As the work done by a fan consists in imparting motion at a stated velocity to a given weight of air, it is very easy to calculate the power which must be expended to do a certain amount of work. The velocity at which the air leaves the fan cannot be greater than that of the fan tips. In a good fan it may be about two-thirds of that speed. The resistance to be overcome will be found by multiplying the area of the fan blades by the pressure of the air and by the velocity of the center of effort, which must be determined for every fan according to the shape of its blades. The velocity imparted to the air by the fan will be just the same as though the air fell in a mass from a given height. This height can be found by the formula h = v² / 64; that is to say, if the velocity be multiplied by itself and divided by 64 we have the height. Thus, let the velocity be 88 per second, then 88 x 88 = 7,744, and 7,744 / 64 = 121. A stone or other body falling from a height of 121 feet would have a velocity of 88 per second at the earth. The pressure against the fan blades will be equal to that of a column of air of the height due to the velocity, or, in this case, 121 feet. We have seen that in round numbers 13 cubic feet of air weigh one pound, consequently a column of air one square foot in section and 121 feet high, will weigh as many pounds as 13 will go times into 121. Now, 121 / 13 = 9.3, and this will be the resistance in pounds per _square foot_ overcome by the fan. Let the aggregate area of all the blades be 2 square feet, and the velocity of the center of effort 90 feet per second, then the power expended will bve (90 x 60 x 2 x 9.3) / 33,000 = 3.04 horse power. The quantity of air delivered ought to be equal in volume to that of a column with a sectional area equal that of one fan blade moving at 88 feet per second, or a mile a minute. The blade having an area of 1 square foot, the delivery ought to be 5,280 feet per minute, weighing 5,280 / 13 = 406.1 lb. In practice we need hardly say that such an efficiency is never attained. [Illustration: FIG. 4] The number of recorded experiments with fans is very small, and a great deal of ignorance exists as to their true efficiency. Mr. Buckle is one of the very few authorities on the subject. He gives the accompanying table of proportions as the best for pressures of from 3 to 6 ounces per square inch: