I shall next speak of the other constellations formed by arrangements of stars, and lying to the right and left of the belt of the signs, in the southern and northern portions of the firmament.



CHAPTER IV

THE NORTHERN CONSTELLATIONS

1. The Great Bear, called in Greek [Greek: arktos] or [Greek: helike], has her Warden behind her. Near him is the Virgin, on whose right shoulder rests a very bright star which we call Harbinger of the Vintage, and the Greeks [Greek: protrygetes]. But Spica in that constellation is brighter. Opposite there is another star, coloured, between the knees of the Bear Warden, dedicated there under the name of Arcturus.

2. Opposite the head of the Bear, at an angle with the feet of the Twins, is the Charioteer, standing on the tip of the horn of the Bull; hence, one and the same star is found in the tip of the left horn of the Bull and in the right foot of the Charioteer. Supported on the hand of the Charioteer are the Kids, with the She-Goat at his left shoulder. Above the Bull and the Ram is Perseus, having at his right...[11] with the Pleiades moving beneath, and at his left the head of the Ram. His right hand rests on the likeness of Cassiopea, and with his left he holds the Gorgon's head by its top over the Ram, laying it at the feet of Andromeda.

[Note 11: From this point to the end of section 3 the text is often hopelessly corrupt. The translation follows, approximately, the manuscript reading, but cannot pretend to be exact.]

3. Above Andromeda are the Fishes, one above her belly and the other above the backbone of the Horse. A very bright star terminates both the belly of the Horse and the head of Andromeda. Andromeda's right hand rests above the likeness of Cassiopea, and her left above the Northern Fish. The Waterman's head is above that of the Horse. The Horse's hoofs lie close to the Waterman's knees. Cassiopea is set apart in the midst. High above the He-Goat are the Eagle and the Dolphin, and near them is the Arrow. Farther on is the Bird, whose right wing grazes the head and sceptre of Cepheus, with its left resting over Cassiopea. Under the tail of the Bird lie the feet of the Horse.

4. Above the Archer, Scorpion, and Balance, is the Serpent, reaching to the Crown with the end of its snout. Next, the Serpent-holder grasps the Serpent about the middle in his hands, and with his left foot treads squarely on the foreparts of the Scorpion. A little way from the head of the Serpent-holder is the head of the so-called Kneeler. Their heads are the more readily to be distinguished as the stars which compose them are by no means dim.

5. The foot of the Kneeler rests on the temple of that Serpent which is entwined between the She-Bears (called Septentriones). The little Dolphin moves in front of the Horse. Opposite the bill of the Bird is the Lyre. The Crown is arranged between the shoulders of the Warden and the Kneeler. In the northern circle are the two She-Bears with their shoulder-blades confronting and their breasts turned away from one another. The Greeks call the Lesser Bear [Greek: kynosoura], and the Greater [Greek: elike]. Their heads face different ways, and their tails are shaped so that each is in front of the head of the other Bear; for the tails of both stick up over them.

6. The Serpent is said to lie stretched out between their tails, and in it there is a star, called Polus, shining near the head of the Greater Bear. At the nearest point, the Serpent winds its head round, but is also flung in a fold round the head of the Lesser Bear, and stretches out close to her feet. Here it twists back, making another fold, and, lifting itself up, bends its snout and right temple from the head of the Lesser Bear round towards the Greater. Above the tail of the Lesser Bear are the feet of Cepheus, and at this point, at the very top, are stars forming an equilateral triangle. There are a good many stars common to the Lesser Bear and to Cepheus.

I have now mentioned the constellations which are arranged in the heaven to the right of the east, between the belt of the signs and the north. I shall next describe those that Nature has distributed to the left of the east and in the southern regions.



CHAPTER V

THE SOUTHERN CONSTELLATIONS

1. First, under the He-Goat lies the Southern Fish, facing towards the tail of the Whale. The Censer is under the Scorpion's sting. The fore parts of the Centaur are next to the Balance and the Scorpion, and he holds in his hands the figure which astronomers call the Beast. Beneath the Virgin, Lion, and Crab is the twisted girdle formed by the Snake, extending over a whole line of stars, his snout raised near the Crab, supporting the Bowl with the middle of his body near the Lion, and bringing his tail, on which is the Raven, under and near the hand of the Virgin. The region above his shoulders is equally bright.

2. Beneath the Snake's belly, at the tail, lies the Centaur. Near the Bowl and the Lion is the ship named Argo. Her bow is invisible, but her mast and the parts about the helm are in plain sight, the stern of the vessel joining the Dog at the tip of his tail. The Little Dog follows the Twins, and is opposite the Snake's head. The Greater Dog follows the Lesser. Orion lies aslant, under the Bull's hoof; in his left hand grasping his club, and raising the other toward the Twins.

3. At his feet is the Dog, following a little behind the Hare. The Whale lies under the Ram and the Fishes, and from his mane there is a slight sprinkling of stars, called in Greek [Greek: harpedonai], regularly disposed towards each of the Fishes. This ligature by which they hang is carried a great way inwards, but reaches out to the top of the mane of the Whale. The River, formed of stars, flows from a source at the left foot of Orion. But the Water, said to pour from the Waterman, flows between the head of the Southern Fish and the tail of the Whale.

4. These constellations, whose outlines and shapes in the heavens were designed by Nature and the divine intelligence, I have described according to the view of the natural philosopher Democritus, but only those whose risings and settings we can observe and see with our own eyes. Just as the Bears turn round the pivot of the axis without ever setting or sinking under the earth, there are likewise stars that keep turning round the southern pivot, which on account of the inclination of the firmament lies always under the earth, and, being hidden there, they never rise and emerge above the earth. Consequently, the figures which they form are unknown to us on account of the interposition of the earth. The star Canopus proves this. It is unknown to our vicinity; but we have reports of it from merchants who have been to the most distant part of Egypt, and to regions bordering on the uttermost boundaries of the earth.



CHAPTER VI

ASTROLOGY AND WEATHER PROGNOSTICS

1. I have shown how the firmament, and the twelve signs with the constellations arranged to the north and south of them, fly round the earth, so that the matter may be clearly understood. For it is from this revolution of the firmament, from the course of the sun through the signs in the opposite direction, and from the shadows cast by equinoctial gnomons, that we find the figure of the analemma.

2. As for the branch of astronomy which concerns the influences of the twelve signs, the five stars, the sun, and the moon upon human life, we must leave all this to the calculations of the Chaldeans, to whom belongs the art of casting nativities, which enables them to declare the past and the future by means of calculations based on the stars. These discoveries have been transmitted by the men of genius and great acuteness who sprang directly from the nation of the Chaldeans; first of all, by Berosus, who settled in the island state of Cos, and there opened a school. Afterwards Antipater pursued the subject; then there was Archinapolus, who also left rules for casting nativities, based not on the moment of birth but on that of conception.

3. When we come to natural philosophy, however, Thales of Miletus, Anaxagoras of Clazomenae, Pythagoras of Samos, Xenophanes of Colophon, and Democritus of Abdera have in various ways investigated and left us the laws and the working of the laws by which nature governs it. In the track of their discoveries, Eudoxus, Euctemon, Callippus, Meto, Philippus, Hipparchus, Aratus, and others discovered the risings and settings of the constellations, as well as weather prognostications from astronomy through the study of the calendars, and this study they set forth and left to posterity. Their learning deserves the admiration of mankind; for they were so solicitous as even to be able to predict, long beforehand, with divining mind, the signs of the weather which was to follow in the future. On this subject, therefore, reference must be made to their labours and investigations.



CHAPTER VII

THE ANALEMMA AND ITS APPLICATIONS

1. In distinction from the subjects first mentioned, we must ourselves explain the principles which govern the shortening and lengthening of the day. When the sun is at the equinoxes, that is, passing through Aries or Libra, he makes the gnomon cast a shadow equal to eight ninths of its own length, in the latitude of Rome. In Athens, the shadow is equal to three fourths of the length of the gnomon; at Rhodes to five sevenths; at Tarentum, to nine elevenths; at Alexandria, to three fifths; and so at other places it is found that the shadows of equinoctial gnomons are naturally different from one another.

