while a body let fall from the top of the wheel will descend through its diameter; nor even quite so great, as a body descending through the same perpendicular space cannot perform the same in so small a time when passing through a semi-circle as would be done in a perpendicular line. Thus, if a wheel is 16 feet one inch in diameter, a body will fall through it in one second: this wheel therefore can never arrive at a velocity equal to the making one turn in two seconds; but, in reality, an overshot-wheel can never come near this velocity; for when it acquires a certain speed, the greatest part of the water is prevented from entering the buckets, and the rest, at a certain point of its descent, is thrown out again by the centrifugal force. As these circumstances depend chiefly upon the form of the buckets, the utmost velocity of overshot-wheels cannnot be generally determined; and, indeed, it is the less necessary in practice, as it is in this circumstance incapable of producing any mechanical effect.

6. The greatest load an overshot-wheel will overcome, considered abstractedly, is unlimited or infinite; for as the buckets may be of any given capacity, the more the wheel is loaded, the slower it turns, but the slower it turns, the more will the buckets be filled with water; and, consequently, though the diameter of the wheel and quantity of water expended are both limited, yet no resistance can be assigned, which it is not able to overcome; but in practice we always meet with something that prevents our getting into infinitesimals. For when we really go to work to build a wheel, the buckets must necessarily be of some given capacity, and consequently such a resistance will stop the wheel, as it is equal to the effort of all the buckets in one semi-circumference filled with water. The structure of the buckets being given, the quantity of this effort may be assigned, but is not of much consequence in practice, as in this case also the wheel loses its power; for though here is the exertion of gravity upon a given quantity of water, yet being prevented by a counterbalance from moving, is capable of producing no mechanical effect, according to our definition. But, in reality, an overshot-wheel generally ceases to be useful before it is loaded to that pitch; for when it meets with such a resistance as to diminish its velocity to a certain degree, its motion becomes irregular; yet this never happens till the velocity of the circumference is less than two feet per second, where the resistance is equable.

The reader having now become acquainted with the valuable course of experiments made by Mr. Smeaton, we shall next offer to his notice a few remarks upon the best mode of delivering water upon an overshot-wheel.

In wheels of this construction, it has been, and still is, the common practice, to allow the water to flow into the buckets at the highest point of the wheel; but this system is decidedly bad; for the centre of gravity of the upper bucket is direct over the axle of the wheel, and, consequently, any water poured into that bucket will, instead of creating a rotatory motion, cause a greater pressure upon the pivots of the axle. The greatest advantage would be obtained by causing the water to fall upon the wheel, at an angle of 42 or 45 degrees, as then the power of the wheel will be augmented by the increased leverage. In constructing wheels upon this principle, however, great care must be taken to allow a sufficiency of room in buckets for the escape of air, otherwise the wheel will not act. The same observation is also applicable to breast-wheels; for we were once present, and witnessed an instance of this kind, at the first starting of a breast-wheel, in which the millwright, in order to obtain the greatest possible effect, had made the back-boards to fit so tight that no water or air could escape; the consequence of which was, the necessity of reducing the whole of the back-boards, to allow air enough to escape for the water to act freely upon the floats.

BURN'S OVERSHOT-wheel WITHOUT A SHAFT.

THIS ingenious machine was invented and erected by the late Mr. Burns, whose mechanical ingenuity we have already had occasion to admire. It is represented in two different sections, in figs. 95 and 96, and forms a large hollow cylinder by its buckets and sole, without having any shaft or axle-tree.

This wheel is 12 feet diameter, and seven feet broad over all, and has 28 buckets. The gudgeon is 6 inches diameter, by 9 inches long. The flaunch is 1 inch thick at the extreme points. The arms are of redwood fir, 6 inches square; one piece making two arms in length, where they cross one another at the wheel's centre, 14 inch of the wood remaining in each, connecting the two opposite arms as one piece. The wheels was made by first fitting the gudgeon into a large piece of hard wood, with the flaunch paralle! to the horizon, and in that position the arms and rings were trained and

bound fast to it. All the grooves for starts or raisers, and buckets, were cut out before it was removed; first one piece was bolted to the flaunch at a a, and so of the others, leaving the distant openings for the cross bars that reach between each arm and its opposite arm. These bars, or pieces, were only 4 inches square, and were of good beech wood, turned round in the body. They were 10 inches square at each end, in which was fitted a strong nut for a bolt, 1 inch thick, to go through b, and connect the two sides together.

After the arms were trained and fixed right upon the gudgeons, the innermost ring was completed; the tenons were trained on the arms first, and the rings 4 inches thick and 8 inches deep, put on by keys driven into the mortice. The remaining tenons were then reduced from 14 to 1 inch thick, and the outermost ring, only 3 inches thick by 6 inches deep, was firmly wedged thereon, and bound fast at the other ends by three strong wooden pins, as at CC; to the lower ring, the outside of the uppermost and undermost rings are flush, all the additional thickness of the lower ring projecting inside the buckets.

Some difficulty was found in laying the water properly into the buckets of this wheel, owing to the narrowness of the months of the buckets, by the high start or raiser, which was remedied by adopting the following plan.

