t =-nt for t in equation (4.9) followed by a summation from 
n=-+pton=+p. The same difficulties apply to this formu- 
lation of the solution that applied to the alternate solution for 
the infinitely long (in time)periodictrain of finite wave groups. 
Energy considerations 
The results so far obtained have been derived from the classi: 
cal theory. There is no physical mechanism in the mathematics 
which would result in the degradation of energy from kinetic and 
potential energy to heat energy from the effects of friction. 
There is one effect present, namely dispersion, which spreads out 
the energy in time and space that was originally concentrated at 
the origin. 
The potential energy at an instant of time for a wit area 
of the sea surface is given by equation (6.18). In classical theory 
in which waves are considered to be purely sinusoidal, it is per- 
missible to average over one wave length or over one period and to 
discuss the average as an average over one cycle of the potential 
energy. For irregular wave records, such as equation (6.5), this 
process is inadequate. 
Any record of the sea surface obtained as a function of time 
can be treated by equation (6.19). If T is increased, for different 
t*, then the average potential energy may settle down to a constant 
value in which P.E. would be independent of time. 
All of the wave records discussed herein are built up of simple 
Sine waves, and for sine waves the potential energy averaged over 
time at a fixed point equals the kinetic energy averaged over time 
at a fixed point. This principle is also true if the disturbance 
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