over those of the smaller streams. The most rapidly growing subsequent branch, G, fig. 5, of the largest transverse master stream, A, may grow headwards so fast as to push away the divide, X, which separates it from the head of the opposing subsequent branch, J, of the next adjacent smaller transverse stream, C, and thus finally to capture and divert the headwaters, H, of the smaller transverse stream to the larger one, as in fig. 6. The divide creeps while the two opposing subsequent branches are in contest; it leaps when the successful subsequent branch reaches the channel of the conquered stream. The first stream captured in this way must necessarily be the nearest to the large stream. The diversion of the considerable volume of headwaters, H, to the channel of the small subsequent branch, G, causes it to deepen its channel rapidly; the same effect is perceptible in H for a distance above its point of capture and diversion: the increased load of sediment thus given to G will be in great part dropped in a fan-delta where it enters the flat valley of the master stream, A, (fig. 6). [Illustration: FIG. 4.] [Illustration: FIG. 5.] [Illustration: FIG. 6.] Gaining strength by conquest, other captures are made, faster for a time, but with decreasing slowness as the head of the diverting subsequent branch recedes from the original master: and at last, equilibrium may be gained when the headwater slope of the diverting branch is no greater than that of the opposing subsequent branch of the next uncaptured transverse stream. After the capture of a transverse stream has been effected in this way, the divide, Y, between its diverted upper portions, H, fig. 6, and its beheaded lower portion, C, will be pushed down stream by the growth of an inverted stream, V. This goes on until equilibrium is attained and further shifting is prevented on reaching the hard transverse lava sheets, Z, fig. 7; here the divide is maturely established. In the case of a system of transverse streams, C, D, etc., fig. 7, successively captured by the subsequent branch of a single master, the divides (Z, Y'), between the inverted (V, V') and beheaded (C, D) portions of the captured streams will for a time present different stages of approach to establishment. The divide on the line of that one of the original streams, C, that is nearest to the master stream, A, may reach a final stable position, Z; while on the next stream further away from the master, the beheaded portion, D, may still retain a short piece above the gap in the upper lava sheet, not yet secured by the inverted stream, V'; and a third stream, further away still from the master (not shown in figure 7) might remain uncaptured and independent. [Illustration: FIG. 7.]