Fig. 52.—A spiral when rotated appears to expand or contract, depending upon direction of rotation.
A striking illusion is obtained by revolving the spiral shown in [Fig. 52] about its center. This may be considered as an effect of angles because the curvature and consequently the angle of the spiral is continually changing. There is a peculiar movement or progression toward the center when revolved in one direction. When the direction of rotation is reversed the movement is toward the exterior of the figure; that is, there is a seeming expansion.
Angles appear to modify our judgments of the length of lines as well as of their direction. Of course, it must be admitted that some of these illusions might be classified under those of “contrast” and others. In fact, it has been stated that classification is difficult but it appears logical to discuss the effect of angles in this chapter apart from the divisions presented in the preceding chapters. This decision was reached because the effect of angles could be seen in many of the illusions which would more logically be grouped under the classification presented in the preceding chapters.
Fig. 53.—Angles affect the apparent length of lines.
In [Fig. 53] the three horizontal lines are of equal length but they appear unequal. This must be due primarily to the size of the angles made by the lines at the ends. Within certain limits, the greater the angle the greater is the apparent elongation of the central horizontal portion. This generalization appears to apply even when the angle is less than a right angle, although there appears to be less strength to the illusions with these smaller angles than with the larger angles. Other factors which contribute to the extent of the illusion are the positions of the figures, the distance between them, and the juxtaposition of certain lines. The illusion still exists if the horizontal lines are removed and also if the figures are cut out of paper after joining the lower ends of the short lines in each case.