to infinity of (sin x')/x' which has the value 7. The final 
expression in equation (8.12) is thus the desired limiting value. 
If A is permitted to approach infinity in equations (8.9), 
the same result will hold. The results hold for any preassigned 
A no matter how large, and therefore they hold for A infinite in 
the limit. 
The initial value problem in the y,t plane for a disturbance 
of finite duration and width 
In a storm.at sea, the waves are quite irregular. There 
are high waves, and low waves. The high waves sometimes appear 
to come in groups followed by times when the waves are relatively 
low. In addition, even when the waves are high the crests are 
not very long, possibly only ten times the distance between suc- 
cessive crests. .Consider then a wave record in deep water ob- 
tained by a whole line of wave recorders along a segment of the 
line x = O parallel to the dominant orientation of the crests. 
If all of the wave records were properly synchronized, it would 
be possible to obtain a plot of wave height as a function of time 
and the position of each of the recorders on the line x = 0. 
The free surface would then be expressible as a function of y 
and t inside of a closed curve given by some function of y and t. 
Inside of this closed curve let the sea surface be given by the 
observations. Outside of the closed curve, let the sea surface 
be identially zero in amplitude, and if desired smooth the sharp 
edges off the boundary. The result is a finite short crested 
wave system observed as a function of y and t at an arbitrary 
origin in deep water. It could represent a whole storm at sea 
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