It is necessary in general to carry out this integration 

 by 'niunerical methods, and an infinite number of solutions corre- 

 sponding to an infinite number of internal waves are possible* 

 This integration yields the solution for the relative amplitudes 

 w» 



The internal vrave motion is then assumed to be of the 

 following form 



^ = A COScrt + B sin crt (26) 



\ifhere the computed amplitudes may be evaluated by the following 

 summations 



A= lon^n B=ibn Wn (2? a,b) 



n=i n=i 



The coefficients a^ and bj-^ may be evaluated by the use of 

 the Fourier theorem 



an=k I A«^(Z)WndZ bn = k (B<^(Z)Wndz (23 a, b) 



It will be noted that in computing the Fourier coefficients a^^ 

 and b it is necessary to have observed amplitudes A and B in 

 equations (28). These coefficients are then used to compute the 

 actual amplitudes in equations (27). No matter what the nature 

 of the orthogonal function w, the Fourier theorem requires that 

 the observed ana computed amplitudes must be Identical, if an 

 infinite number of orders are used. However, Pjeldstad demon- 

 strates that, by employing his particular w, good agreement is 



59 



