the water is let in slowly and sparingly from the source at first, and checked at the elbows or turns by bands, or by the weight of sand ballast. All the other arrangements should be made as in the case of lead pipes. And ashes are to be put in beforehand when the water is let in from the source for the first time, so that if any of the joints have not been sufficiently coated, they may be coated with ashes.
10. Clay pipes for conducting water have the following advantages. In the first place, in construction:—if anything happens to them, anybody can repair the damage. Secondly, water from clay pipes is much more wholesome than that which is conducted through lead pipes, because lead is found to be harmful for the reason that white lead is derived from it, and this is said to be hurtful to the human system. Hence, if what is produced from it is harmful, no doubt the thing itself is not wholesome.
11. This we can exemplify from plumbers, since in them the natural colour of the body is replaced by a deep pallor. For when lead is smelted in casting, the fumes from it settle upon their members, and day after day burn out and take away all the virtues of the blood from their limbs. Hence, water ought by no means to be conducted in lead pipes, if we want to have it wholesome. That the taste is better when it comes from clay pipes may be proved by everyday life, for though our tables are loaded with silver vessels, yet everybody uses earthenware for the sake of purity of taste.
12. But if there are no springs from which we can construct aqueducts, it is necessary to dig wells. Now in the digging of wells we must not disdain reflection, but must devote much acuteness and skill to the consideration of the natural principles of things, because the earth contains many various substances in itself; for like everything else, it is composed of the four elements. In the first place, it is itself earthy, and of moisture it contains springs of water, also heat, which produces sulphur, alum, and asphalt; and finally, it contains great currents of air, which, coming up in a pregnant state through the porous fissures to the places where wells are being dug, and finding men engaged in digging there, stop up the breath of life in their nostrils by the natural strength of the exhalation. So those who do not quickly escape from the spot, are killed there.
13. To guard against this, we must proceed as follows. Let down a lighted lamp, and if it keeps on burning, a man may make the descent without danger. But if the light is put out by the strength of the exhalation, then dig air shafts beside the well on the right and left. Thus the vapours will be carried off by the air shafts as if through nostrils. When these are finished and we come to the water, then a wall should be built round the well without stopping up the vein.
14. But if the ground is hard, or if the veins lie too deep, the water supply must be obtained from roofs or higher ground, and collected in cisterns of "signinum work." Signinum work is made as follows. In the first place, procure the cleanest and sharpest sand, break up lava into bits of not more than a pound in weight, and mix the sand in a mortar trough with the strongest lime in the proportion of five parts of sand to two of lime. The trench for the signinum work, down to the level of the proposed depth of the cistern, should be beaten with wooden beetles covered with iron.
15. Then after having beaten the walls, let all the earth between them be cleared out to a level with the very bottom of the walls. Having evened this off, let the ground be beaten to the proper density. If such constructions are in two compartments or in three so as to insure clearing by changing from one to another, they will make the water much more wholesome and sweeter to use. For it will become more limpid, and keep its taste without any smell, if the mud has somewhere to settle; otherwise it will be necessary to clear it by adding salt.
In this book I have put what I could about the merits and varieties of water, its usefulness, and the ways in which it should be conducted and tested; in the next I shall write about the subject of dialling and the principles of timepieces.
BOOK IX
INTRODUCTION
1. The ancestors of the Greeks have appointed such great honours for the famous athletes who are victorious at the Olympian, Pythian, Isthmian, and Nemean games, that they are not only greeted with applause as they stand with palm and crown at the meeting itself, but even on returning to their several states in the triumph of victory, they ride into their cities and to their fathers' houses in four-horse chariots, and enjoy fixed revenues for life at the public expense. When I think of this, I am amazed that the same honours and even greater are not bestowed upon those authors whose boundless services are performed for all time and for all nations. This would have been a practice all the more worth establishing, because in the case of athletes it is merely their own bodily frame that is strengthened by their training, whereas in the case of authors it is the mind, and not only their own but also man's in general, by the doctrines laid down in their books for the acquiring of knowledge and the sharpening of the intellect.
