角的布置における線の偏向 I -線の隔りの要因-

Abstract

Many authors have referred illusions of direction to a tendency to overestimate acute angles. However, they have not proved that acute angles are in fact overestimated but merely supposed it as the cause of these illusions.The writer attempted to determine whether the seen direction of either side of an acute angle differs from its objective direction. A rotatable disk, on which a line was drawn, was set at a little distance from the vertex of an angle and was so adjusted that the line on the disk appeared to be in a straight line with one side of the angle. The amount of deviation of the adjusted line from the objective direction of that side of the angle was measured.By this means, it was found that The sides of an acute angle were always seen as deflected outwards. Such deflection of side lines could also be found even when the ends of the side lines were a little separate from each other and no longer formed a perfect angle. The amount of the deflection (D) decreased regularly with the increase in the separation (d) between the two sides provided that the objective direction of each side was kept constant (see Fig. 5). The exact relation of D to d was established in a logarismic equation as follows :D=a-b·log dwhere a and b are constants.This fact makes us suppose that some stress, which causes the deflection of lines, must be produced in a certain area around a Figure. The writer would like to call such an area a Vector-Field after BROWN. The stress is strong in the center and is weak at the periphery of the Field. The amount of deflection of the line depends upon the strength of the stress in the Vector-Field. On this assumption the fact of overestimation of acute anglesand there-fore illusions of direction can be explained as the effect of some stress in the Vector-Field.