2. Hence, wherever a sundial is to be constructed, we must take the equinoctial shadow of the place. If it is found to be, as in Rome, equal to eight ninths of the gnomon, let a line be drawn on a plane surface, and in the middle thereof erect a perpendicular, plumb to the line, which perpendicular is called the gnomon. Then, from the line in the plane, let the line of the gnomon be divided off by the compasses into nine parts, and take the point designating the ninth part as a centre, to be marked by the letter A. Then, opening the compasses from that centre to the line in the plane at the point B, describe a circle. This circle is called the meridian.

3. Then, of the nine parts between the plane and the centre on the gnomon, take eight, and mark them off on the line in the plane to the point C. This will be the equinoctial shadow of the gnomon. From that point, marked by C, let a line be drawn through the centre at the point A, and this will represent a ray of the sun at the equinox. Then, extending the compasses from the centre to the line in the plane, mark off the equidistant points E on the left and I on the right, on the two sides of the circumference, and let a line be drawn through the centre, dividing the circle into two equal semicircles. This line is called by mathematicians the horizon.



4. Then, take a fifteenth part of the entire circumference, and, placing the centre of the compasses on the circumference at the point where the equinoctial ray cuts it at the letter F, mark off the points G and H on the right and left. Then lines must be drawn from these (and the centre) to the line of the plane at the points T and R, and thus, one will represent the ray of the sun in winter, and the other the ray in summer. Opposite E will be the point I, where the line drawn through the centre at the point A cuts the circumference; opposite G and H will be the points L and K; and opposite C, F, and A will be the point N.

5. Then, diameters are to be drawn from G to L and from H to K. The upper will denote the summer and the lower the winter portion. These diameters are to be divided equally in the middle at the points M and O, and those centres marked; then, through these marks and the centre A, draw a line extending to the two sides of the circumference at the points P and Q. This will be a line perpendicular to the equinoctial ray, and it is called in mathematical figures the axis. From these same centres open the compasses to the ends of the diameters, and describe semicircles, one of which will be for summer and the other for winter.

6. Then, at the points at which the parallel lines cut the line called the horizon, the letter S is to be on the right and the letter V on the left, and from the extremity of the semicircle, at the point G, draw a line parallel to the axis, extending to the left-hand semicircle at the point H. This parallel line is called the Logotomus. Then, centre the compasses at the point where the equinoctial ray cuts that line, at the letter D, and open them to the point where the summer ray cuts the circumference at the letter H. From the equinoctial centre, with a radius extending to the summer ray, describe the circumference of the circle of the months, which is called Menaeus. Thus we shall have the figure of the analemma.

7. This having been drawn and completed, the scheme of hours is next to be drawn on the baseplates from the analemma, according to the winter lines, or those of summer, or the equinoxes, or the months, and thus many different kinds of dials may be laid down and drawn by this ingenious method. But the result of all these shapes and designs is in one respect the same: namely, the days of the equinoxes and of the winter and summer solstices are always divided into twelve equal parts. Omitting details, therefore,—not for fear of the trouble, but lest I should prove tiresome by writing too much,—I will state by whom the different classes and designs of dials have been invented. For I cannot invent new kinds myself at this late day, nor do I think that I ought to display the inventions of others as my own. Hence, I will mention those that have come down to us, and by whom they were invented.



CHAPTER VIII

SUNDIALS AND WATER CLOCKS

1. The semicircular form, hollowed out of a square block, and cut under to correspond to the polar altitude, is said to have been invented by Berosus the Chaldean; the Scaphe or Hemisphere, by Aristarchus of Samos, as well as the disc on a plane surface; the Arachne, by the astronomer Eudoxus or, as some say, by Apollonius; the Plinthium or Lacunar, like the one placed in the Circus Flaminius, by Scopinas of Syracuse; the [Greek: pros ta historoumena], by Parmenio; the [Greek: pros pan klima], by Theodosius and Andreas; the Pelecinum, by Patrocles; the Cone, by Dionysodorus; the Quiver, by Apollonius. The men whose names are written above, as well as many others, have invented and left us other kinds: as, for instance, the Conarachne, the Conical Plinthium, and the Antiborean. Many have also left us written directions for making dials of these kinds for travellers, which can be hung up. Whoever wishes to find their baseplates, can easily do so from the books of these writers, provided only he understands the figure of the analemma.

2. Methods of making water clocks have been investigated by the same writers, and first of all by Ctesibius the Alexandrian, who also discovered the natural pressure of the air and pneumatic principles. It is worth while for students to know how these discoveries came about. Ctesibius, born at Alexandria, was the son of a barber. Preeminent for natural ability and great industry, he is said to have amused himself with ingenious devices. For example, wishing to hang a mirror in his father's shop in such a way that, on being lowered and raised again, its weight should be raised by means of a concealed cord, he employed the following mechanical contrivance.

3. Under the roof-beam he fixed a wooden channel in which he arranged a block of pulleys. He carried the cord along the channel to the corner, where he set up some small piping. Into this a leaden ball, attached to the cord, was made to descend. As the weight fell into the narrow limits of the pipe, it naturally compressed the enclosed air, and, as its fall was rapid, it forced the mass of compressed air through the outlet into the open air, thus producing a distinct sound by the concussion.

4. Hence, Ctesibius, observing that sounds and tones were produced by the contact between the free air and that which was forced from the pipe, made use of this principle in the construction of the first water organs. He also devised methods of raising water, automatic contrivances, and amusing things of many kinds, including among them the construction of water clocks. He began by making an orifice in a piece of gold, or by perforating a gem, because these substances are not worn by the action of water, and do not collect dirt so as to get stopped up.

5. A regular flow of water through the orifice raises an inverted bowl, called by mechanicians the "cork" or "drum." To this are attached a rack and a revolving drum, both fitted with teeth at regular intervals. These teeth, acting upon one another, induce a measured revolution and movement. Other racks and other drums, similarly toothed and subject to the same motion, give rise by their revolution to various kinds of motions, by which figures are moved, cones revolve, pebbles or eggs fall, trumpets sound, and other incidental effects take place.

6. The hours are marked in these clocks on a column or a pilaster, and a figure emerging from the bottom points to them with a rod throughout the whole day. Their decrease or increase in length with the different days and months, must be adjusted by inserting or withdrawing wedges. The shutoffs for regulating the water are constructed as follows. Two cones are made, one solid and the other hollow, turned on a lathe so that one will go into the other and fit it perfectly. A rod is used to loosen or to bring them together, thus causing the water to flow rapidly or slowly into the vessels. According to these rules, and by this mechanism, water clocks may be constructed for use in winter.

7. But if it proves that the shortening or lengthening of the day is not in agreement with the insertion and removal of the wedges, because the wedges may very often cause errors, the following arrangement will have to be made. Let the hours be marked off transversely on the column from the analemma, and let the lines of the months also be marked upon the column. Then let the column be made to revolve, in such a way that, as it turns continuously towards the figure and the rod with which the emerging figure points to the hours, it may make the hours short or long according to the respective months.

8. There is also another kind of winter dial, called the Anaphoric and constructed in the following way. The hours, indicated by bronze rods in accordance with the figure of the analemma, radiate from a centre on the face. Circles are described upon it, marking the limits of the months. Behind these rods there is a drum, on which is drawn and painted the firmament with the circle of the signs. In drawing the figures of the twelve celestial signs, one is represented larger and the next smaller, proceeding from the centre. Into the back of the drum, in the middle, a revolving axis is inserted, and round that axis is wound a flexible bronze chain, at one end of which hangs the "cork" which is raised by the water, and at the other a counterpoise of sand, equal in weight to the "cork."

9. Hence, the sand sinks as the "cork" is raised by the water, and in sinking turns the axis, and the axis the drum. The revolution of this drum causes sometimes a larger and sometimes a smaller portion of the circle of the signs to indicate, during the revolutions, the proper length of the hours corresponding to their seasons. For in every one of the signs there are as many holes as the corresponding month has days, and a boss, which seems to be holding the representation of the sun on a dial, designates the spaces for the hours. This, as it is carried from hole to hole, completes the circuit of a full month.

10. Hence, just as the sun during his passage through the constellations makes the days and hours longer or shorter, so the boss on a dial, moving from point to point in a direction contrary to that of the revolution of the drum in the middle, is carried day by day sometimes over wider and sometimes over narrower spaces, giving a representation of the hours and days within the limits of each month.

To manage the water so that it may flow regularly, we must proceed as follows.

