This subject was better understood when no element but the length of the crank was to be considered; but now, since bicycles have appeared that are capable of being changed to a high or low gear, some riders persist in treating it as an entirely new problem. It has in one respect a new feature in that greater or less speed can be had without decreasing or increasing the length of the crank; that is, since the comparative speed of the pedal and rim of the wheel in space can be varied either by the length of the crank or the number of revolutions of the same, we can make one turn of a six-inch crank do the same work at the same foot-pressure as two turns of a three-inch crank at the same pressure. Now, this is a valuable feature, because it allows us to increase the vertical amplitude through which to transmit power without change in the velocity of the pedal through space. A convenient standard has been adopted in gearing cycles by comparing the speed of the driver to that of a wheel and crank connected and revolving together, as in the Ordinary; that is to say, a thirty-inch wheel geared to sixty means that one turn of the crank will drive the thirty-inch wheel twice around, as it must do in order to cover the same distance as one turn of a sixty-inch wheel. To find how high the machine is geared, divide the number of teeth in the sprocket-wheel on the crank by the number in the sprocket-wheel on the driver, then multiply the result by the diameter in inches of the drive-wheel. In short, the speed indicated by the size of the drive-wheel of the geared machine is to the real speed as the number of teeth in the gear upon the wheel is to the number of teeth in the gear on the crank-axle. When tricycles first appeared in which the power was transmitted through sprocket-wheels and chain, there was quite a cry for “high-geared” machines; but the mistake was soon discovered, and buyers eventually found that moderate gearing was best, and in fact many adopted a level gearing (equal-sized sprocket-wheels) with thirty-six- to forty-two-inch drivers. Notwithstanding this experience, when the geared bicycles came in there was still a great cry for fancied high speed. An English maker in 1885 complained to the writer that it was the bane of his existence,—this howl for high gears,—when it was well known to him that buyers would eventually be dissatisfied. It was of no use to make, said he, what is really needed; customers will not even try the machines, so sure are they that by their scheme “they can fly through the air with the greatest of ease,” which expression, when used by the ordinary man, means something like pulling a ten-horse load with one mule.