It results also that if one of the waterways is corraded more rapidly than the other the divide moves steadily toward the latter, and eventually, if the process continues, reaches it. When this occurs, the stream with the higher valley abandons the lower part of its course and joins its water to that of the lower stream. Thus from the shifting of divides there arises yet another method of the shifting of waterways, a method which it will be convenient to characterize as that of _abstraction_. A stream which for any reason is able to corrade its bottom more rapidly than do its neighbors, expands its valley at their expense, and eventually “abstracts” them. And conversely, a stream which for any reason is able to corrade its bottom less rapidly than its neighbors, has its valley contracted by their encroachments and is eventually “abstracted” by one or the other. The diverse circumstances which may lead to these results need not be enumerated, but there is one case which is specially noteworthy on account of its relation to the principles of sculpture. Suppose that two streams which run parallel and near to each other corrade the same material and degrade their channels at the same rate. Their divide will run midway. But if in the course of time one of the streams encounters a peculiarly hard mass of rock while the other does not, its rate of corrasion above the obstruction will be checked. The unobstructed stream will outstrip it, will encroach upon its valley, and will at last abstract it; and the incipient corrasion of the hard mass will be stopped. Thus by abstraction as well as by monoclinal shifting, streams are eliminated from hard rocks. _Résumé._—There is a tendency to permanence on the part of drainage lines and divides, and they are not displaced without adequate cause. Hence every change which is known to occur demands and admits of an explanation. (_a_) There are four ways in which abrupt changes are made. Streams are diverted from one drainage system to another, and the watersheds which separate the systems are rearranged, (1) by _ponding_, due to the elevation or depression of portions of the land; (2) by _planation_, or the extension of flood-plains by lateral corrasion; (3) by _alluviation_, or in the process of building alluvial cones and deltas; and (4) by _abstraction_. (_b_) There are two ways in which gradual changes are effected: (1) When the rock texture is variable, it modifies and controls by _monoclinal shifting_ the distribution in detail of divides and waterways. (2) When the rock texture is uniform, the positions of divides are adjusted in accordance with the principle of _equal declivities_. The abrupt changes are of geographic import; the gradual, of topographic.