2. What does it signify to mankind that Milo of Croton and other victors of his class were invincible? Nothing, save that in their lifetime they were famous among their countrymen. But the doctrines of Pythagoras, Democritus, Plato, and Aristotle, and the daily life of other learned men, spent in constant industry, yield fresh and rich fruit, not only to their own countrymen, but also to all nations. And they who from their tender years are filled with the plenteous learning which this fruit affords, attain to the highest capacity of knowledge, and can introduce into their states civilized ways, impartial justice, and laws, things without which no state can be sound.
3. Since, therefore, these great benefits to individuals and to communities are due to the wisdom of authors, I think that not only should palms and crowns be bestowed upon them, but that they should even be granted triumphs, and judged worthy of being consecrated in the dwellings of the gods.
Of their many discoveries which have been useful for the development of human life, I will cite a few examples. On reviewing these, people will admit that honours ought of necessity to be bestowed upon them.
4. First of all, among the many very useful theorems of Plato, I will cite one as demonstrated by him. Suppose there is a place or a field in the form of a square and we are required to double it. This has to be effected by means of lines correctly drawn, for it will take a kind of calculation not to be made by means of mere multiplication. The following is the demonstration. A square place ten feet long and ten feet wide gives an area of one hundred feet. Now if it is required to double the square, and to make one of two hundred feet, we must ask how long will be the side of that square so as to get from this the two hundred feet corresponding to the doubling of the area. Nobody can find this by means of arithmetic. For if we take fourteen, multiplication will give one hundred and ninety-six feet; if fifteen, two hundred and twenty-five feet.
5. Therefore, since this is inexplicable by arithmetic, let a diagonal line be drawn from angle to angle of that square of ten feet in length and width, dividing it into two triangles of equal size, each fifty feet in area. Taking this diagonal line as the length, describe another square. Thus we shall have in the larger square four triangles of the same size and the same number of feet as the two of fifty feet each which were formed by the diagonal line in the smaller square. In this way Plato demonstrated the doubling by means of lines, as the figure appended at the bottom of the page will show.
6. Then again, Pythagoras showed that a right angle can be formed without the contrivances of the artisan. Thus, the result which carpenters reach very laboriously, but scarcely to exactness, with their squares, can be demonstrated to perfection from the reasoning and methods of his teaching. If we take three rules, one three feet, the second four feet, and the third five feet in length, and join these rules together with their tips touching each other so as to make a triangular figure, they will form a right angle. Now if a square be described on the length of each one of these rules, the square on the side of three feet in length will have an area of nine feet; of four feet, sixteen; of five, twenty-five.
7. Thus the area in number of feet made up of the two squares on the sides three and four feet in length is equalled by that of the one square described on the side of five. When Pythagoras discovered this fact, he had no doubt that the Muses had guided him in the discovery, and it is said that he very gratefully offered sacrifice to them.
This theorem affords a useful means of measuring many things, and it is particularly serviceable in the building of staircases in buildings, so that the steps may be at the proper levels.
8. Suppose the height of the story, from the flooring above to the ground below, to be divided into three parts. Five of these will give the right length for the stringers of the stairway. Let four parts, each equal to one of the three composing the height between the upper story and the ground, be set off from the perpendicular, and there fix the lower ends of the stringers. In this manner the steps and the stairway itself will be properly placed. A figure of this also will be found appended below.
9. In the case of Archimedes, although he made many wonderful discoveries of diverse kinds, yet of them all, the following, which I shall relate, seems to have been the result of a boundless ingenuity. Hiero, after gaining the royal power in Syracuse, resolved, as a consequence of his successful exploits, to place in a certain temple a golden crown which he had vowed to the immortal gods. He contracted for its making at a fixed price, and weighed out a precise amount of gold to the contractor. At the appointed time the latter delivered to the king's satisfaction an exquisitely finished piece of handiwork, and it appeared that in weight the crown corresponded precisely to what the gold had weighed.
10. But afterwards a charge was made that gold had been abstracted and an equivalent weight of silver had been added in the manufacture of the crown. Hiero, thinking it an outrage that he had been tricked, and yet not knowing how to detect the theft, requested Archimedes to consider the matter. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment's delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, "[Greek: Eureka, eureka]."
11. Taking this as the beginning of his discovery, it is said that he made two masses of the same weight as the crown, one of gold and the other of silver. After making them, he filled a large vessel with water to the very brim, and dropped the mass of silver into it. As much water ran out as was equal in bulk to that of the silver sunk in the vessel. Then, taking out the mass, he poured back the lost quantity of water, using a pint measure, until it was level with the brim as it had been before. Thus he found the weight of silver corresponding to a definite quantity of water.
