IV.

Fig. 3.) that takes hold of the ram Q by the staple R LECT. for drawing it up.

D is a spiral or fusy fixed to the drum, on which is wound the small rope that goes over the pulley U, under the pulley V, and is fastened to the tope of the frame at 7. To the pulley block V is hung the counterpoise W, which hinders the follower from accelerating as it goes down to take hold of the ram: for, as the follower tends to acquire velocity in its descent, the line T winds downwards upon the fusy, on a larger and larger radius, by which means the counterpoise W acts stronger and stronger against it; and so allows it to come down with only a moderate and uniform velocity. The bolt Y locks the drum to the great wheel, being pushed upward by the small lever 2, which goes through a mortise in the shaft A, turns upon a pin in the bar 3 fixed to the great wheel B, and has a weight 4, which always tends to push up the bolt Y through the wheel into the drum. L is the great lever turning on the axis m, and resting upon the forcing bar 5,5, which goes down through a hollow in the shaft A, and bears up the little lever 2.

By the horses going round, the great rope H is wound about the drum C, and the ram Q is drawn up by the tongs F in the follower G, until the tongs comes between the inclined planes E; which, by shutting the tongs at the top, opens it at the foot, and discharges the ram, which falls down between the guides b b upon the pile P, and drives it by a few strokes as far into the mud as it can go ; after which, the top part is sawed off close to the mud, by an engine for that purpose. Immediately after the ram is discharged, the piece 6 upon the

Note 41. When the piles are driven for the purpose of constructing a cof fer-dam, they may be afterwards raised by the hydrostatic press of Bramah. The plan has been successfully adopted in many cases, and its advantage over our author's mode of sawing them beneath the water, will be sufficiently obvious, when we come to a description of that in. strument.

LECT.
IV.

follower G takes hold of the ropes a, a, which raise the end of the lever L, and cause its end N to descend and press down the forcing bar 5 upon the little lever 2, which by pulling down the bolt Y, unlocks the drum C from the great wheel B; and then, the follower, being at liberty, comes down by its own weight to the ram; and the lower ends of the tongs slip over the staple R, and the weight of their heads causes them to fall outward, and shuts upon it. Then the weight 4 pushes up the bolt Y into the drum, which locks it to the great wheel, and so the ram is drawn up as before.

As the follower comes down, it causes the drum to turn backward, and unwinds the rope from it, whilst the horses, great wheel, trundle, and fly, go on with an uninterupted motion : and as the drum is turning backward, the counterpoise W is drawn up, and its rope T wound upon the spiral fusy D.

There are several holes in the under side of the drum, and the bolt Y always takes the first one that it finds when the drum stops by the falling of the follower upon the ram; until which stoppage, the bolt has not time to slip into any of the holes.

This engine was placed upon a barge on the water, and so was easily conveyed to any place desired.-I never had the good fortune to see it, but drew this figure from a model which I made from a print of it; being not quite satisfied with the view which the print gives. I have been told that the ram was a ton weight, and that the guides 6 b, between which it was drawn up and let fall down, were 30 feet high. I suppose the great wheel might have had 100 cogs, and the trundle ten staves or rounds ; so that the fly would make ten revolutions for one of the great wheel.“

The operation of the pile engine may be best understood by refer- LECT ence to a former note in which the doctrine of accelerated motion is IV. examined, and it may be only necessary to add, that the momentum thus acquired is exactly equivalent to so much additional weight falling upon the head of the pile.

Note 43. The following additional illustration of the preceding subjects will be found valuable to the practical artizan, and they have been introduced at the close of the Lecture to prevent an unnecessary interference with our Author's text.

There are four principal modes of employing the force of water as a prime mover in machinery, and of these the under and over-shot water-wheels, are the most important: of the other two, namely, the breast-wheel and Barker's mill, but little need be said, as the latter is but seldom resorted to, and the breast wheel may be considered but as a modification of the two preceding. The following diagrams will best illustrate the under and over-shot water-wheels.

The over-shot wheel it will be seen owes its power to the weight of the water, while the under-shot, on the contrary, depends on its impulse.

