TM No. 377 



z/ = Alo C0S<T-6 . (v-U9) 



Here w* is of the same form as in equation (V-37). The cT is defined as: 



1 6 fog rr&a* <.z"n" 



and the value of K is small compared with unity. The functions u 1 and w' in 

 equations (V-U8) and (V-k-9) are simply sine and cosine forms, but with the u* 

 term possessing a slightly larger positive amplitude. The traces are shown in 

 figure V-W-C (bottom curves), with the u* function depicted as a broken-line 

 curve. 



Evaluating the covariance u'w' : 



«V = f 



rli. 



(l+&K)SirJCico& <Ti dt . (v-5l) 



\ 



The term ( ft^K) is left inside the integral because, in a sense, it is a 

 function of time. Splitting the integration for positive and negative summation 

 gives: 



(V-52) 



t£j= iti<s.j'(siH 1 rt)0+J\ . sinV* 



-r/2. 



It is easily seen that Uly — O . This integration is seen graphically in 

 figure V-Ml-C. The sum of the shaded areas, in spite of the damped positive 

 amplitude, is equal to zero - just as with equation (V-38). 



150 



