and the teeth on the small chain-wheel attached to the hub of the rear wheel, and divide the former by the latter. To take an example:—The teeth are 75 and 30 in number respectively; the ratio of speed therefore = 75⁄30 = 5⁄2 = 2½. One turn of the pedal turns the rear wheel 2½ times. The gear of the cycle is calculated by multiplying this result by the diameter of the rear wheel in inches. Thus a 28-inch wheel would in this case give a gear of 2½ × 28 = 70 inches.
One turn of the pedals on a machine of this gear would propel the rider as far as if he were on a high "ordinary" with the pedals attached directly to a wheel 70 inches in diameter. The gearing is raised or lowered by altering the number ratio of the teeth on the two chain-wheels. If for the 30-tooth wheel we substituted one of 25 teeth the gearing would be—
75⁄25 × 28 inches = 84 inches.
A handy formula to remember is, gearing = T/t × D, where T = teeth on large chain-wheel; t = teeth on small chain-wheel; and D = diameter of driving-wheel in inches.
Two of the most important improvements recently added to the cycle are—(1) The free wheel; (2) the change-speed gear.
THE FREE WHEEL
is a device for enabling the driving-wheel to overrun the pedals when the rider ceases pedalling; it renders the driving-wheel "free" of the driving gear. It is a ratchet specially suited for this kind of work. From among the many patterns now marketed we select the Micrometer free-wheel hub (Fig. 222), which is extremely simple. The ratchet-wheel R is attached to the hub of the driving-wheel. The small chain-wheel (or "chain-ring,"