a brief description of this may suffice, as preparatory to the account of a machine made in imitation of it, but more ingenious and more perfect.

The tympanum is a great hollow wheel, forming a kind of barrel or drum (as its name imports), composed of several planks joined together, well calked and pitched, and having a horizontal axle on which it turns: the interior of this drum is divided into 3 equal spaces by as many partitions placed in the directions of the radii; each space or cell has an orifice of about half a foot in the rim of the drum or wheel, so shaped as to facilitate the admission of the water: moreover, there are 8 hollow channels running contiguous to each other and parallel to the axle of the wheel, each corresponding to one of the 8 large cells; into these channels the water passes out of the cells just mentioned, and, after running along the channels to a convenient distance, it escapes through orifices into a reservoir placed just under the axle. Thus the water is elevated through a vertical space equal to the radius of the hollow wheel. When the tympanum is used to raise water from a running stream, it is moved by means of float boards which are impelled by the stream: but when it is employed to raise stagnant water, there is commonly a smaller wheel on the same shaft, which is turned by men walking in it, as in the old walking crane. The chief defect of this machine is that it raises the water in the most disadvantageous situation possible for the load being found always toward the extremity of a radius of the wheel, the arm of the effective lever which answers to it increases through the whole quadrant the water describes in passing from the bottom of the wheel to the altitude of its centre; so that the power must act in like manner as if it were applied at a winch handle, and cannot, therefore, act uniformly.

2. To remedy this defect M. de la Faye devised a machine which may here be described, together with the process of reasoning that led to it.

When we develope the circumference of a circle, a curve is described (i. e. the involute) of which all the radii are so many tangents to the circle, and are likewise all respectively perpendicular to the several points of the curve described, which has for its greatest radius a line equal to the periphery of the circle evolved. The truth of which is shewn by geometricians when treating of the genesis of evolute and involute curves.

Hence, having an axle whose circumference a little exceeds the height which the water is proposed to be elevated, let the circumference of the axle be evolved, and make a curved canal whose curvature shall coincide throughout exactly with that of the involute just formed: if the further extremity of this canal

be made to enter the water that is to be elevated, and the other extremity abut upon the shaft which is turned; then in the course of the rotation the water will rise in a vertical direction, tangential to the shaft, and perpendicular to the canal in whatever position it may be. Thus the action of the weight answering always to the extremity of a horizontal radius will be as though it acted upon the invariable arm of a lever, and the power which raises the weight will be always the same: and if the radius of the wheel, of which this hollow canal serves as a bent spoke, is equal to the height that the water is to be raised, and consequently equal to the circumference of the axle or shaft, the power will be to the load of water reciprocally as the radius of a circle to its circumference, or directly as 1 to 64 nearly.

In M. de la Faye's opinion, the machine ought to be composed of four of these canals: but it has often been constructed with 8, as represented in fig. 1. pl. XIX. The wheel being turned by the impulsion of the stream upon the float-boards, the orifices F, E, D, c, &c. of the curvilinear canals, dip one after another into the water which runs into them; and as the wheel revolves the fluid rises in the canals f, e, d, e, &c. and runs out in a stream › from the holes at o; it is received into the trough Q, and conveyed from thence by pipes.

By this construction the weight to be raised offers always the same resistance, and that the least possible, while the power is applied in the most advantageous manner the circumstances will admit of these conditions both fulfilled at the same time furnish the most desirable perfection in a machine. Further, this machine raises the water by the shortest way, namely, the perpendicular, or vertical; in this respect being preferable to Archimedes's screw, where the water is carried up an inclined path and besides this, each curved channel in this wheel empties all the water it receives in every revolution, while the screw of Archimedes delivers only a small portion of the fluid it is charged with, being often loaded with 20 times as much water as is discharged in one rotation; and thus requiring an enormous increase of labour when a large quantity is intended to be raised by it.

The nature and advantages of this wheel evince very forcibly how far the speculations of geometers are from being so unfruitful in useful applications, as is often insinuated by practical

men.

3. The wheel just described would we think be the most perfect of any that could be employed for raising water, had it not the disadvantage attending the tympanum, which is, that it can only raise water to the height of its semidiameter. As in many

cases water is to be raised higher than the radius of any wheel can well be made for practice, we shall next describe a machine called the Noria, common in Spain, which raises water nearly through a diameter. This Noria consists of a vertical wheel of 20 feet diameter, on the circumference of which are fixed a number of little boxes or square buckets, for the purpose of raising the water out of the well, communicating with the canal below, and to empty it in a reservoir above, placed by the side of the wheel. The buckets have a lateral orifice, to receive and to discharge the water. The axis of this wheel is embraced by four small beams, crossing each other at right angles, tapering at the extremities, and forming eight little arms. This wheel is near the centre of the horse-walk, contiguous to the vertical axis, into the top of which the horse-beam is fixed; but near the bottom it is embraced by four little beams, forming eight arms, similar to those above described, on the axis of the water-wheel. As the mule which they use goes round, these horizontal arms, supplying the place of cogs, take hold, each in succession, of those arms which are fixed on the axis of the water-wheel, and keep it in rotation.

This machine, than which nothing can be cheaper, throws up a great quantity of water; yet undoubtedly it has two defects; the first is, that part of the water runs out of the buckets and falls back into the well after it has been raised nearly to the level of the reservoir: the second is, that a considerable proportion of the water to be discharged is raised higher than the reservoir, and falls into it only at the moment when the bucket is at the highest point of the circle, and ready to descend. These inconveniences are both remedied by the contrivance mentioned in the next paragraph.

