is measured the »ther two can be computed 
(equation 4). Numerous measurements (Kriim- 
mel, 1911, or Sverdrup et al., 1942, p.526) are in 
fair agreement with theoretical expectation. The 
theory also requires the ratio H/L not to exceed 
1/7, a fact fully confirmed by measurements 
which rarely give values as high as 1/10. There- 
fore, observations show that the wave formulae 
are applicable to wind waves. 
The empirical knowledge of the relation between 
Wind and waves, however, presents a picture of 
confusion because the variables which influence 
the development of waves have not been properly 
recognized and separated. A complete observa- 
tion should consist of at least the following five 
variables: 
a. Significant wave height, H. 
b. Significant wave period, 7, or velocity, C, 
or length, L. 
c. Wind velocity, U. 
d. Wind fetch, z. 
e. Wind duration, é. 
It must furthermore be bdrne in mind that the 
waves in any one region are the result not only 
of local winds but also of winds in other areas, 
and that the relation between wind and waves 
during the periods of growth or of decay (sea or 
swell) should be considered separately. 
Although ‘numerous wave observations have 
been taken, only relatively few are complete in 
the above sense. Even these observations are 
unreliable, partly because the measured quantities 
are poorly defined. For ready comparison with 
theory, observations of growing waves have been 
grouped into the following five classes: 
Tabulation Graph 
1. 6 as function of 8-__ Appendix 2, table I. Fig. 5. 
2a. gH/U? as function of Appendix 2, table Fig. 6. 
gx/U. Il. 
2b. Basfunctionofgz/U_ Appendix 2, table Fig. 6. 
100 
3a. gH/U? as function of Appendix 2, table Fig. 7. 
gt/U. VOB 
3b. Basfunction of gt/U_ Appendix 2, table Fig. 7. 
1O Me 
These dimensionally correct relations will be 
discussed first, to be followed by a consideration 
of certain well-known empirical relationships: 
4, H=f(z).--- Stevenson’s law. 
5. H=f(t)_--- Boergens law. 
6. H=f(U)_-.- Zimmerman, Cornish, Rossby, and Mont- 
gomery, miscellaneous data. 
7. C=f(U)_-. Zimmerman, Cornish, Schott. 
neous data. 
miscella- 
24 
These latter relationships are incomplete. Ste- 
venson’s law, for example, is applicable to ‘“‘maxi- 
mum wind velocities” only, and objections can be 
raised to most of the other relationships. It will 
be shown, however, that the established empirical 
laws, although dimensionally erroneous, give 
numerical values which appear reasonable in the 
light of their nondimensional relations listed above. 
1. Wave age and steepness.—This relationship is 
based on 128 sets of observations, tabulated in 
table I, appendix 2. The individual observations 
have been numbered because they also appear in 
the other tables where they can be recognized by 
their number. The observations are plotted in 
figure 5, where the solid curve is assumed to repre- 
sent the true relationship. Various constants 
have already been determined on the basis of this 
curve, and the observations have been previously 
discussed (p. 16). 
2a. Wave height against fetch and wind velocity.— 
The observational material consists of 39 observa- 
tions from various sources. Those marked ‘U. 
S. ENGINEERS” were taken from the Milwau- 
kee lightship in Lake Michigan (U. S. Engineers, 
1932). The wave height was determined by 
measuring the rise and fall of the water surface 
along a graduated line. According to the original 
report, “sufficient readings were taken at each 
observation for a representative wave height to be 
obtained.”” Wind velocity, fetch, and duration 
were determined from Daily Synoptic Series 
Northern Hemisphere Sea Level Weather Maps, 
but the direct wind observations on the lightship 
were also taken into consideration. According to 
the minimum duration graph in figure 7, all 
observations were limited by fetch. 
Observations marked ‘U. 8. S. Augusta” were 
taken visually by Commander R. C. Steere, USN, 
off the Normandy Beach Head (unpublished re- 
ports), and the fetch, duration, and wind velocity 
were determined from available weather data. 
Cornish (1934) has compiled some of his own very 
careful observations. Gibson’s observations have 
already been discussed when dealing with wave 
age and steepness (p. 16). 
All observations are expressed by the nondimen- 
sional parameters gH/U?, gz/U and plotted on 
figure 6. They show good agreement with theory. 
2b. Wave velocity against fetch and wind ve- 
locity.—This relationship can be tested by means 
of 19 observations. The wave velocity is ex- 
pressed in nondimensional form by the ratio C/U, 
the wave age. Four observations were obtained 
