14 N. M. FENNEMAN 
water causes the motion which the water loses to be communi- 
cated to the materials of the bottom. The case is roughly 
analogous to the wheels of a locomotive, which in ‘‘flying the 
track’”’ brush the sand on the track backward. 
The case of wind-driven waves.—The above case is applicable 
only to waves of pure oscillation, which have of necessity been 
generated in deep water and are advancing over a shallow 
bottom. If the wind is blowing at the same time in the direc- 
tion of wave movement, the result will be similar to that found 
in considering a mathematical plane above wave-base, provided, 
of course, that the return of the water is by horizontal circula- 
tion. The action of the wind increases the forward motion 
under crests and diminishes the backward motion under troughs. 
When the effect of this action reaches a certain amount, the 
influences named above, which give dominance to the backward 
movement at the bottom, will be counterbalanced, and any 
greater effect of the wind will give, at the bottom, an excess of 
forward movement. A moderate effect of the wind is probably 
usually sufficient to overcome the backward brushing due to 
oscillation alone. If the return is by vertical circulation, any 
increase in current above involves an increased reverse current 
below. 
The case of breaking waves——When waves generated in deep 
water advance over a bottom sufficiently shallow to cause 
breaking, a new factor is introduced. In this case there is a 
tendency to the formation of positive waves of translation, 
which may sometimes develop typically, though doubtless more 
often their motion enters in merely as a component. It is in 
the nature of these that all the particles in and under the wave 
form move forward and not backward, and the forward motion 
is the same at all depths.t To the extent that this factor enters, 
the effect on the bottom will of course be to urge material in 
the direction of wave movement. 
™See RUSSELL, The Wave of Translation, p. 42; Report on Waves, p. 307; also 
D’Aurta, “A New Theory of the Propagation of Waves in Liquids,” Journal of the 
Franklin Institute, 1890, p. 460. The last named is a mathematical discussion. 
