On Architecture

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

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.

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

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.

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

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

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.

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