in one direction. The other solution, given by a Hankel 
function, yields circular wave crests which radiate from a 
point source. 
The first solution is found in the Cartesian coordinate 
system which has been used so far. g is given by equation 
(2.18). 6 is an arbitrary phase lag, and A is the amplitude 
of the wave crest. 
From equations (2.18), (2.13), and (2.16), it follows that 
7) is given by equation (2.19). This representation for the 
free surface has been chosen in order to point out all the arbi- 
trary parameters in the solution. The most important one to 
note is the © which permits the choice of any wave direction, 
if © varies through 27 radians. The equation for the speed 
of waves in water of constant depth follows from equations (2.18), 
(2.16), and (2.17). The fact that the depth is constant per- 
mits the easy treatment of the problem. The speed of the crests 
is given by equation (2.20). Equation (2.19) is the only wave 
with straight crests, which travels with the classical wave 
velocity of waves with small amplitude. As written, it states 
that there are an infinite number of crests present, that the 
wave record will be observed for an infinite time at any point, 
that the period and wave length are everywhere the same and 
everywhere constant, and that the heights of all crests are 
the same. If any single one of these requirements is not 
satisfied in nature, then the equation is not valid, and a 
more refined analysis is needed. 
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