EXPERIMENT. 1. Quantity of water, by floating wax balls, 2461 cubic feet per minute. 2. Quantity, by measuring at the tail of the wheel, 3297 cubic feet, medium 2879. But as the water was gathering in the pool, and as the river was extremely dirty, it is likely that the principal error may be in first experiments; and therefore, instead of taking the medium quantity, we shall call it 3000 cubic feet. Sixteen saws at work in two frames, namely, two slabbing and fourteen deal saws; the water-wheel made twelve turns per minute. Thirty-four saws being put on, the wheel made only eight turns per minute. CALCULATIONS. = The diameter of water-wheel being 16 feet, its circumference is 3.1416 x 16 50-2656; this multiplied by twelve revolutions = 603.18 feet per minute, or 10.05 feet per second. The head of water being 2 feet 9 inches, the velocity due from this is 13.3; thus the velocity of the head of water is to that of the wheel as 13.3 to 10:05, or as 5 to 3.778; hence the effect produced will be nearly equal to twelve horses. The reader will notice that the saws in the present instance are driven, not from the axle of the water-wheel, but from a second motion. The wheel is of larger diameter, and makes a less number of revolutions; for the requisite speed could not have been obtained from so low a head of water, and it is therefore gained by driving the pinion upon the second shaft, which works the saws, by the toothed wheel of greater size upon the water-wheel axle. The speed given to this wheel is somewhat greater than Mr. Smeaton advises, but this is done to render it more readily applicable to the saws, and the fall from the wheel clears it of back water. The public are much indebted to Mr. George Rennie for the very liberal manner in which he has given them these and other results of his father's experience, which will be found in the "Quarterly Papers on Engineering." It is curious to remark, that the boards of the undershot wheel still bear the name of floats, although they are no longer turned by the current of the river. While the E cavities or receptacles for the water on the face of the overshot wheel are called buckets, although they bear no resemblance to a bucket, otherwise than by holding water. In these names we trace their origin from the ancient irrigatingwheel, turned by floats in the stream, and lifting the water in wooden buckets or earthen pitchers fastened upon the rim of the wheel. A very simple and neat method of employing the impulsive force of water, when a small stream descends from a great height, is shown by a working model in the Museum of Practical Geology. A jet of water issuing from a pipe is made to strike the vanes of a small wheel, inclosed in case, and causes it to revolve rapidly. The wheel may be stopped, or its motion reversed, by turning a stop-cock or cylinder. The whole machine may be made of brass, or other metal, in a very compact form; and in a hilly country might be usefully employed at a farm in turning agricultural machines, to save manual labour. Its small size and cost make it well suited for such purposes (See woodcut). The model at the Museum in Jermyn-street is adapted to machinery for winding up ore from a mine. CHAPTER IX. OVERSHOT WHEELS, GRAVITY OF WATER EMPLOYED INSTEAD OF IMPULSE. Ir was not difficult to imagine that if a small stream of water descending from a hill side were directed into the mouths of the earthen vessels or wooden buckets of the wheels used for irrigation, the vessels so loaded would descend and the wheels revolve, so that rotary motion and mechanical power would be gained; the buckets emptying themselves at the lowest point, as they had before been emptied at the highest; the wheel turning in the opposite direction, because the weight, or gravity of the water was now the moving power of this OVERSHOT WHEEL. In the undershot wheel the impulse of the water striking the floats drives the wheel; in the overshot wheel the weight of the water flowing into the buckets turns the wheel, and all impulse must be avoided; the water must flow with the same velocity as the wheel, or just so much in excess as will prevent the buckets from striking the water as they present themselves to be filled. Experience soon showed that the earthen jar or the suspended bucket were cumbrous and inconvenient, and as larger and more powerful wheels were applied to more copious streams, a series of simple wooden troughs formed across the face of the wheel were found to answer the purpose better. When the supply of water was ample and the wheel large, it was found that to fill these troughs well and regularly the stream should be made nearly as broad as the wheel, and shallow in proportion to its width. The wheel was then formed by placing two sets of arms, at a sufficient distance apart, upon the axle, and fixing to their ends segments of wood to form the circle; upon these segments across the face of the wheel, and equal to, or somewhat exceeding in length the width of the stream or sheet of water, were