Once started, each wash or gully becomes the cause of its own growth, for the gully developed by the water of one shower, determines greater concentration of water during the next. Greater concentration means faster flow, faster flow means more rapid wear, and this means corresponding enlargement of the depression through which the flow takes place. The enlargement effected by successive showers affects a gully in all dimensions. The water coming in at its head carries the head back into the land (head erosion), thus lengthening the gully; the water coming in at its sides wears back the lateral slopes, thus widening it; and the water flowing along its bottom deepens it. Thus gullies grow to be ravines, and farther enlargement by the same processes converts ravines into valleys. A river valley therefore is often but a gully grown big. [Illustration: WISCONSIN GEOL. AND NAT. HIST. SURVEY. BULLETIN NO. V., PL. XIII. FIG. 1. A very young valley. Illustration: FIG. 2. A valley in a later stage of development. Illustration: FIG. 3. Young valleys.] _The course of a valley._--In the lengthening of a gully or valley headward, the growth will be in the direction of greatest wear. Thus in Plate XIII, Fig. 1, if the water coming in at the head of the gully effects most wear in the direction a, the head of the gully will advance in that direction; if there be most wear in the direction b or c, the head will advance toward one of these points. The direction of greatest wear will be determined either by the slope of the surface, or by the nature of the surface material. The slope may lead to the concentration of the entering waters along one line, and the surface material may be less resistant in one direction than in another. If these factors favor the same direction of head-growth, the lengthening will be more rapid than if but one is favorable. If there be more rapid growth along two lines, as b and c, Plate XIII, Fig. 1, than between them, two gullies may develop (Plate XIII, Fig. 2). The frequent and tortuous windings common to ravines and valleys are therefore to be explained by the inequalities of slope or material which affected the surface while the valley was developing.