The process may not end even here. If after the diversion of _de_ the point in the channel to the left is lowered faster than the channel of the beheaded stream _f_, the divide between _dg_ and the head of _f_ (Fig. 90) will be shifted down the valley of the latter, as shown in Fig. 91. The shifting will go on until the divide reaches a position of stability, that is, until erosion on its opposite sides is equal. The foregoing case may be called _foreign piracy_ because the valleys of different systems are concerned. _Domestic piracy_ may also take place, as illustrated in the accompanying diagrams (Figs. 92 and 93). Here a tributary to a crooked river may develop, working back until it taps the main at a higher point, thus straightening the course of the stream. The change takes place only when the highest point in the tributary valley is brought below the surface of the water in the main stream at the point where the tapping takes place. This would be likely to occur only after the main stream had attained a low gradient, for so long as it is deepening its channel notably, the small amount of water flowing through the tributary valley would not be likely to bring it down to the level of the main. In any case the flow of water from the main stream through the new valley would be likely to be started during flood, and at such time the erosion in the new channel would be great. The complete and final diversion of the stream through the new channel might be a slow process. [Illustration: +Fig.+ 91.—Diagram showing the shifting of a divide after piracy.] [Illustration: +Figs.+ 92 and 93.—Domestic piracy. The tributary, _a_ of Fig. 92, develops headward until it taps the main stream at _b_, giving the result shown in Fig. 93.] Piracy may occur where the material in which the valleys are cut is homogeneous; but, as will be seen later, heterogeneity of material, by determining unequal rates of erosion, stimulates the piratical proclivities of streams. An actual case of piracy is shown on Plate XI. North and South Lakes formerly drained westward to the Schoharie Creek, the present head of which is in the extreme northwest corner of the map. The head of Kaaterskill Creek, which had a much higher gradient, worked back and captured the head of the westward-flowing stream, diverting the drainage from North and South Lakes to itself. Schoharie Creek was thus beheaded. Plaatekill Creek, near the south limit of the map, appears to have beheaded the creek flowing west and northwest, similarly diverting its head waters. The Dells, Wis., quadrangle (U. S. Geol. Surv.) affords an illustration of domestic piracy. RATE OF DEGRADATION.