A rule always presupposes a repetition. Repetitions, therefore, will
probably be found to play some important part in the production of
agreeable effects. Of course, the nature of agreeable effects is not
exhausted by this. Furthermore, the repetition of a physical event
becomes the source of agreeable effects only when it is connected with
a repetition of sensations.
An excellent example that repetition of sensations is a source of
agreeable effects is furnished by the copy-book of every schoolboy,
which is usually a treasure-house of such things, and only in need of an
Abbé Domenech to become celebrated. Any figure, no matter how crude or
poor, if several times repeated, with the repetitions placed in line,
will produce a tolerable frieze.
[Illustration: Fig. 25.]
Also the pleasant effect of symmetry is due to the repetition of
sensations. Let us abandon ourselves a moment to this thought, yet not
imagine when we have developed it, that we have fully exhausted the
nature of the agreeable, much less of the beautiful.
First, let us get a clear conception of what symmetry is. And in
preference to a definition let us take a living picture. You know that
the reflexion of an object in a mirror has a great likeness to the
object itself. All its proportions and outlines are the same. Yet there
is a difference between the object and its reflexion in the mirror,
which you will readily observe.
Hold your right hand before a mirror, and you will see in the mirror a
left hand. Your right glove will produce its mate in the glass. For you
could never use the reflexion of your right glove, if it were present to
you as a real thing, for covering your right hand, but only for covering
your left. Similarly, your right ear will give as its reflexion a left
ear; and you will at once perceive that the left half of your body could
very easily be substituted for the reflexion of your right half. Now
just as in the place of a missing right ear a left ear cannot be put,
unless the lobule of the ear be turned upwards, or the opening into the
concha backwards, so, despite all similarity of form, the reflexion of
an object can never take the place of the object itself.[20]
The reason of this difference between the object and its reflexion is
simple. The reflexion appears as far behind the mirror as the object is
in front of it. The parts of the object, accordingly, which are nearest
the mirror will also be nearest the mirror in the reflexion.
Consequently, the succession of the parts in the reflexion will be
reversed, as may best be seen in the reflexion of the face of a watch or
of a manuscript.
It will also be readily seen, that if a point of the object be joined
with its reflexion in the image, the line of junction will cut the
mirror at right angles and be bisected by it. This holds true of all
corresponding points of object and image.
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