nailed the sole-boards; on the end of these boards, and at right angles to them, so as to form a projecting rim or ledge on each side of the wheel's face, was fixed the shrouding, formed of stout plank generally from 12 to 18 inches broad; and between these shroudings, across the face of the wheel, were placed the buckets, made of lighter planking, and having their ends let into the shrouding, by which the ends were closed. The edge of the bucket-board meeting the sole-plank formed two sides of a triangular trough, the third being open to receive and discharge the water. Subsequently the bucket was made in two boards, one called the front, and the other the bottom of the bucket, the latter taking off the angle and making the section of the bucket, or form of the trough, that of a trapezium, which form it long retained, until the buckets-of-water wheels were made of iron plate. Since water-wheels have been made wholly of iron, and chiefly of wrought iron, the form of the bucket has been either a part of a circle, a cycloid, an epicycloid, or an Archimedean spiral, and of these last-named forms especially in breast-wheels, which will hereafter be noticed. Great pains are now taken by the best makers of water-wheels to form and adapt the curve of the buckets so that they may readily fill with water, retain their load as long as possible, and discharge it with facility when it has ceased to be useful. Mr. Smeaton's paper on undershot wheels, before quoted, was followed by another on overshot wheels, read before the Royal Society, May 24, 1759. These papers were long considered as the text from which millwrights should deduce their rules of practice, and even now they well deserve the careful study of those who engage in the construction of such machines, together with the later experiments of Rennie, Morin, and Poncelet. Mr. Smeaton had the merit of proving and demonstrating the advantage and the difference of effect resulting from employing the weight instead of the impulse of a volume of water descending from a given height. "In reasoning without experiment, one might be led to imagine that, however different the mode of application is, yet that wherever the same quantity of water descends through the same perpendicular space the natural effective power would be equal; supposing the machinery free from friction, equally calculated to receive the full effect of the power, and to make the most of it: for if we suppose the height of a column of water to be 30 inches and resting upon a base or aperture of one inch square, every cubic inch of water that departs therefrom will acquire the same velocity or momentum, from the uniform pressure of 30 inches above it, that one cubic inch let fall from the top will acquire in falling down to the level of the aperture; one would therefore suppose that a cubic inch of water let fall through a space of 30 inches, and then impinging upon another body, would be capable of producing an equal effect by collision, as if the same cubic inch had descended through the same space with a slower motion, and produced its effects gradually for in both cases gravity acts upon an equal quantity of matter, through an equal space; and consequently, that whatever was the ratio, between power and effect in undershot-wheels, the same would obtain in overshot, and indeed in all others; yet, however conclusive this reasoning may seem, it appears, upon trial, that the effect of the gravity of descending bodies is very different from the effect of the stroke of such as are non-elastic, though generated by an equal mechanical power." : : Gravity, it is true, acts for a longer space of time upon the body that descends slowly, than upon one that falls quickly but this cannot occasion the difference in the effect; for an elastic body falling through the same space in the same time will, by collision upon another elastic body, rebound nearly to the height from which it fell: or, by communicating its motion, cause an equal one to ascend to the same height. The observations and deductions which Mr. Smeaton made from his experiments were as follows First. As concerning the ratio between the power and effect of Overshot-wheels. "The effective power of water must be reckoned upon the whole descent; because it must be raised to that height, in order to be in a condition of producing the same effect a second time. The ratio between the powers so estimated, and the effect at the maximum as deduced from the several sets of experiments, is shown to range from 10 to 7.6 to that of 10 to 5.2; that is, nearly from 4 to 3 and from 4 to 2. In these experiments, where the heads of water and quantities expended are least, the proportion is nearly as 4 to 3; but where the heads and quantities are greatest, it approaches nearer to that of 4 to 2, and by a medium of the whole the ratio is that of 3 to 2 nearly. We have seen before, in our observations upon the effects of undershot-wheels, that the general ratio of the power to the effect when greatest was |