12. After this experiment, he likewise dropped the mass of gold into the full vessel and, on taking it out and measuring as before, found that not so much water was lost, but a smaller quantity: namely, as much less as a mass of gold lacks in bulk compared to a mass of silver of the same weight. Finally, filling the vessel again and dropping the crown itself into the same quantity of water, he found that more water ran over for the crown than for the mass of gold of the same weight. Hence, reasoning from the fact that more water was lost in the case of the crown than in that of the mass, he detected the mixing of silver with the gold, and made the theft of the contractor perfectly clear.
13. Now let us turn our thoughts to the researches of Archytas of Tarentum and Eratosthenes of Cyrene. They made many discoveries from mathematics which are welcome to men, and so, though they deserve our thanks for other discoveries, they are particularly worthy of admiration for their ideas in that field. For example, each in a different way solved the problem enjoined upon Delos by Apollo in an oracle, the doubling of the number of cubic feet in his altars; this done, he said, the inhabitants of the island would be delivered from an offence against religion.
14. Archytas solved it by his figure of the semi-cylinders; Eratosthenes, by means of the instrument called the mesolabe.
Noting all these things with the great delight which learning gives, we cannot but be stirred by these discoveries when we reflect upon the influence of them one by one. I find also much for admiration in the books of Democritus on nature, and in his commentary entitled [Greek: Cheirokmeta], in which he made use of his ring to seal with soft wax the principles which he had himself put to the test.
15. These, then, were men whose researches are an everlasting possession, not only for the improvement of character but also for general utility. The fame of athletes, however, soon declines with their bodily powers. Neither when they are in the flower of their strength, nor afterwards with posterity, can they do for human life what is done by the researches of the learned.
16. But although honours are not bestowed upon authors for excellence of character and teaching, yet as their minds, naturally looking up to the higher regions of the air, are raised to the sky on the steps of history, it must needs be, that not merely their doctrines, but even their appearance, should be known to posterity through time eternal. Hence, men whose souls are aroused by the delights of literature cannot but carry enshrined in their hearts the likeness of the poet Ennius, as they do those of the gods. Those who are devotedly attached to the poems of Accius seem to have before them not merely his vigorous language but even his very figure.
17. So, too, numbers born after our time will feel as if they were discussing nature face to face with Lucretius, or the art of rhetoric with Cicero; many of our posterity will confer with Varro on the Latin language; likewise, there will be numerous scholars who, as they weigh many points with the wise among the Greeks, will feel as if they were carrying on private conversations with them. In a word, the opinions of learned authors, though their bodily forms are absent, gain strength as time goes on, and, when taking part in councils and discussions, have greater weight than those of any living men.
18. Such, Caesar, are the authorities on whom I have depended, and applying their views and opinions I have written the present books, in the first seven treating of buildings and in the eighth of water. In this I shall set forth the rules for dialling, showing how they are found through the shadows cast by the gnomon from the sun's rays in the firmament, and on what principles these shadows lengthen and shorten.
CHAPTER I
THE ZODIAC AND THE PLANETS
1. It is due to the divine intelligence and is a very great wonder to all who reflect upon it, that the shadow of a gnomon at the equinox is of one length in Athens, of another in Alexandria, of another in Rome, and not the same at Piacenza, or at other places in the world. Hence drawings for dials are very different from one another, corresponding to differences of situation. This is because the length of the shadow at the equinox is used in constructing the figure of the analemma, in accordance with which the hours are marked to conform to the situation and the shadow of the gnomon. The analemma is a basis for calculation deduced from the course of the sun, and found by observation of the shadow as it increases until the winter solstice. By means of this, through architectural principles and the employment of the compasses, we find out the operation of the sun in the universe.
2. The word "universe" means the general assemblage of all nature, and it also means the heaven that is made up of the constellations and the courses of the stars. The heaven revolves steadily round earth and sea on the pivots at the ends of its axis. The architect at these points was the power of Nature, and she put the pivots there, to be, as it were, centres, one of them above the earth and sea at the very top of the firmament and even beyond the stars composing the Great Bear, the other on the opposite side under the earth in the regions of the south. Round these pivots (termed in Greek [Greek: poloi]) as centres, like those of a turning lathe, she formed the circles in which the heaven passes on its everlasting way. In the midst thereof, the earth and sea naturally occupy the central point.
3. It follows from this natural arrangement that the central point in the north is high above the earth, while on the south, the region below, it is beneath the earth and consequently hidden by it. Furthermore, across the middle, and obliquely inclined to the south, there is a broad circular belt composed of the twelve signs, whose stars, arranged in twelve equivalent divisions, represent each a shape which nature has depicted. And so with the firmament and the other constellations, they move round the earth and sea in glittering array, completing their orbits according to the spherical shape of the heaven.
4. They are all visible or invisible according to fixed times. While six of the signs are passing along with the heaven above the earth, the other six are moving under the earth and hidden by its shadow. But there are always six of them making their way above the earth; for, corresponding to that part of the last sign which in the course of its revolution has to sink, pass under the earth, and become concealed, an equivalent part of the sign opposite to it is obliged by the law of their common revolution to pass up and, having completed its circuit, to emerge out of the darkness into the light of the open space on the other side. This is because the rising and setting of both are subject to one and the same power and law.
5. While these signs, twelve in number and occupying each one twelfth part of the firmament, steadily revolve from east to west, the moon, Mercury, Venus, the sun, as well as Mars, Jupiter, and Saturn, differing from one another in the magnitude of their orbits as though their courses were at different points in a flight of steps, pass through those signs in just the opposite direction, from west to east in the firmament. The moon makes her circuit of the heaven in twenty-eight days plus about an hour, and with her return to the sign from which she set forth, completes a lunar month.
6. The sun takes a full month to move across the space of one sign, that is, one twelfth of the firmament. Consequently, in twelve months he traverses the spaces of the twelve signs, and, on returning to the sign from which he began, completes the period of a full year. Hence, the circuit made by the moon thirteen times in twelve months, is measured by the sun only once in the same number of months. But Mercury and Venus, their paths wreathing around the sun's rays as their centre, retrograde and delay their movements, and so, from the nature of that circuit, sometimes wait at stopping-places within the spaces of the signs.
7. This fact may best be recognized from Venus. When she is following the sun, she makes her appearance in the sky after his setting, and is then called the Evening Star, shining most brilliantly. At other times she precedes him, rising before day-break, and is named the Morning Star. Thus Mercury and Venus sometimes delay in one sign for a good many days, and at others advance pretty rapidly into another sign. They do not spend the same number of days in every sign, but the longer they have previously delayed, the more rapidly they accomplish their journeys after passing into the next sign, and thus they complete their appointed course. Consequently, in spite of their delay in some of the signs, they nevertheless soon reach the proper place in their orbits after freeing themselves from their enforced delay.
8. Mercury, on his journey through the heavens, passes through the spaces of the signs in three hundred and sixty days, and so arrives at the sign from which he set out on his course at the beginning of his revolution. His average rate of movement is such that he has about thirty days in each sign.
9. Venus, on becoming free from the hindrance of the sun's rays, crosses the space of a sign in thirty days. Though she thus stays less than forty days in particular signs, she makes good the required amount by delaying in one sign when she comes to a pause. Therefore she completes her total revolution in heaven in four hundred and eighty-five days, and once more enters the sign from which she previously began to move.
10. Mars, after traversing the spaces of the constellations for about six hundred and eighty-three days, arrives at the point from which he had before set out at the beginning of his course, and while he passes through some of the signs more rapidly than others, he makes up the required number of days whenever he comes to a pause. Jupiter, climbing with gentler pace against the revolution of the firmament, travels through each sign in about three hundred and sixty days, and finishes in eleven years and three hundred and thirteen days, returning to the sign in which he had been twelve years before. Saturn, traversing the space of one sign in twenty-nine months plus a few days, is restored after twenty-nine years and about one hundred and sixty days to that in which he had been thirty years before. He is, as it appears, slower, because the nearer he is to the outermost part of the firmament, the greater is the orbit through which he has to pass.
