The very first of Mayeux’s illustrations (Fig. 1) introduces the style of the teaching of the volume and of this article. Let me translate his accompanying description: “Here are two recipients of the same height, made of the same material, and with about equal care. Each has two handles and is decorated by the same number of fillets. The one marked _A_ is the work of an ordinary potter, without artistic instinct or education. The other, _B_, is a Greek vase of fine and delicate taste. No one can fail to appreciate the superiority of _B_ to _A_. The purity of its profile, the graceful manner in which the handles are attached, the calculated division of the fillets, establish at once a considerable difference of artistic value between the two objects.” If Mayeux were addressing beginners he might add that one reason why all jugs and vases are round is that the shape is the easiest to make. The potter’s wheel must have been one of the very earliest inventions of semi-civilized races. Besides, as a drop of water is globular, it seems appropriate that liquids should be contained in round receptacles. A square jug would not only seem inappropriate, but it would be ugly and perhaps difficult to handle. Notice in _B_ how much better the different parts are distinguished: the neck from the body of the vessel, and the body of the vessel from the foot. Two fillets are also very appropriately put where the vessel is largest, and where they seem to convey a sense of increased strength exactly where the pressure is greatest. You will find all the way through the study of ornament that utility, or use, is a fundamental principle which can not be violated without impairing beauty. Before presenting objects for comparison it may be well to pass in review the elements which compose all objects. Decoration is the application of ornament to form. It therefore presupposes knowledge of both form and ornament, for form must be understood by itself, and ornament by itself, before the proper ornament may be selected for the given form. The elements of form are length, breadth, and thickness. A mathematical point is conceived to have no dimensions, a mathematical line but one, and a mathematical plane but two. But in actuality there is no tangible object without the third dimension--thickness. Still, where two dimensions are very much more prominent than the third--as, for instance, in a plaque, in the side of a room, in a single elevation of a building, or whenever merely the surface of an object is viewed--the third dimension may be left out of consideration. Lines and the surfaces they bound--that is, length and breadth--are the two elements of form which play the chief part in decoration. [Illustration: FIG. 2.] [Illustration: FIG. 3.]