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 ash.o.r.e 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, encompa.s.sing 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 embarra.s.sment 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 pa.s.sing 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 windla.s.s, causes the load to move upward from its place as the handspikes are turned. The pivots of this windla.s.s, 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 windla.s.s 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 quant.i.ty very quickly. An axle is fashioned on a lathe or with the compa.s.ses, 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 circ.u.mference of the tympanum, and dividing the s.p.a.ce 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 quant.i.ty 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 circ.u.mference 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 pa.s.sed 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 pa.s.s 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 quant.i.ty 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 circ.u.mference with the compa.s.s 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 circ.u.mference 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.

[Ill.u.s.tration: CONSTRUCTION OF THE WATER SCREW]

[Ill.u.s.tration: THE WATER SCREW

(From the edition of Vitruvius by Fra Giocondo, Venice, 1511)]

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, pa.s.sing 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 sh.e.l.l.

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