11. Inside, behind the face of the dial, place a reservoir, and let the water run down into it through a pipe, and let it have a hole at the bottom. Fastened to it is a bronze drum with an opening through which the water flows into it from the reservoir. Enclosed in this drum there is a smaller one, the two being perfectly jointed together by tenon and socket, in such a way that the smaller drum revolves closely but easily in the larger, like a stopcock.

12. On the lip of the larger drum there are three hundred and sixty-five points, marked off at equal intervals. The rim of the smaller one has a tongue fixed on its circumference, with the tip directed towards those points; and also in this rim is a small opening, through which water runs into the drum and keeps the works going. The figures of the celestial signs being on the lip of the larger drum, and this drum being motionless, let the sign Cancer be drawn at the top, with Capricornus perpendicular to it at the bottom, Libra at the spectator's right, Aries at his left, and let the other signs be given places between them as they are seen in the heavens.

13. Hence, when the sun is in Capricornus, the tongue on the rim touches every day one of the points in Capricornus on the lip of the larger drum, and is perpendicular to the strong pressure of the running water. So the water is quickly driven through the opening in the rim to the inside of the vessel, which, receiving it and soon becoming full, shortens and diminishes the length of the days and hours. But when, owing to the daily revolution of the smaller drum, its tongue reaches the points in Aquarius, the opening will no longer be perpendicular, and the water must give up its vigorous flow and run in a slower stream. Thus, the less the velocity with which the vessel receives the water, the more the length of the days is increased.

14. Then the opening in the rim passes from point to point in Aquarius and Pisces, as though going upstairs, and when it reaches the end of the first eighth of Aries, the fall of the water is of medium strength, indicating the equinoctial hours. From Aries the opening passes, with the revolution of the drum, through Taurus and Gemini to the highest point at the end of the first eighth of Cancer, and when it reaches that point, the power diminishes, and hence, with the slower flow, its delay lengthens the days in the sign Cancer, producing the hours of the summer solstice. From Cancer it begins to decline, and during its return it passes through Leo and Virgo to the points at the end of the first eighth of Libra, gradually shortening and diminishing the length of the hours, until it comes to the points in Libra, where it makes the hours equinoctial once more.

15. Finally, the opening comes down more rapidly through Scorpio and Sagittarius, and on its return from its revolution to the end of the first eighth of Capricornus, the velocity of the stream renews once more the short hours of the winter solstice.

The rules and forms of construction employed in designing dials have now been described as well as I could. It remains to give an account of machines and their principles. In order to make my treatise on architecture complete, I will begin to write on this subject in the following book.



BOOK X



INTRODUCTION

1. In the famous and important Greek city of Ephesus there is said to be an ancient ancestral law, the terms of which are severe, but its justice is not inequitable. When an architect accepts the charge of a public work, he has to promise what the cost of it will be. His estimate is handed to the magistrate, and his property is pledged as security until the work is done. When it is finished, if the outlay agrees with his statement, he is complimented by decrees and marks of honour. If no more than a fourth has to be added to his estimate, it is furnished by the treasury and no penalty is inflicted. But when more than one fourth has to be spent in addition on the work, the money required to finish it is taken from his property.

2. Would to God that this were also a law of the Roman people, not merely for public, but also for private buildings. For the ignorant would no longer run riot with impunity, but men who are well qualified by an exact scientific training would unquestionably adopt the profession of architecture. Gentlemen would not be misled into limitless and prodigal expenditure, even to ejectments from their estates, and the architects themselves could be forced, by fear of the penalty, to be more careful in calculating and stating the limit of expense, so that gentlemen would procure their buildings for that which they had expected, or by adding only a little more. It is true that men who can afford to devote four hundred thousand to a work may hold on, if they have to add another hundred thousand, from the pleasure which the hope of finishing it gives them; but if they are loaded with a fifty per cent increase, or with an even greater expense, they lose hope, sacrifice what they have already spent, and are compelled to leave off, broken in fortune and in spirit.

3. This fault appears not only in the matter of buildings, but also in the shows given by magistrates, whether of gladiators in the forum or of plays on the stage. Here neither delay nor postponement is permissible, but the necessities of the case require that everything should be ready at a fixed time,—the seats for the audience, the awning drawn over them, and whatever, in accordance with the customs of the stage, is provided by machinery to please the eye of the people. These matters require careful thought and planning by a well trained intellect; for none of them can be accomplished without machinery, and without hard study skilfully applied in various ways.

4. Therefore, since such are our traditions and established practices, it is obviously fitting that the plans should be worked out carefully, and with the greatest attention, before the structures are begun. Consequently, as we have no law or customary practice to compel this, and as every year both praetors and aediles have to provide machinery for the festivals, I have thought it not out of place, Emperor, since I have treated of buildings in the earlier books, to set forth and teach in this, which forms the final conclusion of my treatise, the principles which govern machines.



CHAPTER I

MACHINES AND IMPLEMENTS

1. A machine is a combination of timbers fastened together, chiefly efficacious in moving great weights. Such a machine is set in motion on scientific principles in circular rounds, which the Greeks call [Greek: kyklike kineois]. There is, however, a class intended for climbing, termed in Greek [Greek: akrobatikon], another worked by air, which with them is called [Greek: pneumatikon], and a third for hoisting; this the Greeks named [Greek: baroulkos]. In the climbing class are machines so disposed that one can safely climb up high, by means of timbers set up on end and connected by crossbeams, in order to view operations. In the pneumatic class, air is forced by pressure to produce sounds and tones as in an [Greek: organon].

2. In the hoisting class, heavy weights are removed by machines which raise them up and set them in position. The climbing machine displays no scientific principle, but merely a spirit of daring. It is held together by dowels and crossbeams and twisted lashings and supporting props. A machine that gets its motive power by pneumatic pressure will produce pretty effects by scientific refinements. But the hoisting machine has opportunities for usefulness which are greater and full of grandeur, and it is of the highest efficacy when used with intelligence.

3. Some of these act on the principle of the [Greek: mechane], others on that of the [Greek: organon]. The difference between "machines" and "engines" is obviously this, that machines need more workmen and greater power to make them take effect, as for instance ballistae and the beams of presses. Engines, on the other hand, accomplish their purpose at the intelligent touch of a single workman, as the scorpio or anisocycli when they are turned. Therefore engines, as well as machines, are, in principle, practical necessities, without which nothing can be unattended with difficulties.

4. All machinery is derived from nature, and is founded on the teaching and instruction of the revolution of the firmament. Let us but consider the connected revolutions of the sun, the moon, and the five planets, without the revolution of which, due to mechanism, we should not have had the alternation of day and night, nor the ripening of fruits. Thus, when our ancestors had seen that this was so, they took their models from nature, and by imitating them were led on by divine facts, until they perfected the contrivances which are so serviceable in our life. Some things, with a view to greater convenience, they worked out by means of machines and their revolutions, others by means of engines, and so, whatever they found to be useful for investigations, for the arts, and for established practices, they took care to improve step by step on scientific principles.

5. Let us take first a necessary invention, such as clothing, and see how the combination of warp and woof on the loom, which does its work on the principle of an engine, not only protects the body by covering it, but also gives it honourable apparel. We should not have had food in abundance unless yokes and ploughs for oxen, and for all draught animals, had been invented. If there had been no provision of windlasses, pressbeams, and levers for presses, we could not have had the shining oil, nor the fruit of the vine to give us pleasure, and these things could not be transported on land without the invention of the mechanism of carts or waggons, nor on the sea without that of ships.

6. The discovery of the method of testing weights by steelyards and balances saves us from fraud, by introducing honest practices into life. There are also innumerable ways of employing machinery about which it seems unnecessary to speak, since they are at hand every day; such as mills, blacksmiths' bellows, carriages, gigs, turning lathes, and other things which are habitually used as general conveniences. Hence, we shall begin by explaining those that rarely come to hand, so that they may be understood.



CHAPTER II

HOISTING MACHINES

1. First we shall treat of those machines which are of necessity made ready when temples and public buildings are to be constructed. Two timbers are provided, strong enough for the weight of the load. They are fastened together at the upper end by a bolt, then spread apart at the bottom, and so set up, being kept upright by ropes attached at the upper ends and fixed at intervals all round. At the top is fastened a block, which some call a "rechamus." In the block two sheaves are enclosed, turning on axles. The traction rope is carried over the sheave at the top, then let fall and passed round a sheave in a block below. Then it is brought back to a sheave at the bottom of the upper block, and so it goes down to the lower block, where it is fastened through a hole in that block. The other end of the rope is brought back and down between the legs of the machine.

2. Socket-pieces are nailed to the hinder faces of the squared timbers at the point where they are spread apart, and the ends of the windlass are inserted into them so that the axles may turn freely. Close to each end of the windlass are two holes, so adjusted that handspikes can be fitted into them. To the bottom of the lower block are fastened shears made of iron, whose prongs are brought to bear upon the stones, which have holes bored in them. When one end of the rope is fastened to the windlass, and the latter is turned round by working the handspikes, the rope winds round the windlass, gets taut, and thus it raises the load to the proper height and to its place in the work.

3. This kind of machinery, revolving with three sheaves, is called a trispast. When there are two sheaves turning in the block beneath and three in the upper, the machine is termed a pentaspast. But if we have to furnish machines for heavier loads, we must use timbers of greater length and thickness, providing them with correspondingly large bolts at the top, and windlasses turning at the bottom. When these are ready, let forestays be attached and left lying slack in front; let the backstays be carried over the shoulders of the machine to some distance, and, if there is nothing to which they can be fastened, sloping piles should be driven, the ground rammed down all round to fix them firmly, and the ropes made fast to them.

4. A block should then be attached by a stout cord to the top of the machine, and from that point a rope should be carried to a pile, and to a block tied to the pile. Let the rope be put in round the sheave of this block, and brought back to the block that is fastened at the top of the machine. Round its sheave the rope should be passed, and then should go down from the top, and back to the windlass, which is at the bottom of the machine, and there be fastened. The windlass is now to be turned by means of the handspikes, and it will raise the machine of itself without danger. Thus, a machine of the larger kind will be set in position, with its ropes in their places about it, and its stays attached to the piles. Its blocks and traction ropes are arranged as described above.

5. But if the loads of material for the work are still more colossal in size and weight, we shall not entrust them to a windlass, but set in an axle-tree, held by sockets as the windlass was, and carrying on its centre a large drum, which some term a wheel, but the Greeks call it [Greek: amphiesis] or [Greek: perithekion].

6. And the blocks in such machines are not arranged in the same, but in a different manner; for the rows of sheaves in them are doubled, both at the bottom and at the top. The traction rope is passed through a hole in the lower block, in such a way that the two ends of the rope are of equal length when it is stretched out, and both portions are held there at the lower block by a cord which is passed round them and lashed so that they cannot come out either to the right or the left. Then the ends of the rope are brought up into the block at the top from the outside, and passed down over its lower sheaves, and so return to the bottom, and are passed from the inside to the sheaves in the lowest block, and then are brought up on the right and left, and return to the top and round the highest set of sheaves.

7. Passing over these from the outside, they are then carried to the right and left of the drum on the axle-tree, and are tied there so as to stay fast. Then another rope is wound round the drum and carried to a capstan, and when that is turned, it turns the drum and the axle-tree, the ropes get taut as they wind round regularly, and thus they raise the loads smoothly and with no danger. But if a larger drum is placed either in the middle or at one side, without any capstan, men can tread in it and accomplish the work more expeditiously.

8. There is also another kind of machine, ingenious enough and easy to use with speed, but only experts can work with it. It consists of a single timber, which is set up and held in place by stays on four sides. Two cheeks are nailed on below the stays, a block is fastened by ropes above the cheeks, and a straight piece of wood about two feet long, six digits wide, and four digits thick, is put under the block. The blocks used have each three rows of sheaves side by side. Hence three traction ropes are fastened at the top of the machine. Then they are brought to the block at the bottom, and passed from the inside round the sheaves that are nearest the top of it. Then they are brought back to the upper block, and passed inwards from outside round the sheaves nearest the bottom.

9. On coming down to the block at the bottom, they are carried round its second row of sheaves from the inside to the outside, and brought back to the second row at the top, passing round it and returning to the bottom; then from the bottom they are carried to the summit, where they pass round the highest row of sheaves, and then return to the bottom of the machine. At the foot of the machine a third block is attached. The Greeks call it [Greek: epagon], but our people "artemon." This block fastened at the foot of the machine has three sheaves in it, round which the ropes are passed and then delivered to men to pull. Thus, three rows of men, pulling without a capstan, can quickly raise the load to the top.

10. This kind of machine is called a polyspast, because of the many revolving sheaves to which its dexterity and despatch are due. There is also this advantage in the erection of only a single timber, that by previously inclining it to the right or left as much as one wishes, the load can be set down at one side.

All these kinds of machinery described above are, in their principles, suited not only to the purposes mentioned, but also to the loading and unloading of ships, some kinds being set upright, and others placed horizontally on revolving platforms. On the same principle, ships can be hauled ashore by means of arrangements of ropes and blocks used on the ground, without setting up timbers.

11. It may also not be out of place to explain the ingenious procedure of Chersiphron. Desiring to convey the shafts for the temple of Diana at Ephesus from the stone quarries, and not trusting to carts, lest their wheels should be engulfed on account of the great weights of the load and the softness of the roads in the plain, he tried the following plan. Using four-inch timbers, he joined two of them, each as long as the shaft, with two crosspieces set between them, dovetailing all together, and then leaded iron gudgeons shaped like dovetails into the ends of the shafts, as dowels are leaded, and in the woodwork he fixed rings to contain the pivots, and fastened wooden cheeks to the ends. The pivots, being enclosed in the rings, turned freely. So, when yokes of oxen began to draw the four-inch frame, they made the shaft revolve constantly, turning it by means of the pivots and rings.

12. When they had thus transported all the shafts, and it became necessary to transport the architraves, Chersiphron's son Metagenes extended the same principle from the transportation of the shafts to the bringing down of the architraves. He made wheels, each about twelve feet in diameter, and enclosed the ends of the architraves in the wheels. In the ends he fixed pivots and rings in the same way. So when the four-inch frames were drawn by oxen, the wheels turned on the pivots enclosed in the rings, and the architraves, which were enclosed like axles in the wheels, soon reached the building, in the same way as the shafts. The rollers used for smoothing the walks in palaestrae will serve as an example of this method. But it could not have been employed unless the distance had been short; for it is not more than eight miles from the stone-quarries to the temple, and there is no hill, but an uninterrupted plain.

13. In our own times, however, when the pedestal of the colossal Apollo in his temple had cracked with age, they were afraid that the statue would fall and be broken, and so they contracted for the cutting of a pedestal from the same quarries. The contract was taken by one Paconius. This pedestal was twelve feet long, eight feet wide, and six feet high. Paconius, with confident pride, did not transport it by the method of Metagenes, but determined to make a machine of a different sort, though on the same principle.

14. He made wheels of about fifteen feet in diameter, and in these wheels he enclosed the ends of the stone; then he fastened two-inch crossbars from wheel to wheel round the stone, encompassing it, so that there was an interval of not more than one foot between bar and bar. Then he coiled a rope round the bars, yoked up his oxen, and began to draw on the rope. Consequently as it uncoiled, it did indeed cause the wheels to turn, but it could not draw them in a line straight along the road, but kept swerving out to one side. Hence it was necessary to draw the machine back again. Thus, by this drawing to and fro, Paconius got into such financial embarrassment that he became insolvent.

15. I will digress a bit and explain how these stone-quarries were discovered. Pixodorus was a shepherd who lived in that vicinity. When the people of Ephesus were planning to build the temple of Diana in marble, and debating whether to get the marble from Paros, Proconnesus, Heraclea, or Thasos, Pixodorus drove out his sheep and was feeding his flock in that very spot. Then two rams ran at each other, and, each passing the other, one of them, after his charge, struck his horns against a rock, from which a fragment of extremely white colour was dislodged. So it is said that Pixodorus left his sheep in the mountains and ran down to Ephesus carrying the fragment, since that very thing was the question of the moment. Therefore they immediately decreed honours to him and changed his name, so that instead of Pixodorus he should be called Evangelus. And to this day the chief magistrate goes out to that very spot every month and offers sacrifice to him, and if he does not, he is punished.



CHAPTER III

THE ELEMENTS OF MOTION

1. I have briefly set forth what I thought necessary about the principles of hoisting machines. In them two different things, unlike each other, work together, as elements of their motion and power, to produce these effects. One of them is the right line, which the Greeks term [Greek: eutheia]; the other is the circle, which the Greeks call [Greek: kyklote]; but in point of fact, neither rectilinear without circular motion, nor revolutions, without rectilinear motion, can accomplish the raising of loads. I will explain this, so that it may be understood.

