maximum amplitude given by A/2/ra when p = 27/T. The larger 
the value of o the more slowly the probability curve dies down 
to zero as varies and the lower the peak amplitude. Aso 
approaches zero, c(p) approaches an infinitely high spike at 
the point p = 2r/f. Note that as o approaches zero, equation 
(4.1) approaches 7 (t) = A sin 2rt/T, that equation (4.8) 
approaches the correct expression for the pressure which would 
be caused by a purely sinusoidal wave, and that equation (4.9) 
approaches 7 (x,t) = A sin(27x/L - 2rt/T) where L is the appro- 
priate wave length for a wave with a period, T, in deep water. 
The continuous spectrum of the disturbances is graphed in 
figure 1 for A equal to unity, 7 = 1/20, 1/30, 1/50, and 1/100 
sec and T = 5 and 10 sec. The shorter the duration of the wave 
group, the wider the spread of the wave spectrum, and it should 
be expected that the more rapidly the shape of the disturbance 
will change as it travels onward. 
In the formulation of the problem, part of the spectrum 
of the wave group at x = O was made to travel in the negative x 
direction. As a result an integral form of the solution was ob- 
tained which could be evaluated in closed form. If this had 
not been done at that time, the solution could only have been 
obtained in series form and it would have been more difficult 
to interpret and evaluate. Figure 1 shows that the contribution 
to the total spectrum of these components is indeed so small 
that it does not show on the graphs for the values of the para- 
meters employed. It can be concluded that the effect of this 
tail of the probability curve which exists for negative values 
of # will not affect the properties of the solution very much. 
Bey 
