ALTERATIONS DUE TO SHOALING 57 



ship explained on page 103, and illustrated in figure 21. At the same 

 time, they first decrease slightly in height, then may increase. But 

 they lose less than one-tenth in height at most by this initial decrease, 

 a loss that is far outbalanced by the decrease that takes place simul- 

 taneously in their lengths, even if their heights do not increase subse- 

 quently, as may or may not happen, for the lengths have decreased by 

 about one-third by the time the wave has reached the point where 

 the depth of water is one-tenth as great as the initial length of the 

 wave, and by nearly one-half when it reaches the point where the 

 depth is only one-twentieth that great. And the steepness of the 

 wave increases accordingly. 



The lengths of the waves offshore and the angle of slope of the 

 bottom together determine the precise distance from shore at which 

 these stages will be reached, in the alteration of any wave, the rule 

 being, that the longer the wave is in deep water, the farther out from 

 the land will it begin to steepen noticeably. Waves, for example, 

 120 feet long, would not be noticeably steeper until they reached, say, 

 the 2-fathom line, although their lengths would begin to decrease 

 measurably from the time they advanced beyond, say, the 4-fathom 

 line, however far out thai; might be from the land. But a 240-foot 

 wave would have steepened noticeably when it reached the 8-fathom 

 line, a 500-foot wave when it reached the 15-fathom line; and waves 

 much longer than 240 feet are common. 



Waves averaging about 9 seconds in period, and hence about 415 

 feet in length offshore, that have been recorded at South Beach, 

 Martha's Vineyard (p. 106), should thus have begun to feel the bottom 

 and hence to steepen when they reached the 30 to 35-fathom (180 to 

 210-foot) line, which lies about 40 miles out off this part of the coast. 

 By the time they reached the 7-fathom line, they should, theoretically, 

 have been only about three-fourths as long as they were while out in 

 deep water, and one-half as long, but correspondingly steeper, by the 

 time they reached the 3-fathom line. A more striking case is illus- 

 trated by a group of very heavy breakers observed on the south coast 

 of England in winter, the lengths of which (as calculated from their 

 periods) averaged about 1,185 feet while they were out in deep water, 

 so that they had begun no doubt to shorten at about the 100-fathom 

 line, on the upper part of the continental slope off the mouth of the 

 English Channel, at least 275 miles out to seaward from the place 

 where they were recorded on the coast (Cornish, 1910, p. 88). And 

 additional illustrations of the same sort, if less extreme, might be 

 cited for other parts of the world. 



The southern part of the North Sea affords an interesting example 

 of the steepening effect of a shoaling bottom on the waves in the 

 downwind parts of partially enclosed waters of broad extent. Strong 