2. As centres, axles are inserted into the sheaves, and these are fastened in the blocks; a rope carried over the sheaves, drawn straight down, and fastened to a windlass, causes the load to move upward from its place as the handspikes are turned. The pivots of this windlass, lying as centres in right lines in its socket-pieces, and the handspikes inserted in its holes, make the load rise when the ends of the windlass revolve in a circle like a lathe. Just so, when an iron lever is applied to a weight which a great many hands cannot move, with the fulcrum, which the Greeks call [Greek: hupomochlion], lying as a centre in a right line under the lever, and with the tongue of the lever placed under the weight, one man's strength, bearing down upon the head of it, heaves up the weight.

3. For, as the shorter fore part of the lever goes under the weight from the fulcrum that forms the centre, the head of it, which is farther away from that centre, on being depressed, is made to describe a circular movement, and thus by pressure brings to an equilibrium the weight of a very great load by means of a few hands. Again, if the tongue of an iron lever is placed under a weight, and its head is not pushed down, but, on the contrary, is heaved up, the tongue, supported on the surface of the ground, will treat that as the weight, and the edge of the weight itself as the fulcrum. Thus, not so easily as by pushing down, but by motion in the opposite direction, the weight of the load will nevertheless be raised. If, therefore, the tongue of a lever lying on a fulcrum goes too far under the weight, and its head exerts its pressure too near the centre, it will not be able to elevate the weight, nor can it do so unless, as described above, the length of the lever is brought to equilibrium by the depression of its head.

4. This may be seen from the balances that we call steelyards. When the handle is set as a centre close to the end from which the scale hangs, and the counterpoise is moved along towards the other arm of the beam, shifting from point to point as it goes farther or even reaches the extremity, a small and inferior weight becomes equal to a very heavy object that is being weighed, on account of the equilibrium that is due to the levelling of the beam. Thus, as it withdraws from the centre, a small and comparatively light counterpoise, slowly turning the scale, makes a greater amount of weight rise gently upwards from below.

5. So, too, the pilot of the biggest merchantman, grasping the steering oar by its handle, which the Greeks call [Greek: oiax], and with one hand bringing it to the turning point, according to the rules of his art, by pressure about a centre, can turn the ship, although she may be laden with a very large or even enormous burden of merchandise and provisions. And when her sails are set only halfway up the mast, a ship cannot run quickly; but when the yard is hoisted to the top, she makes much quicker progress, because then the sails get the wind, not when they are too close to the heel of the mast, which represents the centre, but when they have moved farther away from it to the top.

6. As a lever thrust under a weight is harder to manage, and does not put forth its strength, if the pressure is exerted at the centre, but easily raises the weight when the extreme end of it is pushed down, so sails that are only halfway up have less effect, but when they get farther away from the centre, and are hoisted to the very top of the mast, the pressure at the top forces the ship to make greater progress, though the wind is no stronger but just the same. Again, take the case of oars, which are fastened to the tholes by loops,—when they are pushed forward and drawn back by the hand, if the ends of the blades are at some distance from the centre, the oars foam with the waves of the sea and drive the ship forward in a straight line with a mighty impulse, while her prow cuts through the rare water.

7. And when the heaviest burdens are carried on poles by four or six porters at a time, they find the centres of balance at the very middle of the poles, so that, by distributing the dead weight of the burden according to a definitely proportioned division, each labourer may have an equal share to carry on his neck. For the poles, from which the straps for the burden of the four porters hang, are marked off at their centres by nails, to prevent the straps from slipping to one side. If they shift beyond the mark at the centre, they weigh heavily upon the place to which they have come nearer, like the weight of a steelyard when it moves from the point of equilibrium towards the end of the weighing apparatus.

8. In the same way, oxen have an equal draught when their yoke is adjusted at its middle by the yokestrap to the pole. But when their strength is not the same, and the stronger outdoes the other, the strap is shifted so as to make one side of the yoke longer, which helps the weaker ox. Thus, in the case of both poles and yokes, when the straps are not fastened at the middle, but at one side, the farther the strap moves from the middle, the shorter it makes one side, and the longer the other. So, if both ends are carried round in circles, using as a centre the point to which the strap has been brought, the longer end will describe a larger, and the shorter end a smaller circle.

9. Just as smaller wheels move harder and with greater difficulty than larger ones, so, in the case of the poles and yokes, the parts where the interval from centre to end is less, bear down hard upon the neck, but where the distance from the same centre is greater, they ease the burden both for draught and carriage. As in all these cases motion is obtained by means of right lines at the centre and by circles, so also farm waggons, travelling carriages, drums, mills, screws, scorpiones, ballistae, pressbeams, and all other machines, produce the results intended, on the same principles, by turning about a rectilinear axis and by the revolution of a circle.



CHAPTER IV

ENGINES FOR RAISING WATER

1. I shall now explain the making of the different kinds of engines which have been invented for raising water, and will first speak of the tympanum. Although it does not lift the water high, it raises a great quantity very quickly. An axle is fashioned on a lathe or with the compasses, its ends are shod with iron hoops, and it carries round its middle a tympanum made of boards joined together. It rests on posts which have pieces of iron on them under the ends of the axle. In the interior of this tympanum there are eight crosspieces set at intervals, extending from the axle to the circumference of the tympanum, and dividing the space in the tympanum into equal compartments.

2. Planks are nailed round the face of it, leaving six-inch apertures to admit the water. At one side of it there are also holes, like those of a dovecot, next to the axle, one for each compartment. After being smeared with pitch like a ship, the thing is turned by the tread of men, and raising the water by means of the apertures in the face of the tympanum, delivers it through the holes next to the axle into a wooden trough set underneath, with a conduit joined to it. Thus, a large quantity of water is furnished for irrigation in gardens, or for supplying the needs of saltworks.

3. But when it has to be raised higher, the same principle will be modified as follows. A wheel on an axle is to be made, large enough to reach the necessary height. All round the circumference of the wheel there will be cubical boxes, made tight with pitch and wax. So, when the wheel is turned by treading, the boxes, carried up full and again returning to the bottom, will of themselves discharge into the reservoir what they have carried up.

4. But, if it has to be supplied to a place still more high, a double iron chain, which will reach the surface when let down, is passed round the axle of the same wheel, with bronze buckets attached to it, each holding about six pints. The turning of the wheel, winding the chain round the axle, will carry the buckets to the top, and as they pass above the axle they must tip over and deliver into the reservoir what they have carried up.



CHAPTER V

WATER WHEELS AND WATER MILLS

1. Wheels on the principles that have been described above are also constructed in rivers. Round their faces floatboards are fixed, which, on being struck by the current of the river, make the wheel turn as they move, and thus, by raising the water in the boxes and bringing it to the top, they accomplish the necessary work through being turned by the mere impulse of the river, without any treading on the part of workmen.

2. Water mills are turned on the same principle. Everything is the same in them, except that a drum with teeth is fixed into one end of the axle. It is set vertically on its edge, and turns in the same plane with the wheel. Next to this larger drum there is a smaller one, also with teeth, but set horizontally, and this is attached (to the millstone). Thus the teeth of the drum which is fixed to the axle make the teeth of the horizontal drum move, and cause the mill to turn. A hopper, hanging over this contrivance, supplies the mill with corn, and meal is produced by the same revolution.



CHAPTER VI

THE WATER SCREW

1. There is also the method of the screw, which raises a great quantity of water, but does not carry it as high as does the wheel. The method of constructing it is as follows. A beam is selected, the thickness of which in digits is equivalent to its length in feet. This is made perfectly round. The ends are to be divided off on their circumference with the compass into eight parts, by quadrants and octants, and let the lines be so placed that, if the beam is laid in a horizontal position, the lines on the two ends may perfectly correspond with each other, and intervals of the size of one eighth part of the circumference of the beam may be laid off on the length of it. Then, placing the beam in a horizontal position, let perfectly straight lines be drawn from one end to the other. So the intervals will be equal in the directions both of the periphery and of the length. Where the lines are drawn along the length, the cutting circles will make intersections, and definite points at the intersections.



