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

[Illustration: Half circles with similar spacing.]

or in this

[Illustration: Full circles with similar spacing.]

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

[Illustration: Upper case E with similar spacing and the center letter
reversed.]

or

[Illustration: Upper case R with similar spacing and the center letter
reversed.]

or

[Illustration: Upper case L E D with similar spacing 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

[Illustration: 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.

[Illustration: 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.

{458}

[Illustration: 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.