This familiar phrase means simply that the number of revolutions made by the drive-wheel in proportion to the number made by the cranks is greater or less. Broadly, it varies the relative amount of motion of the pedals, and consequently of the feet of the rider in travelling over a given distance. In the simple crank device no change can be made in this respect except in the length of the cranks, but in all of the sprocket-chain devices it is also possible to change the amount of motion in the pedals by altering the size of one or the other of the sprocket-wheels. In lever machines and in those which have the sun and planet connection, either with an oscillating lever or full revolving crank, it is generally possible, by some alteration, to produce the same effect as that of changing a sprocket-wheel as mentioned. The variation in the length of crank produces an effect comparable to the change of gearing in so far as the distance through which the feet travel in covering a certain distance is concerned, but the difference lies in this, that altering the crank means a given number of revolutions in a circle of varying radius, while altering the gearing means a variable number of revolutions in a circle of given radius, in order to cover a given length of road. In popular language, if a rider wishes more power, he must lengthen the crank or decrease the size of the sprocket-wheel on the crank-axle; _vice versa_, if he desires greater speed and less power, he must shorten the crank or enlarge the sprocket-wheel connected therewith. It is needless to say that enlarging the gear-wheel on the crank-axle produces the same effect as decreasing the size of that on the drive-wheel. In a sprocket-crank machine the real question of gearing is whether to change the length of crank or proportion of the sizes of the gear-wheels; but you can’t by any combination get power and speed both with the same amount of work done by the rider. Simple as all this matter of gearing is, it is probable that there is no feature in cycles so indefinitely understood, or, we might say, so persistently distorted. The only trouble is that riders will not stop to apply a most fundamental law of nature. If we gain speed, we lose power; if we gain power, we must lose speed. To apply this particularly to cycles, if you gear up for speed, you must push harder; if we gear down, we need not push so hard, but must kick faster or go more slowly, provided in each case the length of crank is the same. We cannot go fast and push easy unless we increase the strength of the man. To go over the same distance of given road, the same amount of work is required, no matter how the machine is arranged through which it is done.