Some forms of the wheel and axle have high efficiencies as in bicycles with gear wheels. Other forms in which ropes are employed have more friction. Pulleys have sometimes efficiencies as low as 40 per cent. when heavy ropes are used. =127. Inclined Plane.=--We now come to a type of _simple machine of lower efficiency_ than those previously mentioned. These belong to the inclined plane group, which includes the inclined plane (see Fig. 101), the wedge and the screw. They are extensively used, however, notwithstanding their low efficiency, on account of often giving a high mechanical advantage. The _relation between these machines may be easily shown_, as the _wedge_ is obviously _a double inclined plane_. In Art. 82 it is shown that the effort required to hold a weight upon an inclined plane is to the _weight_ supported as the _height_ of the plane is to its _length_. [Illustration: FIG. 101.--An inclined plane.] Or while the weight is being lifted the vertical height _BC_, the effort has to move the length of the plane _AC_. Since by the law of machines the effort times its distance equals the weight times its distance, or the weight is to the effort as the effort distance is to the weight distance, therefore the mechanical advantage of the inclined plane is the ratio of the length to the height of the inclined plane. _Inclined planes_ are used to raise heavy objects short distances, as barrels into a wagon, and iron safes into a building. Stairways are inclined planes with steps cut into them. =128. The Wedge.=--Wedges are used to separate objects, as in splitting wood (see Fig. 102), cutting wood, and where great force is to be exerted for short distances. An axe is a wedge, so is a knife. A fork consists of several round wedges set in a handle. The edge of any cutting tool is either an inclined plane or a wedge. Our front teeth are wedges. Numerous examples of inclined planes may be seen about us. No definite statement as to the mechanical advantage of the wedge can be given as the work done depends largely on friction. The force used is generally applied by blows on the thick end. In general, the longer the wedge for a given thickness the greater the mechanical advantage. [Illustration: FIG. 102.--One use of the wedge.]