r 
x = 0 at the time t = 0. The free surfiace for large et /4x 
is found by partial differentiation of equation (2.30) with 
respect to t and multiplication by 1/gp. Again the physical 
reality of the problem is seriously open to question. 
The two problems described above have been used (frequently 
in a most uncritical way) by many authors in attempts to devise 
methods for nomecasiamae ocean waves. Until some ship reports 
an infinitely high, infinitely long, infinitesimally wide colunn 
of water over the ocean or an infinitely intense local impulse 
concentrated on a line, it will be necessary to interpret these 
results "cum grano salis." 
There is one remaining classical application of the Fourier 
Integral Theorem which is of great interest in this study. It 
is the Gaussian wave packet. Coulson [1943] gives a readily 
available summary of the chief results obtained (see reference; 
ppe 135-138). The representation for the free surface obtained 
from the Gaussian wave packet depended upon the integration of 
equation (2.31) where to transform to the notation of equation 
(2.29), K would be given by K =p Je and n would be given by 
n= Kee [been 
[o0) 
—O(K-Ke)* i277 (Kx-nt) 
nlx,t) = /Ae e dK (2.31) 
For t = 0, the integral can easily be evaluated and the 
free surface is found to be given by equation (2.32). 
*Coulson [1943] uses ¢ for the free surface and not the 
potential function. 
Li 36) = 
