# Shikukan ni okeru nagasa no chikaku

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• Mathematics

## Abstract

I. Experiments in Dynamic Field-A rectangular cardboard (Fig. II, 1; text p. 3) was mounted on a vertical shaft that rotated at one revolution per 33 seconds, driven by an electric motor. The observer viewed the card from a distance of about 120cm either monocularly or binocularly and compared the lengths of its two vertical sides. When the card assumed the position parallel to the face of O, the sides were judged equal in length. However, as the card revolved, with its one side moving away from and the other moving toward O, the phenomenal length of the former increased gradually and for a while it appeared longer than that of the latter. Finally, as the card drew near the mesial plane, they came to look equal in length again. Similar results were obtained by substituting a trapezoidal cardboard (Fig. II, 2, 3; text p. 3) for the rectangular one. The experiment was also conducted in which the cardboard was turned 90° and mounted on a horizontal shaft as an axis. The results were comparable with those in the preceding experiments, i.e., the length of the side which moved farther away from O increased considerably. II. Experiments in Static Field-Instead of the cardboard, pairs of rods were used as stimuli. In one series of experiments, two rods separated by a distance of 8cm were planted upright in such manner that the vertical plane comprising them would coincide with or intersect the frontal plane passing through the center of the stimulus field at an angle of 15°, 30°, 45°, 60°, 75°, 80° or 85°. The rods were compared in respect of their phenomenal lengths. As in the case of the preceding experiments, the length of the rod that was farther away from O was overestimated. However, the amount of overestimation was very small. In another experiment, three kinds of simple geometrical figures (Fig. III, 9, 10, 11; text p. 10), each of which gave an unmistakable impression of depth, were used as stimuli. In each figure two vertical lines were compared, with the results similar to those in the other experiments, i.e., the line that looked farther away was overestimated.

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