The openings in the bottom of the troughing should be of iron, and so distant from each other that the water from them is thrown into two separate buckets. The iron curved parts should also be movable, to adjust the openings to the quantity of water necessary for the wheel. Unless the head of water is 12 or 14 inches above these openings, it will be difficult to give it the proper direction into the buckets, especially if the openings are pretty wide for them; for then it deviates the more down from the line of direction, and tends to retard the wheel, by striking on the outside of the bucket. The openings from which the buckets are filled, ought to De 10 inches less in length than the buckets, i. e. five inches at each side, otherwise the water is apt to jerk over on each side of the wheel, as the edges of the bucket pass by.

The mode of making and finishing the wheel at Cartside requires very little workmanship, compared to the usual method; and any good joiner will do it as well as a millwright. The joiner finished Cartside wheel in six or seven weeks. The construction will be better understood from the following reference to the figures.

Fig. 95 represents three distinct transverse views. The part marked A supposes a part of the shrouding in section, showing

the pins; the part marked B is a section of the wheel through any part of the buckets, and showing three of the ties, 1,2,3, in section. Part D shows the manner in which the exterior ends of the wheel are finished, also the gudgeons, flaunch, &c.

Fig. 96 is a longitudinal section of the wheel through one of the arms, showing the projection of the shrouding, the manner in which the arms of the wheel are connected together, and likewise the manner in which the ties are connected to the gudgeon.

CHAIN OF BUCKETS.

THIS is applicable in many situations where there is a considerable fall of water. This sketch was taken from one in Scotland used to give motion to a thrashing mill: the fig. 97 is so obvious as to need little explanation. The buckets C, D, G, H, &c. must be connected by several chains to avoid the danger of breaking, and united into an endless chain, which is extended over two wheels A and B, the upper one being the axis which is to communicate motion to the mill-work; E is the spout to supply the water. The principal advantage of this plan is, that no water is lost by running out of the buckets before they arrive at the lowest part, as is the case with the wheel. Another is, that the buckets being suspended over the wheel A of small diameter, it may be made to revolve more quickly than a wheel of large diameter, and without increasing the velocity of the descending buckets beyond what is proper for them. This saves wheel-work when the machine is to be employed, as in a thrashing machine, to produce a rapid motion. On the other hand, the friction of the chain in folding over the wheel at the top, and seizing its cogs, will be very considerable; these cogs must enter the spaces in the open links between the buckets, to prevent the chain slipping upon the upper wheel. We think this machine might be much improved by contriving it so that the chain would pass through the centre of gravity of each bucket, whereas in the present form, the weight of each bucket tends to give the chain an extra bend. The chain-pump reversed, has been proposed as a substitute for a water-wheel when the fall is very great, and we think it would answer the purpose with some chance of success. It would have an advantage over the chain-pump when employed for raising water, in the facility of applying cup leathers to the pistons on the chain, in the same way as other pumps, which leathers expand themselves to the inside of the barrel, and are kept perfectly tight by the pressure of the water. In the chain-pump such leathers cannot be

employed, because the edges of the leather cups would turn down and stop the motion, when the cups were drawn upwards into the barrel. It is the defective mode of leathering the pistons of the chain-pump which occasions its great friction. In the motion of a machine of this kind, the pistons would descend into the barrel, and might therefore be leathered with cups like other pumps, so as to be quite tight without immoderate friction. This machine was proposed by a Mr. Cooper in 1784, who obtained a patent for it, and Dr. Robison has again proposed it with recommendation.

BREAST-WHEELS.

THE breast-wheel partakes of the nature both of an overshot and an undershot: it is driven partly by impulse, but chiefly by the weight of water. The lower part of the wheel is surrounded by a curved wall or sweep of masonry, which is made concentric with the wheel, and the floatboards of the wheel are exactly adapted to the masonry, so as to pass as near as possible thereto without touching it; and the side walls are in like manner adapted to the end of the float-boards or sides of the wheel, the intention being to let the least possible quantity of water pass without causing the float-boards to move before it. In fig. 98, the water is poured upon the top of the wheel over the breasting at I, the efflux from the mill-dam K being regulated by the sluice or shuttle M, which is placed in the direction of a tangent to the wheel, and is provided with the rack R, and pinion P, by which it can be drawn up so as to make any required degree of opening, and admit more or less water to flow on the wheel.

The water first strikes on the float, and urges it by its impulse; but when the floats descend into the sweep, they form as it were close buckets, each of which will contain a given quantity of water, and the water cannot escape from these buckets except the wheel moves, at least this is the intention, and the wheel is fitted as close as it can be to the race with that view. Each of the portions of water contained in these spaces bears partly upon the wall of the sweep, and partly upon the floats of the wheel; and its pressure upon the floats, if not exceeded by the resistance, will cause the wheel to move; hence the action upon all the floats which are within the sweep of the breasting is by the weight of the water alone; but the water is made to impinge upon the first float-board with some velocity, because the surface of the water in the dam K is raised considerably above the orifice beneath the shuttle where the water issues.