2. When these lines have been correctly drawn, a slender withe of willow, or a straight piece cut from the agnus castus tree, is taken, smeared with liquid pitch, and fastened at the first point of intersection. Then it is carried across obliquely to the succeeding intersections of longitudinal lines and circles, and as it advances, passing each of the points in due order and winding round, it is fastened at each intersection; and so, withdrawing from the first to the eighth point, it reaches and is fastened to the line to which its first part was fastened. Thus, it makes as much progress in its longitudinal advance to the eighth point as in its oblique advance over eight points. In the same manner, withes for the eight divisions of the diameter, fastened obliquely at the intersections on the entire longitudinal and peripheral surface, make spiral channels which naturally look just like those of a snail shell.

3. Other withes are fastened on the line of the first, and on these still others, all smeared with liquid pitch, and built up until the total diameter is equal to one eighth of the length. These are covered and surrounded with boards, fastened on to protect the spiral. Then these boards are soaked with pitch, and bound together with strips of iron, so that they may not be separated by the pressure of the water. The ends of the shaft are covered with iron. To the right and left of the screw are beams, with crosspieces fastening them together at both ends. In these crosspieces are holes sheathed with iron, and into them pivots are introduced, and thus the screw is turned by the treading of men.

4. It is to be set up at an inclination corresponding to that which is produced in drawing the Pythagorean right-angled triangle: that is, let its length be divided into five parts; let three of them denote the height of the head of the screw; thus the distance from the base of the perpendicular to the nozzle of the screw at the bottom will be equal to four of those parts. A figure showing how this ought to be, has been drawn at the end of the book, right on the back.

I have now described as clearly as I could, to make them better known, the principles on which wooden engines for raising water are constructed, and how they get their motion so that they may be of unlimited usefulness through their revolutions.



CHAPTER VII

THE PUMP OF CTESIBIUS

1. Next I must tell about the machine of Ctesibius, which raises water to a height. It is made of bronze, and has at the bottom a pair of cylinders set a little way apart, and there is a pipe connected with each, the two running up, like the prongs of a fork, side by side to a vessel which is between the cylinders. In this vessel are valves, accurately fitting over the upper vents of the pipes, which stop up the ventholes, and keep what has been forced by pressure into the vessel from going down again.

2. Over the vessel a cowl is adjusted, like an inverted funnel, and fastened to the vessel by means of a wedge thrust through a staple, to prevent it from being lifted off by the pressure of the water that is forced in. On top of this a pipe is jointed, called the trumpet, which stands up vertically. Valves are inserted in the cylinders, beneath the lower vents of the pipes, and over the openings which are in the bottoms of the cylinders.

3. Pistons smoothly turned, rubbed with oil, and inserted from above into the cylinders, work with their rods and levers upon the air and water in the cylinders, and, as the valves stop up the openings, force and drive the water, by repeated pressure and expansion, through the vents of the pipes into the vessel, from which the cowl receives the inflated currents, and sends them up through the pipe at the top; and so water can be supplied for a fountain from a reservoir at a lower level.

4. This, however, is not the only apparatus which Ctesibius is said to have thought out, but many more of various kinds are shown by him to produce effects, borrowed from nature, by means of water pressure and compression of the air; as, for example, blackbirds singing by means of waterworks, and "angobatae," and figures that drink and move, and other things that are found to be pleasing to the eye and the ear.

5. Of these I have selected what I considered most useful and necessary, and have thought it best to speak in the preceding book about timepieces, and in this about the methods of raising water. The rest, which are not subservient to our needs, but to pleasure and amusement, may be found in the commentaries of Ctesibius himself by any who are interested in such refinements.



CHAPTER VIII

THE WATER ORGAN

1. With regard to water organs, however, I shall not fail with all possible brevity and precision to touch upon their principles, and to give a sufficient description of them. A wooden base is constructed, and on it is set an altar-shaped box made of bronze. Uprights, fastened together like ladders, are set up on the base, to the right and to the left (of the altar). They hold the bronze pump-cylinders, the moveable bottoms of which, carefully turned on a lathe, have iron elbows fastened to their centres and jointed to levers, and are wrapped in fleeces of wool. In the tops of the cylinders are openings, each about three digits in diameter. Close to these openings are bronze dolphins, mounted on joints and holding chains in their mouths, from which hang cymbal-shaped valves, let down under the openings in the cylinders.

2. Inside the altar, which holds the water, is a regulator shaped like an inverted funnel, under which there are cubes, each about three digits high, keeping a free space below between the lips of the regulator and the bottom of the altar. Tightly fixed on the neck of the regulator is the windchest, which supports the principal part of the contrivance, called in Greek the [Greek: kanon mousikos]. Running longitudinally, there are four channels in it if it is a tetrachord; six, if it is a hexachord; eight, if it is an octachord.

3. Each of the channels has a cock in it, furnished with an iron handle. These handles, when turned, open ventholes from the windchest into the channels. From the channels to the canon there are vertical openings corresponding to ventholes in a board above, which board is termed [Greek: pinax] in Greek. Between this board and the canon are inserted sliders, pierced with holes to correspond, and rubbed with oil so that they can be easily moved and slid back into place again. They close the above-mentioned openings, and are called the plinths. Their going and coming now closes and now opens the holes.

4. These sliders have iron jacks fixed to them, and connected with the keys, and the keys, when touched, make the sliders move regularly. To the upper surface of the openings in the board, where the wind finds egress from the channels, rings are soldered, and into them the reeds of all the organ pipes are inserted. From the cylinders there are connecting pipes attached to the neck of the regulator, and directed towards the ventholes in the windchest. In the pipes are valves, turned on a lathe, and set (where the pipes are connected with the cylinders). When the windchest has received the air, these valves will stop up the openings, and prevent the wind from coming back again.

5. So, when the levers are raised, the elbows draw down the bottoms of the cylinders as far as they can go; and the dolphins, which are mounted on joints, let the cymbals fall into the cylinders, thus filling the interiors with air. Then the elbows, raising the bottoms within the cylinders by repeated and violent blows, and stopping the openings above by means of the cymbals, compress the air which is enclosed in the cylinders, and force it into the pipes, through which it runs into the regulator, and through its neck into the windchest. With a stronger motion of the levers, the air is still more compressed, streams through the apertures of the cocks, and fills the channels with wind.

6. So, when the keys, touched by the hand, drive the sliders forward and draw them back regularly, alternately stopping and opening the holes, they produce resonant sounds in a great variety of melodies conforming to the laws of music.

With my best efforts I have striven to set forth an obscure subject clearly in writing, but the theory of it is not easy, nor readily understood by all, save only those who have had some practice in things of this kind. If anybody has failed to understand it, he will certainly find, when he comes to know the thing itself, that it is carefully and exquisitely contrived in all respects.



CHAPTER IX

THE HODOMETER

1. The drift of our treatise now turns to a useful invention of the greatest ingenuity, transmitted by our predecessors, which enables us, while sitting in a carriage on the road or sailing by sea, to know how many miles of a journey we have accomplished. This will be possible as follows. Let the wheels of the carriage be each four feet in diameter, so that if a wheel has a mark made upon it, and begins to move forward from that mark in making its revolution on the surface of the road, it will have covered the definite distance of twelve and a half feet on reaching that mark at which it began to revolve.

2. Having provided such wheels, let a drum with a single tooth projecting beyond the face of its circumference be firmly fastened to the inner side of the hub of the wheel. Then, above this, let a case be firmly fastened to the body of the carriage, containing a revolving drum set on edge and mounted on an axle; on the face of the drum there are four hundred teeth, placed at equal intervals, and engaging the tooth of the drum below. The upper drum has, moreover, one tooth fixed to its side and standing out farther than the other teeth.

3. Then, above, let there be a horizontal drum, similarly toothed and contained in another case, with its teeth engaging the tooth fixed to the side of the second drum, and let as many holes be made in this (third) drum as will correspond to the number of miles—more or less, it does not matter—that a carriage can go in a day's journey. Let a small round stone be placed in every one of these holes, and in the receptacle or case containing that drum let one hole be made, with a small pipe attached, through which, when they reach that point, the stones placed in the drum may fall one by one into a bronze vessel set underneath in the body, of the carriage.

4. Thus, as the wheel in going forward carries with it the lowest drum, and as the tooth of this at every revolution strikes against the teeth of the upper drum, and makes it move along, the result will be that the upper drum is carried round once for every four hundred revolutions of the lowest, and that the tooth fixed to its side pushes forward one tooth of the horizontal drum. Since, therefore, with four hundred revolutions of the lowest drum, the upper will revolve once, the progress made will be a distance of five thousand feet or one mile. Hence, every stone, making a ringing sound as it falls, will give warning that we have gone one mile. The number of stones gathered from beneath and counted, will show the number of miles in the day's journey.

