These wheels are used in falls from 10 to 20 ft., where a large number of revolutions is necessary, as in grain mills, where the moving millstone is hung on the vertical shaft of the wheel, hence intermediate gearing is unnecessary. These crude machines are found in Southern Europe, North Africa, in the Alps, Pyrenees, and in Algiers. They are about 5 ft. in diameter, and the blades are 15 inches high and 8 to 10 inches long (measured radially). [Illustration: FIG. 112.] Fig. 112 shows an “_undershot water wheel_.” In this style of wheel, the work is done by impact alone, as the running water acts only on a few immersed buckets on the under side of the wheel. In the _breast wheel_, Fig. 113, the water is admitted on a level or slightly above the center of the shaft, so that the water acts by impact and weight. [Illustration: FIG. 113.] NOTE.—“_A weir_ is a dam erected across a river to stop and raise the water, as for the purpose of taking fish, of conveying a stream to a mill, of maintaining the water at a level required for navigating it, or for the purposes of irrigation.” For facilitating the computation of the quantity of water flowing over weirs, Weir Tables, are used, based upon approved formulas, of which “Francis’ Formula” is perhaps the most reliable. These tables are applicable to the subject of water wheels but cannot be printed in this work. [Illustration: FIG. 114.] Fig 114 represents an _over-shot water wheel_ (F G H L, with axis at O) in which the water flows upon the top of the wheel at _h_, in the same direction in which it revolves, therefore the impact of the water is utilized upon the upper buckets H, a, b, after which the weight of the water acts in the buckets c, d, e, F, e´, d´ and c´. At b´ the buckets begin to overflow and empty themselves as shown at a´. It will be seen that the water acts upon almost one-half the circumference of this wheel, thus realizing the greatest mechanical effect with the smallest quantity of water. _The current-wheel_ is perhaps the first application of the force of water in motion, to drive machinery. In the first century B. C., water-wheels for driving mills were used in Asia Minor and on the Tiber. In the former case we suppose, but in the latter case we know, that these were current-wheels. [Illustration: FIG. 115.] _The tide or current wheel_, (Fig. 115) erected in the vicinity of the north end of London Bridge, and subsequently under its northern arch, was erected by Peter Morice, a Dutchman, in 1582, and operated force-pumps which supplied a part of London with water. The stand-pipe from the pump was 120 feet high, and conducted the water to a cistern at that height. The amount raised was about 216 gallons per minute. The wheel worked sixteen pumps, each 7 inches in diameter, and having a uniform stroke of 30 inches.