PROPIEE OFx DHE SUBAQGULOUS SHORE, TERRACE 9 
but broader under the troughs than under the crests. Jn any one 
such layer the water is moving forward under the crests (point D, 
Fig. 9) at the same velocity with which it moves backward 
under the troughs (point & of same layer). Of two adjacent 
layers the lower one is composed of slower-moving water. The 
line AB, drawn in a horizontal plane, traverses higher layers of 
water under troughs (at point C) and lower layers under crests 
(point D). Therefore the backward moving water along this 
plane has a more rapid motion than that moving forward. The 
area covered by it on the horizontal plane is also more than that 
covered by the forward moving water. This excess of backward 
movement below is the necessary correlative of the excess of 
forward movement above, for above the plane traversing the 
centers of the topmost orbits the movement on all planes is 
forward. 
The same when waves are wind-driven.— lf now the water be 
conceived to be driven by a wind, the current movement pro- 
duced at any given depth must be added to the forward move- 
ment in the corresponding strips which lie below the crests, and 
subtracted from the backward movement in those under the 
troughs. The forward and backward velocities in any one 
layer between two trochoidal planes are now no longer equal. 
When a certain rate of current is reached, the forward move- 
ment in the lower layer traversed by the horizontal plane under 
the crests (point D, Fig. 9) will equal the backward movement 
in the upper layer which the plane traverses under the troughs 
(point C). A certain force of wind will therefore cause_a bal- 
ance of to-and-fro movements at a horizontal plane below the 
surface. Any greater force will cause an excess of forward 
motion. 
Film representing surface of continuity—If in one of the sur- 
faces of continuity in a system of waves of pure oscillation, a 
film could be introduced which is perfectly flexible and friction- 
less, this film would show alternate depressions and elevations 
corresponding to those on the surface of the water, but less 
sharply curved. The curves would progress after the manner of 
