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 cla.s.s 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 G.o.ds.
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. n.o.body 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 G.o.ds. 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]."