Fig. 54.—The horizontal line appears to tilt downward toward the ends.
Fig. 55.—The horizontal line appears to sag in the middle.
In [Fig. 54] the horizontal straight line appears to consist of two lines tilting slightly upward toward the center. This will be seen to be in agreement with the general proposition that the sides of an angle are deviated in the direction of the angle. In this case it should be noted that one of the obtuse angles to be considered is ABC and that the effect of this is to tilt the line BD downward from the center. In [Fig. 55] the horizontal line appears to tilt upward toward its extremities or to sag in the middle. The explanation in order to harmonize with the foregoing must be based upon the assumption that our judgments may be influenced by things not present but imagined. In this case only one side of each obtuse angle is present, the other side being formed by continuing the horizontal line both ways by means of the imagination. That we do this unconsciously is attested to by many experiences. For example, we often find ourselves imagining a horizontal, a vertical, or a center upon which to base a pending judgment.
A discussion of the influence of angles must include a reference to the well-known Müller-Lyer illusion presented in [Fig. 56]. It is obvious in a that the horizontal part on the left appears considerably longer than that part in the right half of the diagram. The influence of angles in this illusion can be easily tested by varying the direction of the lines at the ends of the two portions.
Fig. 56.—The Müller-Lyer illusion.