4. The Persian wheel is a name given to a machine for raising water, which may be turned by means of a stream AB acting upon the wheel CDE according to the order of the letters; (fig. 1. pl. XIX.) The buckets a, a, a, a, &c. instead of being firmly fastened, are hung upon the wheel by strong pins, b, b, b, b, &c. fixed in the side of the rim; which must be made as high as the water is intended to be raised above the level of that part of the stream in which the wheel is placed. As the wheel turns, the buckets on the right hand go down into the water, where they are filled, and return up full on the left hand, till they come to the top at K; where they strike against the end n of the fixed trough M, by which they are overset, and so empty the water into the trough; from whence it is to be conveyed in pipes to any place it is intended for; and as each bucket gets over the trough, it falls into a perpendicular position again, and so goes down empty till it comes to the water at A, where it is

filled as before. On each bucket is a spring r, which going over the top or crown of the bar m (fixed to the trough м) raises the bottom of the bucket above the level of its mouth, and so causes it to empty all its water into the trough.

To determine the due relation of the power and the weight so that this wheel may be capable of producing the greatest effect, the following may be taken as a good approximation. After having fixed the diameter of the wheel, which must be something greater than the altitude to which the water is to be raised; fix also upon an even number of buckets to be hung at equal distances round the periphery of the wheel, and mark the position of their centres of motion in such a manner that they will stand in corresponding positions in every quarter of the circle: conceive vertical lines drawn through the centre of motion of each bucket in the rising part of the wheel; they will intersect the horizontal diameter of the wheel in points at which if the buckets were hung they would furnish the same resistance to the moving force as they do when hanging at their respective places on the rim of the wheel. Thus, supposing there were 18 equidistant buckets; then while $ hung on each side a vertical diameter of the wheel there would be 8 on the other side, and 2 would coincide with that diameter; in this case the resistance arising from all the full buckets would be the same as if one bucket hung on the prolongation of the horizontal diameter at the distance of 2 sin 20° + 2 sin 40° + 2 sin 60° + 2 sin 80°, these being the sines to the common radius of the wheel.

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To know the quantity of water that each bucket should contain, take of the absolute force of the stream, that is, of the weight of the prism of water whose base is the surface of one of the float-boards, and whose height is that through which water must fall to acquire the velocity of the stream: so have we the power that should be in equilibrio with the weight of water in the buckets of the rising semicircle. Then say, as the sum of the sines mentioned above is to radius, so is the power just found to a fourth term, the half of which will be the weight of water that ought to be contained in one bucket. Lastly, as the velocity of the wheel will be to that of the stream nearly as 1 to 23, the quantity of revolutions it makes in any determinate time becomes known, and, of consequence, the quantity of water the wheel will raise in the same time; since we know the capacity of each bucket, and the number of them emptied in every revolution of the wheel.

5. Another mechanical contrivance for the purpose of raising water is a chain-pump. This is now generally made from 12 to 24 feet in length; consists of two collateral square barrels, and

an endless chain of pistons of the same form fixed at proper distances. The chain is moved round a coarse kind of wheelwork, fixed sometimes at one end, but often at both ends of the machine. The teeth of the wheel-work are so contrived as to receive one half of the flat pistons and let them fold in; and they take hold of the links as they rise. A whole row of the pistons (which go free of the sides of the barrel by about a quarter of an inch) are always lifting when the pump is at work; and, as this machine is generally worked briskly, the pistons or pallets bring up a full bore of water in the pump. Chain-pumps are wrought sometimes by men turning winches, sometimes by horses, and sometimes by the impulse of a stream of water: they are likewise so contrived that by the continual folding in of the pistons, stones, dirt, or whatever comes in the way, may be cleared off: they are therefore often used to drain ponds, sewers, and remove foul water, when no other pump could be employed.

Chain-pumps are not merely fixed in a vertical position, but are often inclined; and in the latter case they are in a state of the greatest perfection, or raise the most water, when the breadth of the pallets is equal to their distance from each other, and the plane is inclined under an angle of 24° 21'.

It is not unusual for chaiu-pumps to be erected without a barrel to receive the pistons, after the manner represented in fig. 3. pl. XIX. The pallets are converted into square boxes $, s, &c. which are raised by means of hexagonal axles, each side of the hexagon being equal to the distance from box to box: the boxes descend with their mouths downwards, and so enter the water.

Another contrivance for raising water similar to the chainpump is an endless rope with stuffed cushions hung upon it, which, by means of two wheels or drums, are caused to rise in succession in the same barrel, and to carry water with them. From the resemblance of this apparatus to a string of beads, it is usually called paternoster-work. But in this, as well as the chain-pump, the magnitude of the friction is a formidable practical objection.

6. Jets and fountains are not now considered as conducive to picturesque beauty; nor can they be reckoned of much utility, except perhaps in hot climates: we have not therefore described any in this work. But in the fountain of Hero of Syracuse a principle is introduced which has been found of great utility in larger works; for the head of water is actually lower than the orifice, but the pressure is communicated by the intervention of a column of air: the construction of this fountain is as follows. It consists of two vessels KLMN (fig. 5. pl. XIX.) and OPOR,