by Stanton (1937) in an experimental 50-foot tank 
under closely controlled conditions. The other 
sources of observations have been discussed 
already. All observations have been tabulated 
(table II, appendix 2) and plotted on figure 6, 
and they are in fair agreement with theory. For 
large values of gz/U? the observed values lie 
slightly above the theoretical values. When 
examining the agreement between theory and 
observation (fig. 6) it should be considered that 
observed values of fetch vary between 50 feet and 
more than a thousand kilometers, and that other 
parameters also vary over wide limits. 
3a. Wave height against duration and wind 
velocity.—Seventeen observations could be found 
to test this relationship. Observations marked 
“BERKELEY” were taken by means of instru- 
ments from weather ships in the Pacific (unpub- 
lished reports). Fetch, duration, and wind veloc- 
ity were determined from weather maps. Dura- 
tions were corrected for initial wave heights 
according to the method given in H. O. Misc. 
11275. One observation off the coast of Massa- 
chusetts by Emmons and Clarke (unpublished 
report) was adjusted in a similar manner, but the 
wave height was determined by a photographic 
method. For the iatter observation the duration 
time was unusually well defined since the waves 
were generated by a storm which formed very 
suddenly. One observation marked ‘“‘DOVER,” 
England, was also taken during a period when the 
wind rose abruptly from zero to Beaufort 4. Ac- 
cording to Kriimmel (1911, p. 75), an old observa- 
tion by Paris is of particular interest: ‘He noticed 
waves in the southern Indian Ocean rising to an 
over-all height of 6 to 7 meters as a result of a 
strong storm which lasted 4 days or, roughly, 100 
hours, with remarkable uniformity. The fetch 
can undoubtedly be set at infinite* * *.” This 
wave height was considered by Kriimmel to repre- 
sent the maximum wave height for the existing 
wind of 16 m/sec, a conclusion which, according to 
figure 7, agrees remarkably well with theory. The 
other observation was taken during the same se- 
quence after a duration of oniy 24 hours. One 
observation by Kriimmel himself in the equatorial 
Pacific is also included (Kriimmel, 1911, p. 17). 
The observations available at this time confirm 
the theoretical relationship between wave height, 
gH/U,? and duration, gt/U, but further observa- 
tions, particularly for short durations and at very 
high wind velocities, are very desirable. 
25 
3b. Wave velocity against duration and wind 
velocity—The manner in which all 15 observations 
plotted in figure 7 were taken has already been 
discussed. Here the agreement between theory 
and observations is poorer than it has been for all 
other relationships. All observations by Berkeley 
and U.S. 8. Augusta give high values for the wave 
velocity; those marked ‘‘Dover, Kriimmel, and 
Paris” are too low. Further observations are 
particularly desirable to check the relationship 
between wave velocity and duration. 
4. Wave height against fetch—Stevenson has 
established an empirical formula giving the 
“greatest’’ wave height, H, in cm. as function of 
the fetch, z, im cm. (Kriimmel, 1911, p. 68), 
according to which 
H=0.105y'2 (80) 
The formula was established by means of data 
from lakes where the value of z ranged from a few 
kilometers up to about 250 km. Stevenson pointed 
out that for small values of z the wave heights 
were greater than those given by the above simple 
equation. For the Mediterranean, Cornish (1934 
p. 33) has verified the relation for fetches up to 
830 km., and it is generally assumed that the rela- 
tionship holds for values of x up to 1,000 km. 
The formula is incomplete since it does not take 
the wind velocity into account but it is intended 
to apply at the highest wind velocity that can be 
expected to occur. A few of the observations 
which served as basis for Stevenson’s law did in- 
clude wind velocity and those, at least, were made 
during unusually strong winds. 
The dimensionless relationship between H, 2, 
and U shown in figure 6 can be made to agree 
with equation 80 if the following relation existed 
between fetch and wind velocity: 
etch\ (km!) Ressssssseee eee 
Wind velocity (cm./sec.)_..-------- 
10 50 100 250 500 1,000 
1,230 1,260 1,370 1,600 1,870 2,100 
Such a relationship may exist because the wind 
velocities are higher over water than over land 
and the greater the body of water, the greater is 
the “‘maximum wind velocity” over the water. 
5. Wave height and wind duration.—According 
to common experience at sea a high wind can 
generate a rough sea in a few hours. C. Boergen 
pointed out (Kriimmel, 1911, p. 73) that the height 
of waves does not increase linearly with the dura- 
tion of the wind, but that the increase is rapid in 
the beginning and becomes slower later on. For 
that reason Boergen suggested a relationship 
