It is obvious all along, of course, since action and reaction are equal, that all of the relations in question are reciprocal. When, for example, we speak of a pound weight on the long end of a lever balancing a ten-pound weight on the short end, it is equally appropriate to speak of the ten-pound weight as balancing the one-pound weight. Similarly, when power is applied to the lever, it may be applied at either end. Ordinarily, to be sure, the power is applied at the long end, since the object is to lift the heavy weight; but in complicated machinery it quite as often happens that these conditions are reversed, and then it becomes desirable to apply strong power to the short end of the lever, in order that the relatively small weight may be carried through the long distance. In the inter-relations of gearing wheels, such conditions very frequently obtain, practical ends being met by a series of wheels of different sizes. But the single rule, already so often outlined, everywhere holds--wherever there is gain of power there is loss of distance, and we can gain distance only by losing power. The words gain and loss in this application are in a sense misnomers, since, as we have already seen, gain and loss are only apparent, but their convenience of application is obvious. A familiar case in which there is first loss of speed and gain of power, and then gain of speed at the expense of power in the same mechanism, is furnished by the bicycle, where (1) the crank shaft turns the sprocket wheel that constitutes a lever of the second class with gain of power; where (2) power is further augmented through transmission from the relatively large sprocket wheel to the small sprocket of the axle; and where (3) there is great loss of power and corresponding gain of speed in transmitting the force from the small sprocket wheel at the axle to the rubber rim of the bicycle proper, this last transmission representing a lever of the third class. The net gain of speed is tangibly represented by the difference in distance traversed by the man's feet in revolving the pedals, and the actual distance covered by the bicycle. INCLINED PLANES AND DERRICKS