Fig. 43. The effect of crossed lines upon their respective apparent directions.
A more complex case is found in [Fig. 43] where the effect of an obtuse angle ACD is to make the continuation of AB apparently fall below FG and the effect of the acute angle is the reverse. However, the net result is that due to the preponderance of the effect of the larger angle over that of the smaller. The line EC adds nothing, for it merely introduces two angles which reinforce those above AB. The line BC may be omitted or covered without appreciably affecting the illusion.
Fig. 44.—Another step toward the Zöllner illusion.
In [Fig. 44] two obtuse angles are arranged so that their effects are additive, with the result that the horizontal lines apparently deviate maximally for such a simple case. Thus it is seen that the tendency of the sides of an angle to be apparently deviated toward the direction of the angle may result in an apparent divergence from parallelism as well as in making continuous lines appear discontinuous. The illusion in [Fig. 44] may be strengthened by adding more lines parallel to the oblique lines. This is demonstrated in [Fig. 38] and in other illustrations. In this manner striking illusions are built up.
| Fig. 45.—The two diagonals would meet on the left vertical line. | Fig. 46.—Poggendorff’s illusion. Which oblique line on the right is the prolongation of the oblique line on the left? |
If oblique lines are extended across vertical ones, as in [Figs. 45] and [46], the illusion is seen to be very striking. In [Fig. 45] the oblique line on the right if extended would meet the upper end of the oblique line on the left; however, the apparent point of intersection is somewhat lower than it is in reality. In [Fig. 46] the oblique line on the left is in the same straight line with the lower oblique line on the right. The line drawn parallel to the latter furnishes an idea of the extent of the illusion. This is the well-known Poggendorff illusion. The upper oblique line on the right actually appears to be approximately the continuation of the upper oblique line on the right. The explanation of this illusion on the simple basis of underestimation or overestimation of angles is open to criticism. If [Fig. 46] is held so that the intercepted line is horizontal or vertical, the illusion disappears or at least is greatly reduced. It is difficult to reconcile this disappearance of the illusion for certain positions of the figure with the theory that the illusion is due to an incorrect appraisal of the angles.