- 3l- 
appears to depend on the heights of the waves that were measured. 
Comparison with observations 
The purpose of this part of this paper is to present the results of 
some observations that suggest that the various models proposed above 
are more nearly in accord with actual waves than models based on the 
Eulerian equations. 
Figure 4 is a copy of a photograph given by Roll [1957] for waves 
a few centimeters high and 8 to 35 cm long. The third photograph from the 
top shows a remarkable similarity to figure 2. For various wave heights 
and apparent lengths, either a rounded crest or a sharp crest occurs. Note 
the marked departure from normality that slopes and curvatures would 
have if they were evaluated from sucha record. 
Figures 5, 6, and 7 show some reproductions of seven selected 
wave profiles obtained by stereo-photogrammetric techniques from photo - 
graphs taken aboarda ship. The height scale is five times that of the 
horizontal scale. The profiles show the presence of sharp crests and 
shallow troughs as these models predict. Note also that the profiles are 
much richer in high wave numbers than corresponding time histories are 
rich in high frequencies. These profiles were kindly furnished the author 
by Dr. Norman F. Jasper of the David Taylor Model Basin. Additional 
information on these records is given by Brooks and Jasper [1957]. 
Figure 8 shows some selected time histories obtained in Buz- 
zards Bay by Harlow G. Farmer [Farmer and Ketchum (in press)]. The 
original records have been reversed, so that time increases from left 
to right, and blackened below the original trace. The wave sensing sys- 
tem consists of a very fine wire (0.015 inch diameter) that appears to 
follow the water elevation more accurately than previous wave poles or 
wave wires. A number of the crests are very sharply pointed. There 
is evidence that a breaker occurred in the top trace where one crest 
shows a nearly vertical rise at the crest. Since these records are much 
richer in high frequency content (sharp crests, and vertical rises), spectra 
computed from them will be richer at high frequencies than spectra pre - 
viously reported for waves in this general range of heights and periods. 
The figures and illustrations in Schulejkin [1960] also suggest 
that the randomized Lagrangian model corresponds well with reality. 
