PROFILE OF THE SUBAQUEOUS SHORE TERRACE 15 
WAVES IN SHALLOWING WATER. 
Tendency to enlargement of orbits—\When a system of waves 
generated in deep water reaches shallow water, certain forces 
operate to increase the sizes of the orbits, while others produce 
the opposite tendency. In general the increase of orbital 
motion is due to the transmittal of the motion of a larger 
amount of water to a smaller amount.? 
If the shallow water be separated from the deep water by a 
vertical face (BC in Fig. 10), the change may operate in some 
manner similar to the following: The deep water on the right 
side of the figure is agitated to the depth of C by waves travel- 
ing toward the left. The motion of particles below the level of 
& is influenced by the vertical face BC, this influence being 
greater in proportion to their nearness. Those in contact with 
the surface must move in straight lines up and down, while 
those farther away describe ovals whose longer diameters are 
vertical, and whose shapes become more circular with distance 
from BC. The energy of the horizontal motion thus lost is, of 
necessity, partly expended in friction on the vertical face. That 
which remains must be devoted to increasing the vertical move- 
ment. By this means it is again communicated to the particles 
above the level of B. 
If the change from-deep to shallow water be gradual, the 
analysis of the process is essentially the same. In this case, 
however, the circular orbits below will give way to straight line 
movement, not vertical, but parallel to the sloping bottom DC. 
As before, friction will consume a part of the energy which 
orbital motion has lost, the remainder being expended in 
increased movement parallel to the sloping bottom. Of this 
movement the vertical component will go to increasing the ver- 
tical axis of the orbits above. 
Tendency to diminishing orbits.—Along with the above tendency 
to increased orbits come two tendencies toward diminution. 
The first of these is the influence of the flatter orbits of the 
lower particles. It tends to diminish the vertical movement 
™Compare C. S. LYMAN, loc. ci¢., p. 193. 