11. The three that complete their circuits above the sun's course do not make progress while they are in the triangle which he has entered, but retrograde and pause until the sun has crossed from that triangle into another sign. Some hold that this takes place because, as they say, when the sun is a great distance off, the paths on which these stars wander are without light on account of that distance, and so the darkness retards and hinders them. But I do not think that this is so. The splendour of the sun is clearly to be seen, and manifest without any kind of obscurity, throughout the whole firmament, so that those very retrograde movements and pauses of the stars are visible even to us.
12. If then, at this great distance, our human vision can discern that sight, why, pray, are we to think that the divine splendour of the stars can be cast into darkness? Rather will the following way of accounting for it prove to be correct. Heat summons and attracts everything towards itself; for instance, we see the fruits of the earth growing up high under the influence of heat, and that spring water is vapourised and drawn up to the clouds at sunrise. On the same principle, the mighty influence of the sun, with his rays diverging in the form of a triangle, attracts the stars which follow him, and, as it were, curbs and restrains those that precede, not allowing them to make progress, but obliging them to retrograde towards himself until he passes out into the sign that belongs to a different triangle.
13. Perhaps the question will be raised, why the sun by his great heat causes these detentions in the fifth sign from himself rather than in the second or third, which are nearer. I will therefore set forth what seems to be the reason. His rays diverge through the firmament in straight lines as though forming an equilateral triangle, that is, to the fifth sign from the sun, no more, no less. If his rays were diffused in circuits spreading all over the firmament, instead of in straight lines diverging so as to form a triangle, they would burn up all the nearer objects. This is a fact which the Greek poet Euripides seems to have remarked; for he says that places at a greater distance from the sun are in a violent heat, and that those which are nearer he keeps temperate. Thus in the play of Phaethon, the poet writes: [Greek: kaiei ta porro, tangythen d eukrat echei].
14. If then, fact and reason and the evidence of an ancient poet point to this explanation, I do not see why we should decide otherwise than as I have written above on this subject.
Jupiter, whose orbit is between those of Mars and Saturn, traverses a longer course than Mars, and a shorter than Saturn. Likewise with the rest of these stars: the farther they are from the outermost limits of the heaven, and the nearer their orbits to the earth, the sooner they are seen to finish their courses; for those of them that have a smaller orbit often pass those that are higher, going under them.
15. For example, place seven ants on a wheel such as potters use, having made seven channels on the wheel about the centre, increasing successively in circumference; and suppose those ants obliged to make a circuit in these channels while the wheel is turned in the opposite direction. In spite of having to move in a direction contrary to that of the wheel, the ants must necessarily complete their journeys in the opposite direction, and that ant which is nearest the centre must finish its circuit sooner, while the ant that is going round at the outer edge of the disc of the wheel must, on account of the size of its circuit, be much slower in completing its course, even though it is moving just as quickly as the other. In the same way, these stars, which struggle on against the course of the firmament, are accomplishing an orbit on paths of their own; but, owing to the revolution of the heaven, they are swept back as it goes round every day.
16. The reason why some of these stars are temperate, others hot, and others cold, appears to be this: that the flame of every kind of fire rises to higher places. Consequently, the burning rays of the sun make the ether above him white hot, in the regions of the course of Mars, and so the heat of the sun makes him hot. Saturn, on the contrary, being nearest to the outermost limit of the firmament and bordering on the quarters of the heaven which are frozen, is excessively cold. Hence, Jupiter, whose course is between the orbits of these two, appears to have a moderate and very temperate influence, intermediate between their cold and heat.
I have now described, as I have received them from my teacher, the belt of the twelve signs and the seven stars that work and move in the opposite direction, with the laws and numerical relations under which they pass from sign to sign, and how they complete their orbits. I shall next speak of the waxing and waning of the moon, according to the accounts of my predecessors.
CHAPTER II
THE PHASES OF THE MOON
1. According to the teaching of Berosus, who came from the state, or rather nation, of the Chaldees, and was the pioneer of Chaldean learning in Asia, the moon is a ball, one half luminous and the rest of a blue colour. When, in the course of her orbit, she has passed below the disc of the sun, she is attracted by his rays and great heat, and turns thither her luminous side, on account of the sympathy between light and light. Being thus summoned by the sun's disc and facing upward, her lower half, as it is not luminous, is invisible on account of its likeness to the air. When she is perpendicular to the sun's rays, all her light is confined to her upper surface, and she is then called the new moon.
