h'^ 



n = l 



IV {z)dz = 0, for r = 1,2,...N 



(12) 



from which, for numerical calculations, 

 N 

 A^.■ L n = 1 



,^ r N 



H/^(2p A2;= 0, forr= 1,2,. ..A' 



(13) 



follows. This equation reduced to (19) only in the case where tsz ^ = constant. 

 If this is not valid, the weighting factors, Ae^- , influence the result consider- 

 ably. Let q be the number of depths for which the amplitudes, a{z ■) , have 

 been determined. For depth range 



Az. 



a{z .) is supposed to be representative. The whole column is divided into ((?+l) 

 subranges and instead of using t^z^ in equation 13 we can use, after 

 multiplication by q+l/H the dimensionless weighting factors 



Az.- 



,)(<?+!) 



H/(q+l) 



2H 



(14) 



The weighting factors are 1 for equally spaced Az^- , that is for 



2 

 Many computations have shown that disregarding the weighting factors (14) 

 leads to erroneous results and further study is recommended. 



Following is a summary of the formulas needed for processing data 

 taken from records at an anchor station. These will permit comparison of 

 spectra from an anchor station and those from towed instruments. 



Suppose we have observed the temperature fluctuation, T(t-, z.)^ at 

 an anchor station at the levels z-. From the mean temperature distribution, 

 T{z) , it follows that the displacement of the particles from their mean position 

 is given by 



0,z,) 



(dT/dz), 



(15) 



From Fourier analysis we find the amplitudes, a and b, for a distinct frequency, 



CO '. 



0, z ■) = a(z ■) cos ajt + b{z-) sin ojt 



(16) 



10 