5. On board ship, also, the same principles may be employed with a few changes. An axle is passed through the sides of the ship, with its ends projecting, and wheels are mounted on them, four feet in diameter, with projecting floatboards fastened round their faces and striking the water. The middle of the axle in the middle of the ship carries a drum with one tooth projecting beyond its circumference. Here a case is placed containing a drum with four hundred teeth at regular intervals, engaging the tooth of the drum that is mounted on the axle, and having also one other tooth fixed to its side and projecting beyond its circumference.

6. Above, in another case fastened to the former, is a horizontal drum toothed in the same way, and with its teeth engaging the tooth fixed to the side of the drum that is set on edge, so that one of the teeth of the horizontal drum is struck at each revolution of that tooth, and the horizontal drum is thus made to revolve in a circle. Let holes be made in the horizontal drum, in which holes small round stones are to be placed. In the receptacle or case containing that drum, let one hole be opened with a small pipe attached, through which a stone, as soon as the obstruction is removed, falls with a ringing sound into a bronze vessel.

7. So, when a ship is making headway, whether under oars or under a gale of wind, the floatboards on the wheels will strike against the water and be driven violently back, thus turning the wheels; and they, revolving, will move the axle, and the axle the drum, the tooth of which, as it goes round, strikes one of the teeth of the second drum at each revolution, and makes it turn a little. So, when the floatboards have caused the wheels to revolve four hundred times, this drum, having turned round once, will strike a tooth of the horizontal drum with the tooth that is fixed to its side. Hence, every time the turning of the horizontal drum brings a stone to a hole, it will let the stone out through the pipe. Thus by the sound and the number, the length of the voyage will be shown in miles.

I have described how to make things that may be provided for use and amusement in times that are peaceful and without fear.



CHAPTER X

CATAPULTS OR SCORPIONES

1. I shall next explain the symmetrical principles on which scorpiones and ballistae may be constructed, inventions devised for defence against danger, and in the interest of self-preservation.

The proportions of these engines are all computed from the given length of the arrow which the engine is intended to throw, and the size of the holes in the capitals, through which the twisted sinews that hold the arms are stretched, is one ninth of that length.

2. The height and breadth of the capital itself must then conform to the size of the holes. The boards at the top and bottom of the capital, which are called "peritreti," should be in thickness equal to one hole, and in breadth to one and three quarters, except at their extremities, where they equal one hole and a half. The sideposts on the right and left should be four holes high, excluding the tenons, and five twelfths of a hole thick; the tenons, half a hole. The distance from a sidepost to the hole is one quarter of a hole, and it is also one quarter of a hole from the hole to the post in the middle. The breadth of the post in the middle is equal to one hole and one eighth, the thickness, to one hole.

3. The opening in the middle post, where the arrow is laid, is equal to one fourth of the hole. The four surrounding corners should have iron plates nailed to their sides and faces, or should be studded with bronze pins and nails. The pipe, called [Greek: syrigx] in Greek, has a length of nineteen holes. The strips, which some term cheeks, nailed at the right and left of the pipe, have a length of nineteen holes and a height and thickness of one hole. Two other strips, enclosing the windlass, are nailed on to these, three holes long and half a hole in breadth. The cheek nailed on to them, named the "bench," or by some the "box," and made fast by means of dove-tailed tenons, is one hole thick and seven twelfths of a hole in height. The length of the windlass is equal to...[12] holes, the thickness of the windlass to three quarters of a hole.

[Note 12: The dots here and in what follows, indicate lacunae in the manuscripts.]

4. The latch is seven twelfths of a hole in length and one quarter in thickness. So also its socket-piece. The trigger or handle is three holes in length and three quarters of a hole in breadth and thickness. The trough in the pipe is sixteen holes in length, one quarter of a hole in thickness, and three quarters in height. The base of the standard on the ground is equal to eight holes; the breadth of the standard where it is fastened into the plinth is three quarters of a hole, its thickness two thirds of a hole; the height of the standard up to the tenon is twelve holes, its breadth three quarters of a hole, and its thickness two thirds. It has three struts, each nine holes in length, half a hole in breadth, and five twelfths in thickness. The tenon is one hole in length, and the head of the standard one hole and a half in length.

5. The antefix has the breadth of a hole and one eighth, and the thickness of one hole. The smaller support, which is behind, termed in Greek [Greek: antibasis], is eight holes long, three quarters of a hole broad, and two thirds thick. Its prop is twelve holes long, and has the same breadth and thickness as the smaller support just mentioned. Above the smaller support is its socket-piece, or what is called the cushion, two and a half holes long, one and a half high, and three quarters of a hole broad. The windlass cup is two and seven twelfths holes long, two thirds of a hole thick, and three quarters broad. The crosspieces with their tenons have the length of... holes, the breadth of three quarters, and the thickness of two thirds of a hole. The length of an arm is seven holes, its thickness at its base two thirds of a hole, and at its end one half a hole; its curvature is equal to two thirds of a hole.

6. These engines are constructed according to these proportions or with additions or diminutions. For, if the height of the capitals is greater than their width—when they are called "high-tensioned,"—something should be taken from the arms, so that the more the tension is weakened by height of the capitals, the more the strength of the blow is increased by shortness of the arms. But if the capital is less high,—when the term "low-tensioned" is used,—the arms, on account of their strength, should be made a little longer, so that they may be drawn easily. Just as it takes four men to raise a load with a lever five feet long, and only two men to lift the same load with a ten-foot lever, so the longer the arms, the easier they are to draw, and the shorter, the harder.

I have now spoken of the principles applicable to the parts and proportions of catapults.



CHAPTER XI

BALLISTAE

1. Ballistae are constructed on varying principles to produce an identical result. Some are worked by handspikes and windlasses, some by blocks and pulleys, others by capstans, others again by means of drums. No ballista, however, is made without regard to the given amount of weight of the stone which the engine is intended to throw. Hence their principle is not easy for everybody, but only for those who have knowledge of the geometrical principles employed in calculation and in multiplication.

2. For the holes made in the capitals through the openings of which are stretched the strings made of twisted hair, generally women's, or of sinew, are proportionate to the amount of weight in the stone which the ballista is intended to throw, and to the principle of mass, as in catapults the principle is that of the length of the arrow. Therefore, in order that those who do not understand geometry may be prepared beforehand, so as not to be delayed by having to think the matter out at a moment of peril in war, I will set forth what I myself know by experience can be depended upon, and what I have in part gathered from the rules of my teachers, and wherever Greek weights bear a relation to the measures, I shall reduce and explain them so that they will express the same corresponding relation in our weights.

3. A ballista intended to throw a two-pound stone will have a hole of five digits in its capital; four pounds, six digits; and six pounds, seven digits; ten pounds, eight digits; twenty pounds, ten digits; forty pounds, twelve and a half digits; sixty pounds, thirteen and a half digits; eighty pounds, fifteen and three quarters digits; one hundred pounds, one foot and one and a half digits; one hundred and twenty pounds, one foot and two digits; one hundred and forty pounds, one foot and three digits; one hundred and sixty pounds, one foot and a quarter; one hundred and eighty pounds, one foot and five digits; two hundred pounds, one foot and six digits; two hundred and forty pounds, one foot and seven digits; two hundred and eighty pounds, one foot and a half; three hundred and twenty pounds, one foot and nine digits; three hundred and sixty pounds, one foot and ten digits.

4. Having determined the size of the hole, design the "scutula," termed in Greek [Greek: peritretos],... holes in length and two and one sixth in breadth. Bisect it by a line drawn diagonally from the angles, and after this bisecting bring together the outlines of the figure so that it may present a rhomboidal design, reducing it by one sixth of its length and one fourth of its breadth at the (obtuse) angles. In the part composed by the curvatures into which the points of the angles run out, let the holes be situated, and let the breadth be reduced by one sixth; moreover, let the hole be longer than it is broad by the thickness of the bolt. After designing the scutula, let its outline be worked down to give it a gentle curvature.

