This is the case with crystallisations, the first artistic products of unconscious nature. If we look at a vast plain covered with snow, a feeling of sublime cold and wretchedness overcomes us; but if we take up one isolated snow-flake, and place it under a microscope, we find that the elements of the crystallised drop of water surround with harmonious regularity a common centre, which is the body, from which radiate as integral parts the diversified forms of the flake. In studying snow-flakes, we find that the three dimensions of space—height, breadth, and depth, limited by symmetry, proportion and direction—are the principal elements of every form which in itself has to represent a detached total. In all the crystallisations there is one ‘momentum’ of formation—the centre, from which all the parts emanate perfectly well-balanced and complete in themselves. The elements of which all artistic works, whether natural or produced by men, are composed, are the straight line and the waving line. With these elements we can obtain the three principal conditions of every work of art—symmetry, proportion, and direction. Snow-flakes may be used in any direction, and therefore they may be set down as without distinct direction. The rays with their radiation, however, are formed according to the principal law of the universe. They represent the dynamic force; they strive at isolation from the centre which must be looked upon as their static momentum. Thus in the first artistic products of nature positive and negative, or rather dynamic and static forces are clearly perceptible. The horizontal line is the representative of the static, whilst the vertical line is the indicator of the dynamic force.

      Symmetry is a perfect equality of form to the right and left of a vertical line on a horizontal base.

      Eurythmy consists in a repetition of variegated forms.

      In order to produce eurythmy we must confine symmetry within a certain compass; for this purpose we have the frame. Our doors are nothing but frames for the entering or departing individuals; as our windows are frames for the landscape, sky, or walls on which we look, or for ourselves when seen from without. The frame, whether it be real or imaginary, as the correct limitation of forms, is of the very highest importance in decorative and pictorial art.

      Eurythmy may be alternating. This alternating principle is observed in metopes and triglyphs. The alternation may be interrupted by a cæsura (a mark or sign of rest). Masks, heads of lions, or any other figures may form the cæsura, as decorative elements in the long lines of the tops of houses, palaces, or temples. The cæsura, combined with eurythmy and symmetry, will give us the best patterns for flat decorations, as in carpets, paper-hangings, keramic works and metal or wood ornaments.

      Applying what we have said of crystallisations to plants and animals, we find that symmetry is undoubtedly the predominant element in every flower. The plant developes itself from the ground, which is its horizontal basis. It shoots up generally in a vertical direction, as a radiation from our globe. In trees the branches, leaves, flowers, and fruits are clustered around a central line in eurythmical proportion. In flowers symmetry predominates, whilst in trees eurythmy prevails. In considering the branches of a tree in relation to its trunk, we find the same symmetry and eurythmy, though the direction be changed. We can study these forms best in plants of the coal formation—the Sigillaria, Stigmaria, Lepidodendra, and Calamites; and in ferns, fir-trees, cedars, &c.

      In the palm tree we see most distinctly the working of the conflicting forces of nature. The dynamic force of vitality drives the stem upwards, and the static force of gravitation towards a common centre is expressed in the beautifully-drooping curves of the leaves. Symmetry is further to be observed in the lowest animals, in polyps, radiata, &c., but never in higher species, in which it is not planimetrical (viz., cannot be treated on a plane) but linear, none of them being perfectly regular in any of the three dimensions of space.

       Man is altogether different from the products of the mineral or vegetable kingdoms, which give us the prototypes of conventional art. Man is not in all directions symmetrical in the strict sense of the word. He has not two heads, two noses, or two mouths. The component elements in man are different. His very nature revolts against a planimetrical treatment. This was perfectly understood by the masters of arabesque, who have always turned man half into a fish, a plant, a serpent, a tendril, or some other form adapted for planimetrical treatment. Eurythmy and Proportion are the elements of higher organic forms—to which must be added direction or Action, and finally Expression.

      In most of the lower animals the vertebræ are horizontal, and coincident with the moving direction of the whole creature. In man, on the other hand, the vertebræ are vertical, in opposition to the moving direction which is horizontal; so that the vertebræ and line of motion are at right angles.

      In men, detached as they are from their horizontal basis, the soil—carrying their static force with them, and able to change it either from below, upwards, or from front to back—direction is of a complicated nature, and must be well studied, so as not to produce incongruities.

      If a woman or man were painted with the most beautiful and expressive face, but having it twisted round, so as to crown the spine, we should turn from it with disgust, as anyone endowed with the sense of beauty turns from acrobats, because the natural laws of gravitation and symmetry would be violated. This illustration may serve to prove, that there are laws in art with which we must make ourselves acquainted, and that the mere ‘right of taste,’ in the general sense of the words, cannot promote the understanding and appreciation of our artistic productions.

      Next to direction we have to take into account motion. This element is in animals and men produced by their inherent dynamic force, counteracted by the body itself, which represents the static force, or the ‘vis inertiæ,’ chaining them to the centre of gravitation in the earth.

      Motion again leads to expression and action.

      Expression is the effect of the conflicting static or dynamic (passive or active) state of the mind, so far as this state is revealed in the lineaments of the face.

      Action is the effect of the same conflicting force so far as it is expressed in the limbs and the position of the body.

      A third force, which is often used unconsciously, necessarily grows out of these elements—the controlling or ruling element, or, as Vitruvius has it, ‘the principle of authority.’ This element points out the preponderance of certain forms as the visible representatives of the general principles which we have stated, bringing into the variety of details, harmony and unity. This controlling element stands to the surrounding and united parts in the same relation as the key-note to a harmonious melody. Without that key-note no harmony—without the controlling element no beauty, were possible.

      Having proceeded step by step from the formation of matter in crystals to man, we may set down the following as the five principal elements necessary to beauty in art:—

      1. Symmetry.

       2. Eurythmy.

       3. Proportion.