VIEWS OF RUNNING WATER. 651 



it strikes. Persons of delicate ear believe that they can distin- 

 guish 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 distin- 

 guish, then, the periodical ranges of jets which are partly trans- 

 formed 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 aban- 

 doned 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, as- 

 sumes the same form Figs. 8 (x), 13, 14, 15, 16, and 17. The ex- 



