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the first wave in the group it is seen to decrease continually in height, 

 finally disappearing altogether in the undisturbed water ahead of the 

 group. The last wave in the group is usually not so clearly defined 

 as the first but, if the plunger is stopped quickly, another wave is 

 seen to develop behind the last wave generated. As the wave group 

 continues through the tank this process is repeated, the leading waves 

 gradually disappearing whUe new waves develop in the rear. Further- 

 more, if attention is fixed on any one wave initially at the rear of the 

 group, it will be seen to advance in group position and, if the tank 

 is long enough, finally disappear at the front. The same phenomenon 

 appears in the bow waves of a ship, each wave as it moves diagonally 

 outward loses height and finally disappears whUe at the rear waves 

 appear which are not attached to the ship. 



The reason for this behavior of a group of waves lies in the rate 

 of transmission of energy. The mathematical treatment will be 

 summarized later but an approximately correct physical explanation 

 can be made in simple terms. Assume to be correct Gaillard's state- 

 ment that half of the wave energy moves forward with the wave 

 form (at the wave velocity) . As the first wave in the group advances 

 one wave length, its form induces corresponding velocities in the pre- 

 viously undisturbed water and the kinetic energy corresponding to 

 these velocities must be drawn from the energy flowing ahead with 

 the form. If there is equipartition of energy in the wave, half of 

 the potential energy which advanced with the wave must be given 

 over to the kinetic form and the wave loses height. Advancing 

 another wave length another half of the potential energy is used to 

 supply kinetic energy to the undisturbed liquid. The process con- 

 tinues until the first wave is too small to identify. The second, 

 third, and subsequent waves move into water already disturbed 

 and the rate at which they lose height is less than for the first wave. 

 At the rear of the group, the potential energy might be imagined as 

 moving ahead, leaving a flat surface and half of the total energy 

 behind as kinetic energy. But the velocity pattern is such that flow 

 converges toward one section thus developuig a crest and diverges 

 from another section forming a trough. Thus the kinetic energy is 

 converted into potential and a wave develops in the rear of the 

 group. This description is crude. The phenomenon does not pro- 

 ceed in the stepwise fashion described; but the general conclusion is 

 correct, namely, that if the whole wave energy does not move with the 

 wave velocity, the leading wave in the group must lose height and 

 other waves develop at the rear. It is apparent that the group of 

 waves considered as an entity moves more slowly than the waves 

 comprising it at any moment. 



If we imagine the entire wave energy to advance with the wave 

 velocity, then energy is being supplied to the undisturbed water ahead 



