ble volume of water acting upon it, while the friction of the axis is by no means doubled by the added breadth.
Water is generally made to act upon machines, particularly water-wheels, by means of its momentum when in motion. We have already sheer n, under the heads Of HYDRAULICS and H DROSTATICS, how water derives force from its depth, or gravity. The effect of water in motion will depend manifestly upon the quantity of fluid and Its velocity jointly Bess guliers, in his Experimental Philosophy, vol. ii. p. 419, gives the following easy mode of ascertaining these data. "Ob serve a place where the banks of the ri ver are steep, and nearly parallel, so ao to make a kind of trough for the water to run through ; then by taking the depth in various parts of the stream's breadth, obtain a correct section of the river. Stretch one line over it at right angles, and another at a small distance above or below, but perfectly parallel. Now throw in some buoyant body (such as an apple, which will not float so high as to be affected by the wind) immediately above the upper line : observe the time it occupies in passing from one to the other string. Thus you ascertain how many feet the current runs in a second, or in a minute. Then having the two sec tions, i. e. one at each line, reduce them to a mean depth, and compute the area of the mean section, which, being multi plied by4Ilse distance between the lines, will give the solid contents of the interme diate volume of which in the noted time passed from one string to the other. Now this way, by the rule of three, is adapted to any portion of time ; the ques tion being merely if the velocity be such in such an area, or trough, what would be the velocity in another of less size. It is obvious that if the area give twelve solid feet, and that water passed at the rate of four feet in a second, through a conduit of one foot square ; if the conduit were on ly six inches square, the velocity would be as 16 to 4; or, in other words, quad rupled. The arch of a bridge is an excellent station for observing the force of a stream ; because the sides are there regular, and the intermediate space may be correctly ascertained. But the depth is not always to be ascertained in such places without the aid of a boat, or of two intelligent assistants, who should be very correct in their observa tions."
The late Mr. John Smeaton made a va riety of experiments on the powers, ve locities, and friction, attendant upon water wheels of various sizes, and under differ ent influences. He observed, that, in re gard to power, it is most accurately mea sured by the raising of a weight to any given height in a given time according to the weight raised, the height, and the time, so is the product to the power by which it is effected. For a power that can raise ten pounds to the height of ten feet in one second will correspond with that power, which, in the same period, can raise five pounds to twenty feet in height; it being evident that the products must be the same. But in such case the power is supposed to be equable, without the least acceleration or diminution of velo city : and even then we are rather to con sider this as a popular and simple mode of estimation : for the quantity of motion extinguished, or produced, and not the product of the weight and height, is the true, unequivocal, and perfect measure of the mechanical power really expend ed, or the mechanical effect actually pro duced : these two are always equal and opposite. Yet it is true that Mr. Smea ton's mode is most applicable to the cases in which he adopts it.
To compute the effects of water-wheels with precision, it is necessary to ascer tain, 1. The real velocity of the water which impinges or acts upon the wheel ; 2. the quantity of water expended in a given time, and, 3, how much of the pow er is counterbalanced, or lost, by the fric tion of the machinery. Mr. Smeaton established, after a variety of experi ments, that the mean power of a volume of water, 15 inches in height, gave 8.96 feet of velocity in each minute to a wheel on which it impinged. The computation of the power to produce such an effect, allowing the head of water to be 105.8 inches, gave 264.7 pounds of water de scending in one minute through the space of fifteen inches; therefore, 264.7, multiplied by 15, was equal to 3.970. But as that power is found equal to rais ing no more than 9.375 pounds to the height of 135 inches, it was manifest that a major part of the power was lost; for the multiplication of these two sums amounted to no more than 1.266 ; of course the friction was equal to fths of the power.