Put another way, for the same value of o , the amplitude of 
the envelope decreases twice as fast for 10-second waves as at 
does for 5-second waves. Forty-two and four tenths seconds be- 
fore and after the time, t_, the amplitude of the envelope is 
0.80. One hundred eighty-three seconds before and after t. the 
ampitude is 0.10. 
The above examples show that this method of computation 
breaks down the dependence on time of the amplitude of the enve- 
lope into two different parts. The time is given by t = t, ti ie 
The part, tos evaluates the gross effect of the speed of travel 
and it is of the order of magnitude of hours in the computations. 
t, depends only .on the value of Xy considered and the period of 
the waves under the envelope. The part t', evaluates the time 
it actually takes the wave group to pass a given point, and it 
is measured in seconds. t' depends only on the value of X, con- 
sidered and the value ofo. ‘Computation of the actual time t 
would require prohibitive accuracy in order to compute the time 
of passage of the wave group at large values of xy because t! 
is essentially the difference between two large numbers. 
Now compare Table 4 with Table 1. In Table 4, 0 equals 
1/20 sec7+, The maximum amplitude of the envelope dies down much 
more rapidly. In fact, Xj need be only four hundredths of the 
distance given in Table 1 for the amplitude to decrease a cor= 
responding amount. In Table 1, the envelope could travel 17.7 
km before the amplitude would decrease to nine tenths of its 
original value. In Table 4, the envelope would travel only .71 
km and then its amplitude would decrease to nine tenths of its 
pe 
