In like manner, a bushel of coals consumed in working two engines may produce the same useful effect, but it may produce that useful effect in the one in half the time it takes to produce it in the other. In that case the _duty_ of the engines will be the same, but the _power_ of the one will be double that of the other. [Pg295] In fine, _power_ has reference to _time_,—_duty_, to _fuel_. The more rapidly the engine produces its mechanical effect, the greater its power will be, whatever may be the fuel consumed in working it. And, on the other hand, the greater the useful effect produced by a given weight of fuel, the greater will be the duty, however long the time may be which the fuel may take to produce the useful effect. (176.) The proportion of the stroke to the diameter of the cylinder must be determined by the velocity intended to be given to the piston. With the same capacity of cylinder, and the same evaporation in the boiler, the velocity of the piston will augment as the magnitude of its diameter is diminished. The proportion of the diameter to the stroke of the cylinder is very various. In engines used for steam-vessels the length of the cylinder very little exceeds its diameter. In land engines, however, the proportion of the length to the diameter is greater. It is maintained by some that the proportion of the diameter and length of the cylinder should be such as to render its surface exposed to the cooling of the external air, the smallest possible. Tredgold has maintained that since, during the stroke, the steam is gradually exposed to contact with the surface of the cylinder from the top to the bottom, the mean surface exposed in contact with steam being half that of the entire cylinder, the proportion of the diameter to the stroke should be such that the surface of half the length of the cylinder, added to the magnitude of the top and bottom, shall be a minimum. If this principle be admitted, then the best proportion of the diameter to the stroke would be that of one to two, the length of the stroke being twice the diameter of the cylinder; but since the whole surface of the cylinder is constantly exposed to the cooling effects of the air, and since in the intervals of the stroke there is no sensible change of the temperature of the surface, the loss of heat by cooling will in effect be the same, especially in double-acting engines, as if the cylinder were constantly filled with steam. If this be admitted, then the object should be to give the cylinder such a proportion, that its entire surface, including the top and bottom, shall be a minimum. [Pg296] The proportion given by this condition would be very nearly that which is observed in the cylinders of marine engines, viz. that the length of the cylinder should be equal to its diameter.