undisturbed again. Figures 3 and 4 are a group of graphs which 
show the wave records which would be observed at various fixed 
Xj» as a function of time. The graphs have been obtained by con- 
sidering Tables 4, 12, and 13 and hence values of 9 equal to 
1/20 sect and of T equal to 10 and 20 seconds. The phase of the 
wave crests has been chosen to go through zero at t, =0O. A 
slight variation in x' and t, within the accuracy of the last 
significant figure given for them would make this possible. The 
wave crests have been sketched in from the data given in these 
tables. It is simply too long and difficult a procedure to evalu- 
ate equation (4.9) by letting t vary through 2 second increments 
throughout a range of several thousand seconds in order to graph 
the free surface. Figures 3 and 4 are sufficiently accurate, 
however, to show the major features in the transformation of the 
wave group. 
From equation (4.12), it would also be possible to discuss 
the shape of the envelope as a function of x for a fixed time. 
The envelope is not a normal probability curve as a function of 
x for a fixed t since D varies with x. This aspect of the problem 
of evaluating the solution has not been investigated in as much 
detail as the problem of the variation in time at a fixed x. For 
T= tol sacwands on l= M/dloonsecas 
» the graphs shown in figure 5 have 
been obtained. The slight skewness shown by equation (4.12) 
(which is not so great as one might expect because the D's in the 
two places where they occur counteract each other) is not evident 
in the graphs. It might show up for other values of the parameters. 
- 67 =- 
