Now each period r^ produces a whole set of spikes similar to those shown in 

 figure 4. In general, several apparent periods may coincide. For two internal 

 waves with different periods '"^ and r^, each one composed of eigen- 

 functions of the order n and ii*, apparent periods are coincident, i.e., 



n, m 



= 'n* m*' if 





U 



n 



1 cos a^ 



'-n 



'~~ 



U 







is fulfilled. In this case we find instead of (38) and (39) , 



(41) 



A (u,', z) 



4>(ci)\ z) = 



elsewhere 



n^m ^n, m ^n ^^> 



1/2 



for cj ' = w ; 



tor o) '= (D ', 



277 



(42) 



not defined elsewhere 



Again the apparent spectrum A((x>',z) reflects separation into the different modes 

 similar to the case given by equation 33. Amplitudes of the modes are not 

 given directly. The method of least squares is used for computation of A 



All these considerations have dealt only with one section, for example 

 section AB, of figure 1. The main problem is to find the apparent periods 



t' rn n- '^' m n i" ^^^ spectra for the different legs which belong together. Whether 

 this is possible or not depends on the form of the true spectrum. A peak in the 

 true spectrum will occur as an identical peak but at a different apparent period in 

 each of the spectra from two different legs. These peaks must be identified in 

 order to use equations 27, 28, and 30 for r and a. Until now, records have been 

 available only from rather complicated areas. In this case we have not been 

 able to identify peaks of different legs. 



The same could be shown for the power spectrum, P(co,z), instead of 

 the amplitude spectra. Consider a real situation, given by 

 N 



F (z, t) = 2_, [ ^n'^n ^^^ cos OjQt + B^^W^ (z) sin coqI ] 



« = 1 

 N 

 = y l^n^n (2)cos{cjQt~a„{z))] 



/!=1 



The chain, even in this simple case, gives a complicated pattern: 



(43) 



19 



