equation for the envelope takes the form -( o7/D)(t)* 
(equation (4.14)). This shows that it takes longer for the 
envelope to decrease to 1/e of its maximum value at x = Xy 
than it does at x = 0. 
The behavior of the envelope as a function of time at a 
fixed point is shown by Tables 1 through 4 for the same values 
of o and T which were employed in graphing figure 1 and for 
G =) 1720, La= 20)sec. ‘Table shows) the appropriate values 
for o equal to 1/100 sec™+ and T equal to either 5 seconds or 
10 seconds. At x equal to zero and t equal to zero the amplitude 
of the envelope is one. Thirty-two and four tenths seconds be-=- 
fore or after t equal to zero the amplitude of the envelope at 
X equal to zero is nine tenths. On hundred fifty-two seconds 
before or after t equal to zero the amplitude of the envelope 
is one tenth. The highest part of the wave group passes the point 
x equal to zero in three hundred and four seconds (5.07 min). 
Of course, the wave group never completely passes a given point. 
For example, it takes five hundred twenty-two seconds (or 8.7 
minutes) for the .O1 values of the envelope to pass. 
When the maximum amplitude of the wave group reaches the 
point x equal to 17.7 km, the maximum possible value of the enve- 
lope is 0.90. The maximum amplitude of the wave group passes 
that point x = 1.77 km at the time indicated by too which in 
this case is given by 4,560 seconds (or 1.27 hours) if the period 
of the waves under the envelope is 5 seconds and by 2280 seconds 
(or -635 hours) if the period of the waves under the envelope is 
10 seconds. This shows that the envelope of the 10 second waves 
travels twice as fast as the envelove of the five second waves. 
SAG) 
