near t = 0. The parameter, o0 , determines the rate at which 
the probability curve envelope dies out from t = O as t becomes 
large either positively or negatively. The parameter, T, deter- 
mines the period of the sinusoidal term which is modulated by 
the probability curve. For example if a0 = 1/30 sec7-, A = 3 
meters, and t = 10 seconds, in three cycles of the sinusoidal 
term the amplitude of the disturbance would die down from a peak 
near 3 meters to a value of about 1.1 meters. In six cycles the 
amplitude would be .4 meters; in nine cycles it would be 9 db5) 
meters; and in twelve cycles it would be .055 meters. Thus for 
these values of the parameters, the disturbance would essentially 
pass completely in two hundred and forty seconds (four minutes). 
For this reason, the wave group will be referred to as a finite 
wave group because it lasts for only a finite length of time at 
the origin. 
Two hours later at the point x = 0, y = 0, z = 0, the sea 
surface is essentially undisturbed. It would be nice to know 
where the disturbance is at two hours after the time t = 0, and 
what disturbance of the free surface it is causing wherever it 
is. It would also be nice to know what pressure disturbance at 
depths below the free surface is being caused by the passage of 
the wave group overhead. 
Method of solution 
The first step in solving the problem is to find the contin- 
uous Fourier spectrum of the function given by equation Cami 
The expression,7) (0,0,t),is an odd function, that is, 7 (0,0,t) 
equals =m) (0,0,-t), and so only b(y ) must be found as given by 
=- 37 = 
