Stilwell 



length. The constant a can be determined by computing the spectrum 

 for a known situation (not necessarily realizable) by eq_uation 

 (21) (modified to have dimensions of wave angle rather than wave 

 height) and also by the photographic technique. The ratio of the 

 two solutions yields 



a = (2jt In 10)"^ (23) 



The solution for the spectrum is manifest in either equation (24) 

 or (25). 



= { } X (25) 



A is the area of the sea analyzed and the other terms are 

 s 



previously defined. 



EXPERIMEMIAL RESULTS 



Figure 5 is a composite of the scene photograph, the 

 transform photograph, and an isodensitometer trace of the transform 

 density contours. The photograph was taken from the South Capitol 

 Street Bridge crossing the Anacostia River in D.G. from a height 

 of about 30' in a wind of about ij-5 knots. Since for a given 

 analysis equation (24) is simply a constant times the base ten 

 power of the optical density (letting gamma be one for discussion 

 purposes) the density contours correspond to spectral contours. 

 The radial distance from the dc term is proportional to the wave 

 number of the water wavelength. The spectral information is what is 

 expected for the low wind velocity involved when the analyzed 

 spectral region spans the minimum in the wave velocity -wavelength 

 curve for water waves. The high frequency spectral peak is about 

 1.5 cm wavelength and the corresponding "gravity wave" is about 4 

 cm long, as indicated by the peak in the spectrum. It may be noted 

 that the curves of velocity vs wavelength would not give the 

 above values for paired frequencies. The surface tension on the 

 polluted river is probably significantly larger than that for 

 pure water which would shift the null in the velocity cuirve to 

 longer wavelengths so the measurement is not unreasonable. 



Fig-ure 6 is a similar composite of data taken from Wilson 

 Bridge across the Potomac River from a height of 50'. The wind 

 was about 12-16 mph, blowing almost directly into the camera from 

 the north. The bench parameters for this analysis resulted in a 

 large magnification of the region about the dc term in order to 



178 



