Some of the methods by which the growth of the many is arrested are easily understood. Some of the young valleys on a given coast will work their heads back into the land faster than others because of inequalities of slope and material. This will be true of the tributaries no less than of their mains. If valleys develop in ways other than by head erosion (see p. 73) the chances are also against their equality of growth. If two streams, such as _a_ and _c_, Fig. 86, develop faster than the intermediate stream _b_, it is clear that their tributaries may work back into the territory which at the outset drained into _b_, so as to cut off the supply of water from the latter stream (compare _a′b′c′_, Fig. 87). As a result, the growth of _b_ will be checked, and ultimately stopped. Similarly other valleys, such as _f_, will get the better of their neighbors, and many of the competitors, as _b_, _d_, _e_, and _g_ will soon drop out of the race. Between the stronger streams competition still goes on. If _a′_ and _f′_ develop faster than _c′_ its prospective drainage territory will be preëmpted by its rivals (compare Figs. 87 and 88). Thus as the result of the unequal rate at which valleys are lengthened, the larger number of those which come into existence are arrested in their development. As a result of growth in the manner indicated, the basins of even the large streams remain narrow at their lower ends while they expand above. This is the usual form of a drainage basin the development of which has been normal. [Illustration: +Figs.+ 86–88.—Diagrams to illustrate successive stages in the struggle for existence and dominion among streams.] Did valleys grow in length only, competition would not destroy the small ones; it would simply limit them. But valleys widen as well as lengthen, and by widening, adjacent valleys may eliminate the divide between them and become one. The elimination of the intervening ridge may be by lateral planation (p. 82), or, if the valleys be of unequal depth, by slope wash (see Fig. 85). By these and other processes many young valleys are dwarfed, and many others are destroyed. =Piracy.=—Streams do not always hold the courses which they establish for themselves at the outset. If the valley occupied by the stream _a_, Fig. 89, is deepened more rapidly than the valley occupied by _b_, a tributary from the former, _c_, may work back across the inter-stream area to e and steal the head waters of that stream (Fig. 90). The tributary which does the stealing is known as a _pirate_. Stream _f_ (Fig. 90) is said to be _beheaded_, and its upper portion, _de_, diverted. The beheaded stream is diminished in volume; or if its total supply of water came in above the point of tapping it would disappear altogether. [Illustration: +Figs.+ 89 and 90.—Diagrams to illustrate piracy.]