a regular dam or gliding over a smooth, rock, the irregularities of the latter may produce lines in the direction of the current; but true painters make only the most moderate use of the straight line.
Are there not more grounds of resemblance between the points A and B or α and β which appertain, however, to different generators than between the points A and α of the same generator? Suppose the liquid sheet decomposed into its elementary veins; each of them is differently constituted in its several parts. At its
Fig. 5.
origin it is full, uniform, and transparent; lower down it shows real or apparent swellings and contractions; and still farther down it resolves itself into distinct drops. The water-sheet should consequently have an entirely different constitution at A from that at α, but the same at A and at B. It is proper, therefore, to represent as similar, not the points of the same parabola, but those of the same horizontal range; so, in the reflection of surrounding objects, the surface at the upper part of the parabola, making a smaller angle with the horizon, would produce a different effect from that at the lower part. At A and B it would reflect chiefly the sky; at a and b, perhaps, the rocks; while at α and β it would be white and reflect nothing.
Independently of phenomena which we are still to study, and paradoxical as it may appear, we can say that, if there are bands or zones in a cascade, they are rather horizontal than vertical. Our design vi, Fig. 5, still false and incomplete in many respects, looks more like a real fall of water than the design v, Fig. 5, with which we started. By this horizontal rather than vertical disposition of the effects of light, color, and reflections, the image gains much in life and truth.
When the eye has become accustomed, by repeated observations, to the peculiarities of the liquid elements, it can at last distinguish, in each jet of any velocity, a jerking or vibratory movement, a kind of trepidation or pulsation, directed horizontally, up and down, or down and up. It was believed formerly to be an optical illusion; but instantaneous photography and other obser-
