Jtn Wu. 
A typical trace of a series of automatic sorting and counting for one 
instrument inclination is shown in figure 12a. Channel 10 represents 
the lower cutoff, below which the intensity of signal is comparable 
with noise; such light pulses are not counted. The upper bound of 
channel 50 is set just above the saturation voltage, so that the satu- 
rated signals can be counted. From the digitized data, the total num- 
ber of signals for each angle can be obtained. A gaussian curve, fitted 
on the basis of the least-square principle, is shown in figure 13 to re- 
present the distribution of water-surface slope for each wind velocity. 
(For clarity, the data points are not shown in figure 13), 
The data shown in figure 12a are first replotted in figure 12b, 
where the horizontal axis is transformed from channel number (or vol- 
tage) into radius of curvature. The lower cutoff radius of curvature 
of the present optical instrument is marked by a long vertical line 
shown on the left in figure 12b. The centroid is then determined of the 
area, shown in figure 12b, enclosed by the measured distribution cur- 
ve, the horizontal axis and the lower cutoff radius of curvature. The 
centroid, indicated in the same figure, is the average absolute radius 
of curvature. The average (absolute) radii of curvature, viewed from 
different angles for various wind velocities, are presented in figure 13. 
V.3 Features of surface-curvature measurements. 
The typical distribution of radii of curvature is shown in fi- 
gure 12b, of which the shape is in rough agreement with that obtained 
analytically by Longuet-Higgins (1959) for a gaussian surface, A com- 
plete distribution of radii of curvature, extending to very small radii 
of curvature, was not obtained. The present measurements, however, 
are sufficient for determining the average radius of curvature, Any 
uncertainty on the lower end of the data, the righ-hand side of figure 
12b, would not affect the determination of the centroid of the area 
under the distribution curve. 
The average radius of curvature is seen in figure 13 to have 
its minimum value at a small but positive viewing angle. The average 
radius generally increases when the observation changes continuously 
from zero to negative viewing angles and reaches a rather high value 
at a steep negative viewing angle. On the other hand, the average ra- 
dius of curvature first decreases to the minimum value, then increases 
when the observation angle increases, and finally reaches a high value 
at a steep positive viewing angle. A continuous curve was drawn to 
indicate the trend of the data, which is believed to be the first set of 
radii of curvature of wind-disturbed water surfaces measured from 
various viewing angles and at different wind velocities. 
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