A Mass of Mountain ; its Measurement and Geographical Signification

Abstract

(1) A mass of mountain is measured by various methods and commonly represented by a mean altitude per unit area. (2) The present author measured the mean altitudes per various unit areas in central Honshu, Japan. The method was by means of statistical mesh. (Fig. 1, 2, 3, ) (3) That includes the following steps: (A) Each sheet of 1: 50, 000 map was divided into 1/4 sheets by the middle meridian and parallel of latitude of that map. (B) Each 1/4 sheet was covered with a mesh which divided the 1/4 sheets into 20 sections. (C) The altitudes (A1, A2, A3, …… A20) were measured by 20 nodes of the mesh. (D) The mean altitude per 1/4 sheet is 1/20Σ20i=1Ai. (E) A unit area was selected from various points of view. The writer selected 1, 4 and 16 sheets of 1: 50, 000 map respectively as unit meshes. 80 3-20(F) The mean altitude per 1 sheet is 1/80Σ80i=1Ai that is 4 sheets 1/320Σ320i=1Ai and that is 16 sheets 1/2080Σ1280i=1Ai. (G) The mean altitudes are mapped at the centers of the unit meshes. (H) The unit mesh is moved aside by halves of the sheets in order to smooth the isoarithmS of the mean altitudes and to correct errors arising from accidental situation of the mesh.(4) The standard error of the mean altitudes is little. That of Norikura-dake sheet is 97.2m, more than 0.06 of the mean altitude, 1634m. That of 4 sheets is decreased to 1/2 and that of 16 sheets to 1/4 of the error per 1 sheet. (5) The more the mass of mountain grows, the higher are the vertical limits of the tree or forest line and the upper limits of agricultural settlements or paddy fields. (6) Fig. 5 and Fig 6 show the relation of the mean altitude to the forest line and the upper limit of paddy fields. In the profile A-B the correlation coefficient between the mean altitudes per 1 sheet and the forest line is+0.712, and that between the mean altitudes per 4 sheets and the forest line+0.806. (n=9). The correlation coefficient between the mean altitudes per 1 sheet and the upper limit of paddy fields is+0.693, and that between the mean altitudes per 4 sheets and the upper limit of paddy fields+0.786. (n=14) (7) The generalized upper limit of the agricultural settlements and paddy fields is related to more generalized patterns of distribution of the mean altitules than to the mean altitudes per 1 or 4 sheets. Fig. 3 and Fig. 7 show this relation. (8) We can comprehend easily the relation of in-situ-correspondence between the upper limit of agricultural settlements and that of, paddy fields, but it is not easy to explain perfectly the relation between those and the mass of mountain.