16 N. M. FENNEMAN 
above, but not the horizontal. The second influence toward 
diminution is the friction on the bottom which is shared by the 
particles above. 
Opposite tendencies simultaneous—On a sloping surface the 
opposing tendencies act at the same time. It is evident that in 
proportion as the slope is steep, sudden enlargement will be 
favored, and that slow shallowing favors reduction in size 
because of the long continued action of friction. Theoretically, 
there should be a grade on which an incoming wave should 
suffer no change of height, but since the form and internal 
movements would change, this ideal grade is not of importance 
in considering the work of water on the bottom. 
Tendency to decreased wave-length.— If the supposed tendency 
toward orbital increase be balanced by the opposite tendency 
arising from friction, there will, of course, be no increase in the 
length or height. However, when waves do increase in height, 
showing that the orbits have enlarged, they are still very com- 
monly diminished in length and of necessity increased in steep- 
ness. This is readily explained by the increased differential 
movement of particles, initiated by friction on the bottom. 
Tendency to steepening due to wind.—The largest on-shore 
waves usually act in conjunction with the wind blowing in the 
approximate direction of their movement. The effect of wind 
on waves in deep water was seen to be similar to the effect of a 
shallow bottom, namely, (1) increase of orbits; (2) increase of 
steepness ; (3) asymmetrical form. These effects may be carried 
to the point of breaking, even in water of infinite depth (white- 
caps). Ona shallow bottom the effects are increased by the 
concurrent action of the two factors. Where there is no wind 
waves are commonly supposed to break in water whose depth is 
equal to or a little greater than the height of the waves above 
the level of repose.* When waves advancing on a shallow bot- 
tom are already strained by the wind, they may break with much 
regularity in much greater depths of water, equal to perhaps two, 
three, or four times the height of the wave. Thus while the 
* RUSSELL, Report on Waves, p. 245. 
