In attempting to compare the two horizontal lines one is confused so as to regard the line with outward-extending obliques longer than that with inward-extending obliques, though, measured from point to point, they are equal. The same illusion occurs in a variety of similar figures, such as

[Ill.u.s.tration: Inward and outward arrowheads.]

where the main lines are not drawn, but the distances from point to point are to be compared; or such as

[Ill.u.s.tration: Inward and outward solid arrowheads.]

where the two distances between points are again to be compared.

Angles, however, are not necessary to give the illusion, as can be seen in this figure

[Ill.u.s.tration: Half circles with similar s.p.a.cing.]

or in this

[Ill.u.s.tration: Full circles with similar s.p.a.cing.]

In the last the lengths to be compared extend (_a_) from the right-hand rim of circle 1 to the left-hand rim of circle 2, and (_b_) from this last to the right-hand rim of circle 3. The same illusion can be got with squares, or even with capital letters as

[Ill.u.s.tration: Upper case E with similar s.p.a.cing and the center letter reversed.]

or

[Ill.u.s.tration: Upper case R with similar s.p.a.cing and the center letter reversed.]

or

[Ill.u.s.tration: Upper case L E D with similar s.p.a.cing and the center letter reversed.]

where the distances between the main vertical lines are to be compared.

Here is an another form of the same illusion

[Ill.u.s.tration: Two sets of three parallel horizontal lines. In the first set the center line is longest. In the second set the center line is shortest, but the same length as the first center line.]

the middle lines being affected by those above and below.

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Though these illusions seem like curiosities, and far from every-day experience, they really do enter in some degree into almost every figure that is not perfectly square and simple.

[Ill.u.s.tration: Fig. 70.--The Poggendorf illusion. Are the two obliques parts of the same straight line?]

Any oblique line, any complication of any sort, is pretty sure to alter the apparent proportions and directions of the figure. A broad effect, a long effect, a skewed effect, may easily be produced by extra lines suitably introduced into a dress, into the front of a building, or into a design of any sort; so that the designer needs to have a practical knowledge of this type of illusion.

Extra lines have an influence also upon esthetic perception. The esthetic effect of a given form may be quite altered by the introduction of apparently insignificant extra lines.

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[Ill.u.s.tration: Fig. 71.--The barber-pole illusion. The rectangle represents a round column, around which runs a spiral, starting at _a_. Which of the lines, 1, 2, 3, 4, and 5, comes closest to being a continuation of _a?_]

Esthetic perception is very much subject to the law of combination, and to the resulting difficulty of isolation.

One of the most interesting illusions, not being visual, can {459} only be described and not demonstrated here.

[Ill.u.s.tration: Fig. 72.--By aid of this simple figure, the Poggendorf and barber-pole illusions can be seen to be instances of the Muller-Lyer illusion, Try to bisect the horizontal line in this figure. The oblique line at the right tends to displace the right-hand end of the horizontal to the right, while the oblique at the left tends to displace the left-hand end of the horizontal also to the right. Similar displacements account for the Poggendorf and barber-pole illusions.]

[Ill.u.s.tration: Fig. 73.--The Zoellner illusion. The long lines are really parallel. The illusion is increased by holding the figure so that these main lines shall be neither vertical nor horizontal. It is more difficult to "deceive the eye" in regard to the direction of vertical and horizontal lines, than in regard to the direction of oblique lines. This illusion must be related in some way to the Muller-Lyer and Poggendorf illusions, since the elements employed in constructing the three figures are so much the same.

If you treat this figure according to the directions given for Fig.

67, and sight along the obliques, you get an illusion of perspective.]

It is called the "size-weight illusion", and may be said to be based on the old catch, "Which is heavier, a pound of lead or a pound of feathers?" Of course, we shrewdly answer, a pound's {460} a pound. But lift them and notice how they feel! The pound of lead feels very much heavier. To reduce this illusion to a laboratory experiment, you take two round wooden pill-boxes, one several times as large as the other, and load them so that they both weigh the same; then ask some one to lift them and tell which is the heavier. He will have no doubt at all that the smaller box is the heavier; it may seem two or three times as heavy. Young children, however, get the opposite illusion, a.s.similating the weight to the visual appearance; but older persons switch over to the contrast effect, and perceive in opposition to the visual appearance. What seems to happen in the older person is a motor adjustment for the apparent weights, as indicated by their visual appearance, with the result that the weight of larger size is lifted more strongly than the weight of smaller size; so that the big one comes up easily and seems light, the little one slowly and seems heavy.

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EXERCISES

1. Outline the chapter.

2. Show that the law of combination accounts both for many correct perceptions, and for many illusions.

3. Through which of the senses are spatial facts best perceived?