139. Then think what the investigation of the bottle branches into, joined with that of its necessary companion, the cup. There is a sketch for you of the cup of cups, the pure Greek +kantharos+, which is always in the hand of Dionusos, as the thunderbolt is in that of Zeus. Learn but to draw that thoroughly, and you won't have much more to learn of abstract form; for the investigation of the kinds of line that limit this will lead you into all the practical geometry of nature; the ellipses of her sea-bays in perspective; the parabolas of her waterfalls and fountains in profile; the catenary curves of their falling festoons in front; the infinite variety of accelerated or retarded curvature in every condition of mountain debris. But do you think mere science can measure for you any of these things? That book on the table is one of the four volumes of Sir William Hamilton's "Greek Vases." He has measured every important vase vertically and horizontally, with precision altogether admirable, and which may, I hope, induce you to have patience with me in the much less complex, though even more scrupulous, measurements which I shall require on my own examples. Yet English pottery remains precisely where it was, in spite of all this investigation. Do you fancy a Greek workman ever made a vase by measurement? He dashed it from his hand on the wheel, and it was beautiful: and a Venetian glass-blower swept you a curve of crystal from the end of his pipe; and Reynolds or Tintoret swept you a curve of colour from their pencils, as a musician the cadence of a note, unerring, and to be measured, if you please, afterwards, with the exactitude of Divine law.
140. But, if the truth and beauty of art are thus beyond attainment by help of science, how much more its invention? I must defer what I have chiefly to say on this head till next lecture; but to-day I can illustrate, simply, the position of invention with respect to science in one very important group of inorganic forms--those of drapery.
141. If you throw at random over a rod a piece of drapery of any material which will fall into graceful folds, you will get a series of sinuous folds in catenary curves: and any given disposition of these will be nearly as agreeable as any other; though, if you throw the stuff on the rod a thousand times, it will not fall twice alike.