5. It should be given the thickness of seven twelfths of a hole. The boxes are two holes (in height), one and three quarters in breadth, two thirds of a hole in thickness except the part that is inserted in the hole, and at the top one third of a hole in breadth. The sideposts are five holes and two thirds in length, their curvature half a hole, and their thickness thirty-seven forty-eighths of a hole. In the middle their breadth is increased as much as it was near the hole in the design, by the breadth and thickness of... hole; the height by one fourth of a hole.

6. The (inner) strip on the "table" has a length of eight holes, a breadth and thickness of half a hole. Its tenons are one hole and one sixth long, and one quarter of a hole in thickness. The curvature of this strip is three quarters of a hole. The outer strip has the same breadth and thickness (as the inner), but the length is given by the obtuse angle of the design and the breadth of the sidepost at its curvature. The upper strips are to be equal to the lower; the crosspieces of the "table," one half of a hole.

7. The shafts of the "ladder" are thirteen holes in length, one hole in thickness; the space between them is one hole and a quarter in breadth, and one and one eighth in depth. Let the entire length of the ladder on its upper surface—which is the one adjoining the arms and fastened to the table—be divided into five parts. Of these let two parts be given to the member which the Greeks call the [Greek: chelonion], its breadth being one and one sixth, its thickness one quarter, and its length eleven holes and one half; the claw projects half a hole and the "winging" three sixteenths of a hole. What is at the axis which is termed the... face... the crosspieces of three holes?

8. The breadth of the inner slips is one quarter of a hole; their thickness one sixth. The cover-joint or lid of the chelonium is dove-tailed into the shafts of the ladder, and is three sixteenths of a hole in breadth and one twelfth in thickness. The thickness of the square piece on the ladder is three sixteenths of a hole,... the diameter of the round axle will be equal to that of the claw, but at the pivots seven sixteenths of a hole.

9. The stays are... holes in length, one quarter of a hole in breadth at the bottom, and one sixth in thickness at the top. The base, termed [Greek: eschara], has the length of... holes, and the anti-base of four holes; each is one hole in thickness and breadth. A supporter is jointed on, halfway up, one and one half holes in breadth and thickness. Its height bears no relation to the hole, but will be such as to be serviceable. The length of an arm is six holes, its thickness at the base two thirds of a hole, and at the end one half a hole.

I have now given those symmetrical proportions of ballistae and catapults which I thought most useful. But I shall not omit, so far as I can express it in writing, the method of stretching and tuning their strings of twisted sinew or hair.



CHAPTER XII

THE STRINGING AND TUNING OF CATAPULTS

1. Beams of very generous length are selected, and upon them are nailed socket-pieces in which windlasses are inserted. Midway along their length the beams are incised and cut away to form framings, and in these cuttings the capitals of the catapults are inserted, and prevented by wedges from moving when the stretching is going on. Then the bronze boxes are inserted into the capitals, and the little iron bolts, which the Greeks call [Greek: epizygides], are put in their places in the boxes.

2. Next, the loops of the strings are put through the holes in the capitals, and passed through to the other side; next, they are put upon the windlasses, and wound round them in order that the strings, stretched out taut on them by means of the handspikes, on being struck by the hand, may respond with the same sound on both sides. Then they are wedged tightly into the holes so that they cannot slacken. So, in the same manner, they are passed through to the other side, and stretched taut on the windlasses by means of the handspikes until they give the same sound. Thus with tight wedging, catapults are tuned to the proper pitch by musical sense of hearing.

On these things I have said what I could. There is left for me, in the matter of sieges, to explain how generals can win victories and cities be defended, by means of machinery.



CHAPTER XIII

SIEGE MACHINES

1. It is related that the battering ram for sieges was originally invented as follows. The Carthaginians pitched their camp for the siege of Cadiz. They captured an outwork and attempted to destroy it. But having no iron implements for its destruction, they took a beam, and, raising it with their hands, and driving the end of it repeatedly against the top of the wall, they threw down the top courses of stones, and thus, step by step in regular order, they demolished the entire redoubt.

2. Afterwards a carpenter from Tyre, Bright by name and by nature, was led by this invention into setting up a mast from which he hung another crosswise like a steelyard, and so, by swinging it vigorously to and fro, he threw down the wall of Cadiz. Geras of Chalcedon was the first to make a wooden platform with wheels under it, upon which he constructed a framework of uprights and crosspieces, and within it he hung the ram, and covered it with oxhide for the better protection of the men who were stationed in the machine to batter the wall. As the machine made but slow progress, he first gave it the name of the tortoise of the ram.

3. These were the first steps then taken towards that kind of machinery, but afterwards, when Philip, the son of Amyntas, was besieging Byzantium, it was developed in many varieties and made handier by Polyidus the Thessalian. His pupils were Diades and Charias, who served with Alexander. Diades shows in his writings that he invented moveable towers, which he used also to take apart and carry round with the army, and likewise the borer, and the scaling machine, by means of which one can cross over to the wall on a level with the top of it, as well as the destroyer called the raven, or by others the crane.

4. He also employed the ram mounted on wheels, an account of which he left in his writings. As for the tower, he says that the smallest should be not less than sixty cubits in height and seventeen in breadth, but diminishing to one fifth less at the top; the uprights for the tower being nine inches at the bottom and half a foot at the top. Such a tower, he says, ought to be ten stories high, with windows in it on all sides.

5. His larger tower, he adds, was one hundred and twenty cubits high and twenty-three and one half cubits broad, diminishing like the other to one fifth less; the uprights, one foot at the bottom and six digits at the top. He made this large tower twenty stories high, each story having a gallery round it, three cubits wide. He covered the towers with rawhide to protect them from any kind of missile.

6. The tortoise of the battering ram was constructed in the same way. It had, however, a base of thirty cubits square, and a height, excluding the pediment, of thirteen cubits; the height of the pediment from its bed to its top was seven cubits. Issuing up and above the middle of the roof for not less than two cubits was a gable, and on this was reared a small tower four stories high, in which, on the top floor, scorpiones and catapults were set up, and on the lower floors a great quantity of water was stored, to put out any fire that might be thrown on the tortoise. Inside of this was set the machinery of the ram, termed in Greek [Greek: kriodoche], in which was placed a roller, turned on a lathe, and the ram, being set on top of this, produced its great effects when swung to and fro by means of ropes. It was protected, like the tower, with rawhide.

7. He explained the principles of the borer as follows: that the machine itself resembled the tortoise, but that in the middle it had a pipe lying between upright walls, like the pipe usually found in catapults and ballistae, fifty cubits in length and one cubit in height, in which a windlass was set transversely. On the right and left, at the end of the pipe, were two blocks, by means of which the iron-pointed beam, which lay in the pipe, was moved. There were numerous rollers enclosed in the pipe itself under the beam, which made its movements quicker and stronger. Numerous arches were erected along the pipe above the beam which was in it, to hold up the rawhide in which this machine was enveloped.

8. He thought it needless to write about the raven, because he saw that the machine was of no value. With regard to the scaling machine, termed in Greek [Greek: epibathra], and the naval contrivances which, as he wrote, could be used in boarding ships, I have observed that he merely promised with some earnestness to explain their principles, but that he has not done so.

I have set forth what was written by Diades on machines and their construction. I shall now set forth the methods which I have learned from my teachers, and which I myself believe to be useful.



CHAPTER XIV

THE TORTOISE

1. A tortoise intended for the filling of ditches, and thereby to make it possible to reach the wall, is to be made as follows. Let a base, termed in Greek [Greek: eschara], be constructed, with each of its sides twenty-one feet long, and with four crosspieces. Let these be held together by two others, two thirds of a foot thick and half a foot broad; let the crosspieces be about three feet and a half apart, and beneath and in the spaces between them set the trees, termed in Greek [Greek: hamaxopodes], in which the axles of the wheels turn in iron hoops. Let the trees be provided with pivots, and also with holes through which levers are passed to make them turn, so that the tortoise can move forward or back or towards its right or left side, or if necessary obliquely, all by the turning of the trees.

2. Let two beams be laid on the base, projecting for six feet on each side, round the projections of which let two other beams be nailed, projecting seven feet beyond the former, and of the thickness and breadth prescribed in the case of the base. On this framework set up posts mortised into it, nine feet high exclusive of their tenons, one foot and a quarter square, and one foot and a half apart. Let the posts be tied together at the top by mortised beams. Over the beams let the rafters be set, tied one into another by means of tenons, and carried up twelve feet high. Over the rafters set the square beam by which the rafters are bound together.