In equation (8. 24), the W„'s are given by Table 8.1, M^ is the average 

 number of x points, and M is the average number of y points used in com- 

 puting a value of Q. 



It can be shown that the average number of x points used in computing 

 the Q values is N - (rn/2) and the average number of y points is 

 N^ - (m /2). All of the Q's enter in each value of U. The number of x 

 points used for the individual Q's ranges by integer steps from N to N -m 



X X X 



•with an average value of N - (m^/2), and similarly for the y points. 



The value of ( S Wj^)^/4(Z; Wj^^) is equal to 1. 58, and hence the final 

 expression for the number of degrees of freedom is given by equation (8.25). 



Nx 1 



(8.25) f = 1. 58 



1 



A 1 

 my "Zj 



Equation (8. 25) may iinder estimate the number of degrees of freedom. 



Instead of (-^ ■* — ) as in equation (8. 23), it has the product of two terms 



Nx 1 " V 1 



/ " T ) and ( _, "'"7) and instead of a factor of 2 it has a 1.58. The values 

 mx 2 vm^ ^/ 



of Q near Q(0, 0) are much larger than the values of Q on the edges, and 

 therefore values of 1/4 instead of 1/2 might weight them more properly in 

 equation (8. 25). 



A Correction for the Wave Pole Spectrum 

 The wave pole used by the R. V. ATLANTIS was free floating, and its 

 dimensions are shown in figure 8. 1. Therefore it probably underwent a 

 rather complex non-linear motion in heave, pitch and surge. If the motions 

 can be linearized, the heaving motion is the most important, and the pitch 



73 



