The total area under the paw^r spectnmi may be obtained in a number of 

 ways. The simplest method, of course, is to use a planimeter. The method 

 more frequently followed, however, consists of dividing the frequency /axis 

 into a set of intervals and determining the valu^ of the power curve at the 

 midpoint of each interval. The product of this value and the length of the 

 interval summed over the entire range of frequencies is approximately Epvna)c(yU) 



Figure 4 shows the experimental data /\p {n,) at a depth of 150 feet. 

 The associated Ep(yU.) curve was determined by integrating over the spectrum, 

 with a planimeter. The total area was found to be .oLSf -Px. over the signifi- 

 cant band of frequencies, which approximates closely the irailue EpTnaxC/LO^ •2CH-f't 

 already obtained by machine analysis. The numerical value E = tp_^^Cu)is the 

 quantity used in forecasting the wave amplitudes. Once E. is known, the 

 ogive curve representing the number of waves with amplitudes greater than a 

 specified amplitude, r^ , can be obtained from table II, if it is assumed 

 that the values therein hold for all wave records. 



Using £_ -K .^t*j. -^-V- , i.e. VE = .51H- -t"t- the cumulativ-e distribu- 

 tion of waves with amplitudes greater than r^ inches was determined for 

 the power curve shown in figure 4. Figure 5 shows the comparison of the 

 predicted curve and the curve obtained from a hand analysis of the original 

 wave record. 



The next step is to consider the distribution of waves with periods 

 greater than a specif isd period, T . Theoretically, very little has been 

 done along this line because of the variation of periods from wave to wave. 

 However, Rice (1944 and 1945) has derived an expression for the expected 

 number of zeros per second which may occur in a random time series. It is 

 assumed that the number of times the record crosses the moan line is the 

 number of zeros; thus the expected number of zeros per second is tv/ice 



13 



