of less than one tenth to maximum amplitude in 2300 seconds 
(38 minutes). This means that after the passage of 230 waves, 
the train is essentially constant in amplitude. 
An analysis of equations (5.15), (5.16) and (5.17) would 
show that the trailing end of the wave train would pass near the 
time t' = 2nT after the forward end. The procedure employed in 
the study of the forward end of the wave train could be employed 
to study the trailing end of the wave train, and similar equations 
and results could be obtained. 
Between the time t' equals zero and t' = 2nT, for the example 
considered above there would always be essentially 3600 wave crests 
in the wave train. A few extra would be found before t' = O and 
after t' = 2nT. From K = O to K = 4 in figure 10, for the example 
considered above when xy equals 439 km there would be only 300 
waves which are not quite of constant amplitude. At the trailing 
end, there would be another 300 waves. Thus only a total of 600 
waves out of the 3600 waves, or 16.7%, would be modulated at the 
ends of the train. 
Other quantities of interest are also graphed in figure 9. 
The relative amplitudes of the potential energy at various times 
is shown by the dashed graph. The gradual phase shift as a position 
of t' is also shown above the graphs of the envelope and the po- 
tential energy. In the forward part of the wave train before 
t' = 0, the phase shifts might cause waves which are not approxi- 
mately sinusoidal in form. 
For the relatively large values of xy employed in figure 9, 
the wave record as a function of t! which would be observed at Xy 
- 98 - 
