3I have briefly explained the principles of machines of draught, in which, as the powers and nature of the motion are different, so they generate two effects, one direct, which the Greeks call εὐθεῖα, the other circular, which they call κυκλωτὴ; but it must be confessed, that rectilinear without circular motion, and, on the other hand, circular without rectilinear motion can neither without the other be of much assistance in raising weights.
2I will proceed to the explanation of this. The pulleys revolve on axles which go across the blocks, and are acted upon by straight ropes which coil round the axle of the windlass when that is put in motion by the levers, thus causing the weight to ascend. The pivots of the windlass axle are received into, or play in the gudgeons of the cheeks, and the levers being inserted in the holes provided for them in the axle, are moved in a circular direction, and thus cause the ascent of the weight. Thus also, an iron lever being applied to a weight which many hands could not remove; if a fulcrum, which the Greeks call ὑπομόχλιον, be placed under it, and the tongue of the lever be under the weight, one man’s strength at the end will raise the weight.
3This is accounted for by the fore part of the lever being under the weight, and at a shorter distance from the fulcrum or centre of motion; whilst the longest part, which is from the centre of motion to the head being brought into circular motion, the application of few hands to it will raise a great weight. So if the tongue of the lever be placed under the weight, and instead of the end being pressed downward it be lifted up, the tongue then having the ground for a fulcrum, will act on that as in the first instance it did on the weight, and the tongue will press against the side thereof as it did on the fulcrum: though by this means the weight will not be so easily raised, yet it may be thus moved. If the tongue of the lever lying on the fulcrum be placed too far under the weight, and the end be too near the centre of pressure, it will be without effect; so, as hath been already mentioned, will it be, unless the distance from the fulcrum to the end of the lever be greater than from the fulcrum to the tongue thereof.
4Any one will perceive the application of this principle in the instruments called steelyards (stateræ); for when the handle of suspension, on which as a centre the beam turns, is placed nearer the end from which the scale hangs, and, on the other side of the centre, the weight be shifted to the different divisions on the beam, the further it is from the centre, the greater will be the load in the scale which it is capable of raising, and that through the equilibration of the beam. Thus, a small weight, which, placed near the centre, would have but a feeble effect, may in a moment acquire power, and raise with ease a very heavy load.
5Thus also the steersman of a merchant ship, holding the tiller which the Greeks call οἴαξ with only one hand, by the situation of the centre moves it in a moment as the nature of the case requires, and turns the ship though ever so deeply laden. The sails also, if only half mast high, will cause the vessel to sail slower than when the yards are hoisted up to the top of the mast, because not then being near the foot of the mast, which is as it were the centre, but at a distance therefrom, they are acted on by the wind with greater force.
6For as, if the fulcrum be placed under the middle of a lever, it is but with difficulty that the weight is moved, and that only when the power is applied at the extremity of the lever, so when the sails are no higher than the middle of the mast, they have less effect on the motion of the vessel: when, however, raised to the top of the mast, the impulse they receive from an equal wind higher up, causes a quicker motion in the ship. For the same reason the oars, which are made fast with rope to the thowls, when plunged into the water and drawn back by the hand, impel the vessel with great force, and cause the prow thereof to cleave the waves, if their blades are at a considerable distance from the centre, which is the thowl.
7Also, when loads of great weight are carried by porters in gangs of four or six, the levers are so adjusted in the middle that each porter may be loaded with a proper proportion of the burden. The middle parts of the levers for four persons over which the tackle passes, are provided with pins to prevent it sliding out of its place, for if it shift from the centre, the weight will press more on the shoulders of him to whom it is nearest, just as in the steelyard the weight is shifted towards the end of the beam.
8Thus also oxen have an equal draft when the piece which suspends the pole hangs exactly from the middle of the yoke. But when oxen are not equally strong, the method of apportioning to each his due labour is by shifting the suspending piece so that one side of the yoke shall be longer than the other, and thus relieve the weaker animal. It is the same in the porters’ levers as in yokes, when the suspending tackle is not in the centre, and one arm of the lever is longer than the other, namely that towards which the tackle has shifted; for in this case if the lever turn upon the points to which the tackle has slid, which now becomes its centre, the longer arm will describe a portion of a larger circle, and the shorter a smaller circle.
9Now as small wheels revolve with more difficulty than larger ones, so levers and yokes press most on the side which is the least distance from the fulcrum, and on the contrary they ease those who bear that arm which is at the greatest distance from the fulcrum. Inasmuch as all these machines regulate either rectilinear or circular motion by means of the centre or fulcrum, so also waggons, chariots, drumwheels, wheels of carriages, screws, scorpions, balistæ, presses, and other instruments, for the same reasons produce their effects by means of rectilinear and circular motions.