2 NV. M. FENNEMAN 
consider waves first in their free forms, while meeting no resist- 
ance and hence doing no external work. This condition is found 
in deep water. The various ways in which the bottom or shore 
may offer resistance and be subject to work may then be dis- 
cussed. 
WAVES IN WATER OF INFINITE DEPTH. 
When wave agitation does not reach the bottom of a body of 
water it is customary to speak of the depth as infinite, because 
the wave is not influenced by the existence of a bottom. 
PURE OSCILLATION. 
Orbits —In simple oscillatory waves each water particle 
moves ina circular and closed orbit. The water body itself, 
therefore, has no onward motion. These orbits diminish rapidly 
with depth, but so long as agitation does not reach the bottom, 
the orbits are circles at all depths. The particles on the crest 
are moving in the direction in which the wave is traveling and 
particles in the trough are moving with the same velocity in the 
opposite direction. 
Differential movement.— On a line in the direction of the wave 
movement (hence crossing the waves at right angles) each par- 
ticle is subject to a gliding between its neighbors. The amount 
of this gliding is of molecular dimensions, hence not infinitely 
small. It will be spoken of here as the differential movement of 
particles. For diagrammatic purposes it is convenient to consider 
this differential as a considerable arc of the orbit, hence particles 
are chosen which are removed from one another by a consider- 
able fraction of the length of the diameter. 
General form of wave.—In a series of particles moving in 
equal orbits each particle is more advanced in its orbit (has a 
more advanced phase) than the one in front of it. If a series 
«This principle was clearly elucidated by Gerstner in 1804. This and other fun- 
damental principles of oscillatory wave motion are clearly set forth in the report of the 
brothers Weber on their experiments conducted in the early part of the last century. 
See “‘ Wellenlehre, ERNST HEINRICH und WILHELM WEBER, Leipzic, 1825. This. 
report also summarizes Gerstner’s work and all other previous studies on waves from 
the time of Newton to 1820. 
