Chap. XVII. THEORY OF THE MOTION OF FLUIDS.

149

giving the body a certain velocity, but if in falling, it be made to act upon some other, so asto produce a mechanical effect, the falling body will be retarded, because a portion of theaction of gravity is then spent in producing that effect, and the remainder only will givemotion to the falling body; therefore the slower a body descends, the greater will be theportion of the action of gravity applicable to producing a mechanical effect, consequentlythe greater that effect will be. A stream of water falling into the bucket of an overshotwheel is there retained until the rotary motion of the wheel discharges it; the slower thewheel moves the more water each bucket receives so that what is lost in speed is gained bythe pressure of a greater quantity of water acting on the buckets at once; thus themechanical power of an overshot wheel produces equal effects, whether it move quickly orslowly : when the wheel, according to the experiments, made 20 turns in a minute, theeffect was nearly the greatest; when 30 turns the effect was diminished one-twentieth ; when40 turns it was diminished one quarter; when less than 18$ its motion was irregular, andwhen loaded so as not to admit of its making 18 turns, it was overpowered. The velocitymost available in practice is that produced by a wheel making SO turns in a minute, andthe velocity of the circumference is a little more than 3 feet in a second. Experience alsoproves that the velocity is applicable to the highest overshot wheels, as well as thelowest.

Smeaton, in the year 1796, put up an overshot wheel at Hull, some years after these ex-periments were made, the diameter of which was 27 feet, and he directed that it shouldmove at the rate of 8$ feet per second, remarking that its motion would not be equal andregular if it moved at the rate of 3 feet per second.

The load for an overshot wheel that will produce a maximum effect is that which reduces thecircumference of the wheel to its proper velocity ; and this will be ascertained by dividingthe effect it ought to produce in a given time by the space intended to be described by thecircumference of the wheel in the same time; the quotient will be the resistance over-come at the circumference, and is equal to the load required, the friction of the machineryincluded.

The greatest possible velocity of which the circumference of an overshot wheel is capable de-pends jointly upon the height of the wheel and the velocity of falling bodies.

The greatest load thatan overshot wheel can

overcome is unlimited _

According to Eytel-wein the power whichoperates upon overshotwater-wheels is dividedinto two parts ; one de-rived from the weightof the water in thebuckets, the other fromthe impulse of thewater falling on it: theeffect of the first isconstant, that of thesecond varies with thevelocity; the maximumis said to be when thevelocity is half that ofthe water received, butthe variable portionbeing the smaller, therule is of little practicalimportance, and thevelocity of the wheel isgenerally greater thanthis; by turning thestream back upon the

nearer half of the wheel, we remove the resistance of the lower water, which runs off in thesame direction as that of the water-wheel. The iron overshot wheels have the same ar-rangement of the pen.trough and shuttle for the supply of water as the other descriptionof wheels, and can be regulated in a similar manner.

On the Construction of Overshot Water-wheels. —When the water is permitted to fall into thebucket c, (fig. 1740.) from the horizontal mill-course E F, the weight of water in the bucketacting at the end of the levers equal to m O puts the wheel in motion in the direction erf, andall the buckets, which are filled in succession as the wheel turns round. When the bucket creaches the position rf, its power to turn the wheel is increased, becoming equal to the

Fig. 1739.

OVERSHOT WHEEL