Fig. 41.—Simple effect of angles.
This illusion apparently is due to the presence of the angle and the effect is produced by the presence of right and acute angles to a less degree. The illusion decreases or increases in general as the angle decreases or increases respectively.
Although it is not safe to present simple statements in a field so complex as that of visual illusion where explanations are still controversial, it is perhaps possible to generalize as Jastrow did in the foregoing case as follows: If the direction of an angle is that of the line bisecting it and pointing toward the apex, the direction of the sides of an angle will apparently be deviated toward the direction of the angle. The deviation apparently is greater with obtuse than with acute angles, and when obtuse and acute angles are so placed in a figure as to give rise to opposite deviations, the greater angle will be the dominant influence.
Although the illusion in such simple cases as [Fig. 41] is slight, it is quite noticeable. The effect of the addition of many of these slight individual influences is obvious in accompanying figures of greater complexity. These individual effects can be so multiplied and combined that many illusory figures may be devised.
In [Fig. 42] the oblique lines are added to both horizontal lines in such a manner that A is tilted downward at the angle and B is tilted upward at the angle (the letters corresponding to similar lines in [Fig. 41]). In this manner they appear to be deviated considerably out of their true straight line. If the reader will draw a straight line nearly parallel to D in [Fig. 41] and to the right, he will find it helpful. This line should be drawn to appear to be a continuation of C when the page is held so D is approximately horizontal. This is a simple and effective means of testing the magnitude of the illusion, for it is measured by the degree of apparent deviation between D and the line drawn adjacent to it, which the eye will tolerate. Another method of obtaining such a measurement is to begin with only the angle and to draw the apparent continuation of one of its lines with a space intervening. This deviation from the true continuation may then be readily determined.
Fig. 42. The effect of two angles in tilting the horizontal lines.