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Of the factors peculiar to friction, that of indeterminate value doubtless suffers increasing relative diminution as the depth of ice increases, and its platted ordinates (expressed in terms of the valley-profile) will hence form a curve of materially less depth than the triangle formed by the tangents to its extremities (fig. 2). The disposition of the factor is accordingly to widen the gorge and develop the U profile.

Fig 2.

With the less lateral velocity common to ice-streams will go reduced lateral friction, and hence erosion, in a ratio corresponding to the velocity curve; and for a second reason, therefore, will concavity of the valley-sides be engendered and developed; though the concurrent disposition will be to deepen the gorge.

Whenever concavity of the valley-sides obtains, the contact surface of the vertical prism will become variable. If, now, friction vary approximately with the pressure of the incumbent ice, the consequent erosion will diminish with the increasing slope toward the edges of the glacier; when the disposition will be to deepen the gorge and restore the V form; but if the friction vary more nearly with the contact area, it will increase with the slope, and the resulting erosion will tend to widen the gorge and, in another manner, to restore the V profile. Whichever tendency obtains will, however, be secondary and ever subordinate to that of the principal factors of friction. (Subglacial water will at once reduce friction and promote transportation directly and corrasion indirectly; also it will tend, ceteris paribus, to form a continuous film between ice and rock reaching upward to 0.92 of the thickness of the glacier, or, if the glacial surface be highly convex, perhaps quite to its margins. On the whole, then, its