Now, since the work to be had from this water varies directly with _quantity_ and _head_, it is obvious that a stream _one-half_ as big falling _twice_ as far, would still give one horsepower at the wheel; or, a stream of 189 cubic feet a minute falling _ten times_ as far, 30 feet, would give _ten times_ the power, or _ten_ horsepower; a stream falling _one hundred times_ as far would give _one hundred_ horsepower. Thus small quantities of water falling great distances, or large quantities of water falling small distances may accomplish the same results. From this it will be seen, that the simple formula for determining the theoretical horsepower of any stream, in which Quantity and Head are known, is as follows: Cu. Ft. per Feet minute × head × 62.5 (A) Theoretical Horsepower = ---------------------- 33,000 _As an example, let us say that we have a stream whose weir measurement shows it capable of delivering 376 cubic feet a minute, with a head (determined by survey) of 13 feet 6 inches. What is the horsepower of this stream?_ Answer: Cu. ft. p. m. head pounds 376 × 13.5 × 62.5 H.P. = ----------------------------- = 9.614 horsepower 33,000 This is _theoretical horsepower_. To determine the _actual_ horsepower that can be counted on, in practice, it is customary, with small water wheels, to figure 25 per cent loss through friction, etc. In this instance, the actual horsepower would then be 7.2. _The Size of the Wheel_ Water wheels are not rated by horsepower by manufacturers, because the same wheel might develop one horsepower or one hundred horsepower, or even a thousand horsepower, according to the conditions under which it is used. With a given supply of water, the head, in feet, determines the size of wheel necessary. The farther a stream of water falls, the smaller the pipe necessary to carry a given number of gallons past a given point in a given time. A small wheel, under 10 × 13.5 ft. head, would give the same power with the above 376 cubic feet of water a minute, as a large wheel would with 10 × 376 cubic feet, under a 13.5 foot head. This is due to the _acceleration of gravity_ on falling bodies. A rifle bullet shot into the air with a muzzle velocity of 3,000 feet a second begins to diminish its speed instantly on leaving the muzzle, and continues to diminish in speed at the fixed rate of 32.16 feet a second, until it finally comes to a stop, and starts to descend. Then, again, its speed accelerates at the rate of 32.16 feet a second, until on striking the earth it has attained the velocity at which it left the muzzle of the rifle, less loss due to friction.