be extended to the more complicated patterns. 
The simplest short crested wave system could be represented 
by equation (8.1) where O<a<1. The sea surface at t = 0 is 
an alternating sequence of elliptically shaped hills and valleys. 
As t varies they appear to move in the positive x direction. 
At any fixed y, the sea surface is sinusoidal in the x direction 
with an apparent length in the x direction given by Lex) in 
equation (8.2). The velocity in the x direction of the crests 
is given by C;,) in equation (8.3). Note that L(,) is not equal 
to C(xte 
Equations (8.1), (8.2) and (8.3) describe a possible con- 
figuration of the sea surface, but the particular method of pre- 
sentation employed is limited to that one particular form and 
minor modifications and extensions thereof. By a trigonometric 
identity equation (8.1) can be written in the form of equation 
(8.4). The short crested waves then turn out to be simply the 
interference pattern between two long crested waves which are 
traveling in different directions. The first wave is traveling 
in the direction of the line /1 - a- x + ay = 0. It has in- 
finitely long crests oriented perpendicularly to this line. 
The individual crests have the classical wave length and travel 
with the classical speed. The second wave is traveling in the 
direction of the line /1-a* x -ay = 0. In this direction, 
it has all the properties of classical waves. 
Equation (8.1) is thus another way to analyze equation (8.4). 
It can be employed only if the two waves have the same amplitude 
although interesting results can be found if the two waves in 
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