23 



of waves, and the respective wave systems are different. It is recog- 

 nized that natural conditions may not approximate this supposition. 

 The bar base depths of the bars in the different zones are defined by 

 lines joining the troughs of the bars. According to the definition, the 

 segment of the line under the body of a given bar becomes the bar 

 base. From figure 11 the average value of the bar base depth, Hb for 

 the bars in the first zone of the profiles is 7.2 feet; in the second zone, 

 13.2 feet; and in the third zone, 19.5 feet. If it be assumed, for 

 example, that the bars are formed under waves of steepness ratio 

 ^^/Xq=0.03, the required value Go/Hb from figure 7A is 0.75. Accordingly, 

 the bar of the first zone required 5.4-foot waves for its formation, that 

 of the second zone required 10.5-foot waves, and the third zone 14.5- 

 foot waves. H. A. Montgomery observed wave heights in Lake 

 Michigan, near Milwaukee, from 10 April 1931 to 28 September 1932 

 (reference 7). The maximuiri wave heights recorded over the first 12 

 months of the investigation were: 



Number of 

 Maximum wave height days on which 



(in feet) recorded 



14 1 



13-14 



12-13 



11-12 1 



10-11 2 



9-10 7 



8-9 - 6 



7-8 5 



6-7 22 



5-6 32 



4-5 48 



3^ "1 



The average period of the waves of lowest height was 4.3 seconds, 

 with a minimum period of 3.5 and a maximum of 5.0 seconds. Since 

 the water at the location of the measurements was quite deep, the 

 inference is that the low waves were about 95 feet long. The wave 

 steepness ratio was about 0.03. The above measurements were 

 made on the western shore of the Lake. If they apply to the eastern 

 shore near Wliite Lake, the waves are of the order of magnitude 

 expected to create bars of the dimensions observed in the first and 

 second zones. 



The above comparison of laboratory experiments and natm-al 

 processes would be of gi-eater value were it possible to discuss simul- 

 taneously the effect of a spectrum of waves operating over a beach. 

 Actually it may be surmised that waves in natm-e are far from a singu- 

 lar system. 



