[Illustration: Fig. 20]
The opposite directions, right and left, balance on the point from
which they are taken.
28. Equal distances in opposite directions balance on the point from
which the directions are taken.
[Illustration: Fig. 21]
The equal distances AB and AC, taken in the directions AB and AC
respectively, balance on the point “A” from which the directions are
taken.
29. Two directions balance when, taken from any point, they diverge at
equal angles from any axis, vertical, horizontal, or diagonal.
[Illustration: Fig. 22]
The directions AB and AC balance on the vertical axis AD from which
they diverge equally, that is to say, at equal angles.
30. Equal distances balance in directions which diverge equally from a
given axis.
[Illustration: Fig. 23]
The equal distances AB and AC balance in the directions AB and AC which
diverge equally from the axis AD, making the equal angles CAD and DAB.
Both directions and distances balance on the vertical axis AD.
31. The positions B and C in Fig. 23, depending on balancing directions
and distances, balance on the same axis. We should feel this balance of
the positions A and B on the vertical axis even without any indication
of the axis. We have so definite an image of the vertical axis that
when it is not drawn we imagine it.
[Illustration: Fig. 24]
In this case the two positions C and B cannot be said to balance,
because there is no suggestion, no indication, and no visual image of
any axis. It is only the vertical axis which will be imagined when not
drawn.
32. Perfect verticality in relations of position suggests stability
and balance. The relation of positions C-B in Fig. 24 is one of
instability.
[Illustration: Fig. 25]
These two positions are felt to balance because they lie in a perfectly
vertical relation, which is a relation of stability. Horizontality in
relations, of position is also a relation of stability. See Fig. 28, p.
21.
33. All these considerations lead us to the definition of Symmetry.
By Symmetry I mean opposite directions or inclinations, opposite and
equal distances, opposite positions, and in those positions equal,
corresponding, and opposed attractions on a vertical axis. Briefly,
Symmetry is right and left balance on a vertical axis. This axis will
be imagined when not drawn. In Symmetry we have a balance which is
perfectly obvious and instinctively felt by everybody. All other forms
of Balance are comparatively obscure. Some of them may be described as
occult.
[Illustration: Fig. 26]
In this case we have a symmetry of positions which means opposite
directions, opposite and equal distances, and similar and opposite
attractions in those positions. The attractions are black dots
corresponding in tone, measure, and shape.
[Illustration: Fig. 27]
In this case we have a balance of positions (directions and distances)
and attractions in those positions, not only on the vertical axis
but on a center. That means Symmetry regarding the vertical axis,
Balance regarding the center. If we turn the figure, slightly, from
the vertical axis, we shall still have Balance upon a center and axial
Balance; but Symmetry, which depends upon the vertical axis, will be
lost.
34. The central vertical axis of the whole composition should
predominate in symmetrical balances.
[Illustration: Fig. 28]
In this case we do not feel the balance of attractions clearly or
satisfactorily, because the vertical axis of the whole arrangement
does not predominate sufficiently over the six axes of adjacent
attractions. It is necessary, in order that symmetrical balance shall
be instinctively felt, that the central vertical axis predominate.
[Illustration: Fig. 29]
The central vertical axis is clearly indicated in this case.
[Illustration: Fig. 30]
Here, also, the central vertical axis is clearly indicated.
35. All relations of position (directions, distances, intervals), as
indicated by dots or points, whether orderly or not, being inverted on
the vertical axis, give us an obvious symmetrical balance.
[Illustration: Fig. 31]
This is a relation of positions to be inverted.
[Illustration: Fig. 32]
Here the same relation is repeated, with its inversion to the right on
a vertical axis. The result is an obvious symmetrical balance. If this
inversion were made on any other than the vertical axis, the result
would be Balance but not Symmetry. The balance would still be axial,
but the axis, not being vertical, the balance would not be symmetrical.
36. In the case of any unsymmetrical arrangement of dots, the dots
become equal attractions in the field of vision, provided they are
near enough together to be seen together. To be satisfactorily seen
as a single composition or group they ought to lie, all of them,
within a visual angle of thirty degrees. We may, within these limits,
disregard the fact that visual attractions lose their force as
they are removed from the center of the field of vision. As equal
attractions in the field of vision, the dots in any unsymmetrical
arrangement may be brought into a balance by weighing the several
attractions and indicating what I might call the center of equilibrium.
This is best done by means of a symmetrical inclosure or frame. In
ascertaining just where the center is, in any case, we depend upon
visual sensitiveness or visual feeling, guided by an understanding
of the principle of balance: that equal attractions, tensions or
pulls, balance at equal distances from a given center, that unequal
attractions balance at distances inversely proportional to them. Given
certain attractions, to find the center, we weigh the attractions
together in the field of vision and observe the position of the
center. In simple cases we may be able to prove or disprove our visual
feeling by calculations and reasoning. In cases, however, where the
attractions vary in their tones, measures, and shapes, and where there
are qualities as well as quantities to be considered, calculations and
reasoning become difficult if not impossible, and we have to depend
upon visual sensitiveness. All balances of positions, as indicated by
dots corresponding in tone, measure, and shape, are balances of equal
attractions, and the calculation to find the center is a very simple
one.
[Illustration: Fig. 33]
Here, for example, the several attractions, corresponding and equal,
lie well within the field of vision. The method followed to balance
them is that which I have just described. The center of equilibrium
was found and then indicated by a symmetrical framing. Move the frame
up or down, right or left, and the center of the frame and the center
of the attractions within it will no longer coincide, and the balance
will be lost. We might say of this arrangement that it is a Harmony
of Positions due to the coincidence of two centers, the center of the
attractions and the center of the framing.
37. It will be observed that the force of the symmetrical inclosure
should be sufficient to overpower any suggestion of movement which may
lie in the attractions inclosed by it.
[Illustration: Fig. 34]
In this case the dots and the inclosure are about equally attractive.
[Illustration: Fig. 35]
In this case the force of attractions in the symmetrical outline is
sufficient to overpower any suggestion of instability and movement
which may lie in the attractions inclosed by it.
There is another form of Balance, the Balance of Inclinations, but I
will defer its consideration until I can illustrate the idea by lines.