3. To determine the velocity which the circumference of the wheel ought to have in order to produce the greatest effect, Mr. Smeaton observes, that the slower a body descends, the greater will be the portion of tht action of gravity applicable to the producing a mechanical effect, and, inconsequence, the greater will be the effect. If a stream of water falls into the bucket of an overshot-wheel, it is there retained till the wheel by moving round discharges it, and consequently the slower the wheel moves, the more water each bucket will receive : so that what is lost in speed, is gained by the pressure of a greater quantity v. c water acting in the buckets at once.
From the experiments, however, it appeared, that when the wheel made about 20 turns in a minute, the effect was near upon the greatest. When it made 30 turns, the effect was diminished about 1/20th part; and that when it made 40, it was diminished about 1/4, when it made less than 18, its motion was irregular; and when it was loaded so as not to admit its making 18 turns, the wheel was overpowered by its load. It is an advantage in practice, that the velocity of the wheel should not be diminished further than -will procure some solid advantage in point of power, because cœteris paribus, as the motion is slower, the buckets must be made larger, and the wheel being more loaded with water, the stress upon every part of the work will be increased in proportion.
The best velocity for practice, therefore, will be such, as when the wheel made 30 turns in a minute, that is, when the velocity of the circumference is a little more than three feet in a second. Experience confirms that this velocity of three feet in a second is applicable to the highest overshot-wheels, as well as the lowest ; and all other parts of the work being properly adapted thereto, will produce very
nearly the greatest effect possible ; it is also determined by experience, that high wheels may deviate further from this rule, before they will lose their power, by a given aliquot part of the whole, than low ones can be admitted to do.
For a wheel of 24 feet high may move at the rate of six feet per second without losing any part of its power; and, on the other hand, the author had seen a wheel of 33 feet high that moved very steadily and well, with a velocity but little exceeding two feet. The reason of the superior velocity of
the 24 feet wheel seems to have been owing to the small proportion that the head, requisite to give the water the proper velocity of the wheel, bears to the whole height.
4. The maximum load for an overshot-wheel, is that which reduces the circumferences of the wheel to its proper velocity; which will be known by dividing the effect it ought to produce in a given time, by the space intended to be described by the circumference of the wheel in the same time ; the quotient will be the resistance overcome at the circumference of the wheel, and is equal to the load required, the friction and resistance of the machinery included.
5. The greatest velocity of which the circumference of an overshot-wheel is capable, depends jointly upon the diameter of the height of the wheel, and the velocity of falling bodies; for it is plain that the velocity of the circumference can never be greater than to describe a semi-circumference 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 saine 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 beronds ; 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 prevent 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.