Page:Elementary Text-book of Physics (Anthony, 1897).djvu/155

§ 121] moving, in the lower part of the circle in the opposite direction. The velocity of the wave was found to be dependent on its height and on the period of oscillation in the wave, and to be independent of the density of the liquid. The disturbance of the liquid by the wave is not merely on the surface, but extends to a considerable depth; as the depth increases the elliptic paths of the particles approach more and more closely to short horizontal lines.

The theory of these waves is extremely complicated, and has not yet been satisfactorily worked out; but we can indicate in a general way their causes and the mode of their propagation. Imagine a small hillock of water elevated at some print in the surface, and consider a particle at the base of this hillock; the hydrostatic pressure arising from the elevated column near it will tend to move it upward and outward from the centre of the hillock. It will accordingly begin to move in the upper half of its circular path and in the direction in which the wave is propagated; the precise form of its path being determined by the changes of pressure which it experiences and by its inertia. Since the pressure which sets it in motion will be different for different heights of the hillock which gives rise to it, the velocity of the particles, and therefore also the velocity of the wave, will depend on the height of the wave, being greater as this is greater; the velocity of the wave is also greater as the wave length is greater. Since the pressure behind the particle and the inertia are both proportional to the density of the liquid, it is evident that the acceleration of the particle will be the same under similar circumstances, whatever be its density, so that the velocity of the wave should not depend on the density of the liquid.

The form of a wave is greatly modified by the character of the channel in which it moves, on account of the motion of the particles extending to a considerable depth, and on account of their viscosity. On the free surface of a large and very deep body of water the successive waves have the same form; the slope of the crest is a little steeper than the slope of the hollow, and its length is less than that of the hollow. As the depth decreases, the slope