The second solution is found in cylindrical coordinates, 
and the solution is given in terms of the distance r from a 
fixed point, r, = 0. @ is given by equation (2.21) where 
HS (2rmr/L) is the first Hankel function of order zero (see 
Sommerfeld [1949]). If r is large and x,,y, are the coordi- 
nates where r = 0, then 9 is approximated by equation (2.22). 
The free surface,7, is then given by equation (2.23) under 
the same assumption that r is large. The same condition for 
the speed of the wave crests holds that was given in equation 
(2.20). The point of origin of the circular wave crest is 
arbitrary. 
Equations (2.21), (2.22), and (2.23) will not be used in 
this paper. Mathematical techniques similar to the ones which 
will be employed in this paper (but more difficult) are appli- 
cable to problems involving these equations. They are given 
here in the interest of completeness, and in order to make one 
very important point. 
For narrow fetches with very turbulent and extremely vari- 
able winds, and for wave generating areas such as those found 
in hurricanes, a detailed study of the sea surface would have 
to be made with these equations as a starting point. Problems 
in wave decay in particular must be studied because the form 
of equation (2.23) provides a means for the decrease of wave 
height with distance traveled. In view of these considerations, 
the results of this paper will be based upon the assumption 
that the elemental unit of.analysis is a wave of the form of 
equation (2.19). The consequences of this assumption will be 
Ages 
