Abstract
The writer has proposed a mathematical model of slope development in a previous paper. The model is given by
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in which a=subdueing coefficient, b=recessional coefficient, and c=denudational coefficient, respectively. The term f (x, t) gives the effect of the crustal movements.
Some additional properties of the model mentioned above are discussed, that is, the relative ratio of the three erosional coefficients, modification of a finite mountain, and the boundary conditions which are geomorphologically significant. A classification of the slopes obtained from the mathematical model is also attempted and compared with those derived by W. Penck.
It may be concluded that the slopes given by the model are classified into two types, that is, symmetrical slopes and asymmetrical slopes. The latter contains further, 1) convex slopes which result from rapid removal of debris piled up at the foot of the mountain, 2) concave slopes which appear in the later stage of slope development of a finite mountain, and 3) irregular slopes which occur with varying erosional coefficients. All of these types are generated following instantaneous upheaval.
