_Falls and rapids._--If in lowering its channel a stream crosses one layer of rock much harder than the next underlying, the deepening will go on more rapidly on the less resistant bed. Where the stream crosses from the harder to the less hard, the gradient is likely to become steep, and a rapids is formed. These conditions are suggested in Fig. 16 which represents the successive profiles (a b, a c, d e, f e, g e, and h e) of a stream crossing from a harder to a softer formation. Below the point a the stream is flowing over rock which is easily eroded, while above that point its course is over a harder formation. Just below a (profile a b) the gradient has become so steep that there are rapids. Under these conditions, erosion is rapid just beyond the crossing of the hard layer, and the gradient becomes higher and higher. When the steep slope of the rapids approaches verticality, the rapids become a _fall_ (profile a c). [Illustration: Fig. 16.--Diagram to illustrate the development of a rapid and fall. The upper layer is harder than the strata below. The successive profiles of the stream below the hard layer are represented by the lines a b, a c, d e, f e, g e, and h e.] As the water falls over the precipitous face and strikes upon the softer rock below, part of it rebounds against the base of the vertical face (Fig. 16). The result of wear at this point is the undermining of the hard layer above, and sooner or later, portions of it will fall. This will occasion the recession of the fall (profile d e and f e). As the fall recedes, it grows less and less high. When the recession has reached the point i, or, in other words, when the gradient of the stream below the fall crosses the junction of the beds of unequal hardness, as it ultimately must, effective undermining ceases, and the end of the fall is at hand. [Illustration: WISCONSIN GEOL. AND NAT. HIST. SURVEY. BULLETIN NO. V., PL. XVI. Skillett Falls, in the Potsdam formation, three miles southwest of Baraboo. The several small falls are occasioned by slight inequalities in the hardness of the layers.] When the effective undercutting ceases because the softer bed is no longer accessible, the point of maximum wear is transferred to the top of the hard bed just where the water begins to fall (g, Fig. 16). The wear here is no greater than before, though it is greater relatively. The relatively greater wear at this point destroys the verticality of the face, converting it into a steep slope. When this happens, the fall is a thing of the past, and rapids succeed. With continued flow the bed of the rapids becomes less and less steep, until it is finally reduced to the normal gradient of the stream (h e), when the rapids disappear.