The safety cycle is always "geared up"--that is, one turn of the pedals will turn the rear wheel more than once. To get the exact ratio of turning speed we count the teeth on the big chain-wheel, 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 = 2-1/2. One turn of the pedal turns the rear wheel 2-1/2 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 2-1/2 x 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 x 28 inches = 84 inches. A handy formula to remember is, gearing = T/_t_ x 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," as it is often called) turns outside this, on a number of balls running in a groove chased in the neck of the ratchet. Between these two parts are the _pawls_, of half-moon shape. The driving-wheel is assumed to be on the further side of the ratchet. To propel the cycle the chain-ring is turned in a clockwise direction. Three out of the six pawls at once engage with notches in the ratchet, and are held tightly in place by the pressure of the chain-ring on their rear ends. The other three are in a midway position. [Illustration: FIG. 222.] When the rider ceases to pedal, the chain-ring becomes stationary, but the ratchet continues to revolve. The pawls offer no resistance to the ratchet teeth, which push them up into the semicircular recesses in the chain-ring. Each one rises as it passes over a tooth. It is obvious that driving power cannot be transmitted again to the road wheel until the chain-wheel is turned fast enough to overtake the ratchet. THE CHANGE-SPEED GEAR.