In order to determine the effect of any force employed in machinery, we must consider not only its magnitude, but also the velocity with which it can be brought into action, and we must estimate the ultimate value of the power, by the joint ratio, or the product, of the force and the velocity. Thus, if we had a corn-mill, for example, in which we wished the mill-stone to re

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LECT. volve with a certain velocity, and to overcome a given resistance, IV.

and supposing that this effect could be obtained by means of a certain train of wheels from a given source of motion; if the velocity of the motion at its source be reduced to one half, we must double the diameter of one of the wheels by which the force is communicated, in order togive the mill-stone the desired velocity; and thus we must introdnce a mechanical disadvantage, which can only be compensated by a double intensity in the force at its origin.

If we apply this estimation of effect to the motion of an overshot wheel, we shall find that the velocity of the wheel, and consequently its breadth, and the magnitude of its buckets, is perfectly indifferent with respect to the value of its operation : for, supposing the stream to enter the buckets with the uniform velocity of the wheel, the quantity of water in the wheel at any one time, and consequently the pressure, must be inversely as the velocity, so that the product of the force into the velocity will be the same, however they may separately vary. If, however, the velocity were to become very considerable, it would be necessary to sacrifice a material part of the fall in order that the water might acquire this velocity before its arival at the wheel; but a fall of one foot or even less, is sufficient for producing any velocity that would be practically convenient: and it is obvious, on the other hand, that a certain velocity may be procured from a wheel moving rapidly, with less machinery than from another which moves more slowly. In general, the velocity of the surface of the wheel is between two and six feet in a second; and whether it be greater or smaller, the force actually applied will always be equal in effect to the weight of a portion of the stream employed, equal in length to the height of the wheel. In order to avoid the resistance which might be occasioned by the stagnant water below the wheel, it is a good practice to turn the stream backwards upon its nearer half, so that the water, when discharged, may run off in the general direction of its motion.

If we suffer the stream of water to acquire the utmost velocity that the whole fall can produce, and to strike horizontally against the float-boards of an under-shot wheel, or if we wish to employ the force of a river running in a direction nearly horizontal, the wheel must move, in order to produce the greatest effect, with half the velocity of the stream. For the whole quantity of water impelling the float-boards is nearly the same, whatever may be the velocity, especially if the wheel is properly inclosed in a narrow channel, and hence it is easy to calculate that the greatest possible effect will be produced when the relative velocity of

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the stream, striking the float-boards, is equal to the velocity of LECT. the wheel itself. The pressure on the float-boards is equal to IV that of a stream containing the same quantity of water, and striking a fixed obstacle with half the velocity, that is, such a stream as escapes from the wheel, which must be twice as deep or twice as wide as the original stream, since its motion is only one half as rapid ; and a column of such a stream, of twice the height due to its velocity, that is, of half the height of the fall, being as we have already seen, the measure of the hydraulic pressure, this force will be precisely half as great as that of a similar column, acting on an over-shot wheel, which moves with the same velocity. But the stream thus retarded will not retain the other half of its mechanical power; since its greatest effect will be in the same proportion to that of an equal stream acting on an overshot wheel with one fourth of the fall of the former; and the remaining fourth of the power is lost in producing the change of form of the water and in overcoming its friction. In whatever way we apply the force of water, we shall find that the mechanical power which it posesses must be measured by the product of the quantity multiplied by the height from which it descends: for example, a hogshead of water capable of descending from a height of ten feet, possesses the same power as ten hogsheads descending from a height of one foot; and a cistern filled to the height of ten feet above its orifice possesses 100 times as much power as the same cistern filled to the height of one foot only.

When, therefore, the fall is sufficiently great, an over-shot wheel is far preferable to an under-shnt wheel, and where the fall is too small for an over-shot wheel, it is most advisable to employ a breast-wheel, which partakes of its properties; its Anat-boards consisting of two portions meeting at an angle, so as to approach to the nature of buckets, and the water being also in some ineasure confined within thein by the assistance of a sweep or arched channel which follows the curve of the wheel, without coming too nearly into contact with it, so as to produce unnecessary friction. When the circumstances do not admit even of a breast-wheel, we must be contented with an under-shot wheel: it is recommended, for such a wheel, that the float-boards be so placed as to be perpendicular to the surface of the water at the time that they rise out of it: that only one half of each should ever be below the surface, and that from three to five should be immersed at once, according to the magnitude of the wheel. Sometimes, however, it has been thought eligible to employ a much smaller number: thus the water-wheel which

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