it strikes. Persons of delicate ear believe that they can distinguish the fundamental note of a cascade. Savart has determined the tone of a liquid vein. Another cause of discontinuity in a cascade is derived from waves in the river or the supply-basin, which, continuing into the fall, produce puffs and ripples. The phenomenon is accentuated by the resistance of the air. When, by any means, one of these jets deviates a little from the route which the one before it followed, the masses projected ahead, having to open the way, are retarded, and are then joined by those which follow them. The phenomenon is one of accumulation, like that which produces the billows on the sea-coast and the bars at the mouths of rivers, under the action of the tide. But shortly these bold spurts, rended and scattered by the same cause that produced them, the friction of the air, meet their end by being reduced to dust. When too near, the observer, engaged with a thousand details, is not struck so much as he is at a distance, by the phenomena as a whole and their periodicity. We can distinguish, then, the periodical ranges of jets which are partly transformed into spurts, and in the tumultuous rush between two rocks the bubbles or vibrations produced by the shock. The line is nowhere vertical.
When the waves coming down from the feeding-basin reach the upper edge of the cascade parallel to that edge, the bubbles are dispersed in horizontal bands. But if the wave comes down at an angle, it forms rows of inclined fringes; while, if the cascade is fed by a brook with the characteristic waves of Fig. 2 (iv), starting from both shores toward the middle, those waves will continue the same in the cascade in the shape of more or less stationary lozenges. In this case, again, we are far away from vertical parallel lines.
It is time to look more closely at the form and constitution of the liquid sheet. In Fig. 5 (v) it is represented by two parallel lines as a ribbon, such as any person not instructed would design from memory. It is in reality wholly different, as will appear from Fig. 8 (x). Let us begin at the top. Immediately at the opening of the flow, from the moment when it is wholly abandoned to itself, the sheet begins to narrow and take the form of a triangular tongue, pointed below. Let us, before we go further, look into the cause of this first change of form. When we make the experiment with an inclined cylindrical vessel, as in Fig. 5 (v), our inclination is at first to attribute the contraction to the oblique centripetal direction communicated to the lateral molecules by the elliptical form of the surface of the water in the interior of the vessel. This explanation is insufficient, for the sheet escaping from a tube, a canal, or a prismatic vase with parallel sides, assumes the same form Figs. 8 (x), 13, 14, 15, 16, and 17. The ex-
