10 NM. M. FENNEMAN 
surface waves. Any one point in the film would rise and fall 
vertically ; any particle of water adjacent to it would continue 
to describe its normal circle, gliding to-and-fro on the friction- 
less film and tracing a straight line upon its surface. The 
diameter of this orbit is represented by the vertical distance 
through which any point in the film swings. If the water above 
the film be viewed in cross section, the area in which it is mov- 
ing forward would equal that in which it moves backward. 
Action on a solid horizontal plane surface.—Ilf the film be sup- 
posed now to be stretched to a horizontal plane and to become 
a solid bottom of the ordinary kind, several changes become 
ecessary in the behavior of the adjacent water particles. The 
up-and-down movement in their orbits becomes impossible, but 
the to-and-fro movement, tracing straight lines on the surface, 
can be continued. Observation shows that this does occur, that 
particles near a shallow bottom move back and forward in straight 
lines, and that vertical movement gradually appears in the paths 
of higher particles, these paths being at first very flat ovals, but 
becoming higher and more nearly circular as the surface is 
approached." 
The energy of the vertical movement thus interfered with is 
partly expended in friction on the bottom, though it is quite 
possible that a part of it may be used in an increased horizontal 
amplitude.? It is a matter of observation that this flattening of 
orbits affects the movements of surface particles as well as of 
those below. This effect on the topmost orbits is in proportion 
to the degree of interference at the bottom. Very much elon- 
gated orbits indicate large friction, just as circular orbits indi- 
cate that there is no appreciable interference at the bottom. 
Effect on wave-length, etc— The immediate effect of retarda- 
tion of particles in contact with the bottom must be an increased 
"WEBER, Wellenlehre, p. 124. 
? The observations of the brothers Weber, as recorded in the table given in We/- 
lenlehre, p. 124,seem to show that the horizontal motion on a shallow bottom, while 
less than at the surface, is actually greater than a certain intermediate point. 
3 WEBER, Joc. cit. 
