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. 4. Direction or motion. 5. Expression. α. Symmetry has already been amply treated. β. Eurythmy is either stereometric or planimetric. It is stereometric in balls and in regular solid bodies, such as the tetrahedron, a figure of four equal triangular faces, or the polyhedron, a figure with many sides. These forms are symmetrical without any controlling element. Such an element shows itself first in the ellipsoid--distinct from the oval--in the prism, and the pyramid. Planimetric eurythmy preponderates in snow-crystals, flowers, plants, trees, and the lowest animals. The controlling element shows itself in the grouping of the single parts round a common centre, which is often distinguished by a contrast in forms or colours. It is unconsciously expressed by a sign or mark.