2. As she moves on, passing by to the east, the effect of the sun upon her relaxes, and the outer edge of the luminous side sheds its light upon the earth in an exceedingly thin line. This is called the second day of the moon. Day by day she is further relieved and turns, and thus are numbered the third, fourth, and following days. On the seventh day, the sun being in the west and the moon in the middle of the firmament between the east and west, she is half the extent of the firmament distant from the sun, and therefore half of the luminous side is turned toward the earth. But when the sun and moon are separated by the entire extent of the firmament, and the moon is in the east with the sun over against her in the west, she is completely relieved by her still greater distance from his rays, and so, on the fourteenth day, she is at the full, and her entire disc emits its light. On the succeeding days, up to the end of the month, she wanes daily as she turns in her course, being recalled by the sun until she comes under his disc and rays, thus completing the count of the days of the month.
3. But Aristarchus of Samos, a mathematician of great powers, has left a different explanation in his teaching on this subject, as I shall now set forth. It is no secret that the moon has no light of her own, but is, as it were, a mirror, receiving brightness from the influence of the sun. Of all the seven stars, the moon traverses the shortest orbit, and her course is nearest to the earth. Hence in every month, on the day before she gets past the sun, she is under his disc and rays, and is consequently hidden and invisible. When she is thus in conjunction with the sun, she is called the new moon. On the next day, reckoned as her second, she gets past the sun and shows the thin edge of her sphere. Three days away from the sun, she waxes and grows brighter. Removing further every day till she reaches the seventh, when her distance from the sun at his setting is about one half the extent of the firmament, one half of her is luminous: that is, the half which faces toward the sun is lighted up by him.
4. On the fourteenth day, being diametrically across the whole extent of the firmament from the sun, she is at her full and rises when the sun is setting. For, as she takes her place over against him and distant the whole extent of the firmament, she thus receives the light from the sun throughout her entire orb. On the seventeenth day, at sunrise, she is inclining to the west. On the twenty-second day, after sunrise, the moon is about mid-heaven; hence, the side exposed to the sun is bright and the rest dark. Continuing thus her daily course, she passes under the rays of the sun on about the twenty-eighth day, and so completes the account of the month.
I will next explain how the sun, passing through a different sign each month, causes the days and hours to increase and diminish in length.
CHAPTER III
THE COURSE OF THE SUN THROUGH THE TWELVE SIGNS
1. The sun, after entering the sign Aries and passing through one eighth of it, determines the vernal equinox. On reaching the tail of Taurus and the constellation of the Pleiades, from which the front half of Taurus projects, he advances into a space greater than half the firmament, moving toward the north. From Taurus he enters Gemini at the time of the rising of the Pleiades, and, getting higher above the earth, he increases the length of the days. Next, coming from Gemini into Cancer, which occupies the shortest space in heaven, and after traversing one eighth of it, he determines the summer solstice. Continuing on, he reaches the head and breast of Leo, portions which are reckoned as belonging to Cancer.
2. After leaving the breast of Leo and the boundaries of Cancer, the sun, traversing the rest of Leo, makes the days shorter, diminishing the size of his circuit, and returning to the same course that he had in Gemini. Next, crossing from Leo into Virgo, and advancing as far as the bosom of her garment, he still further shortens his circuit, making his course equal to what it was in Taurus. Advancing from Virgo by way of the bosom of her garment, which forms the first part of Libra, he determines the autumn equinox at the end of one eighth of Libra. Here his course is equal to what his circuit was in the sign Aries.
3. When the sun has entered Scorpio, at the time of the setting of the Pleiades, he begins to make the days shorter as he advances toward the south. From Scorpio he enters Sagittarius and, on reaching the thighs, his daily course is still further diminished. From the thighs of Sagittarius, which are reckoned as part of Capricornus, he reaches the end of the first eighth of the latter, where his course in heaven is shortest. Consequently, this season, from the shortness of the day, is called bruma or dies brumales. Crossing from Capricornus into Aquarius, he causes the days to increase to the length which they had when he was in Sagittarius. From Aquarius he enters Pisces at the time when Favonius begins to blow, and here his course is the same as in Scorpio. In this way the sun passes round through the signs, lengthening or shortening the days and hours at definite seasons. |
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