For simplication, we take r=rQ = constant, i.e., piz) sp^expCFpz). Now 

 consider a rectangular basin 



-L < X < + L, 



Q<z<H 



The tide - generating force ( equation 55 ) is developed into a Fourier series 

 with regard to the dimensions of the basin. 



feg exp [ ;■ (kqX + i7Qy + wq^^J 



I (.nx mny 



(57) 



i. = ±1,...; m = ±1, 





4LB 



exp iTj 

 -L -B \ '^0 



L rS /2L- IL\q 2B-mAQ 



.Y + V I dxdy 



'C- 



Setting 



;7(2L--gA^) g _ 77(2B-mAo) 



A ' f" ~ !i ' 



(58) 



we have after integration 



sin a„ sm 



fe» _=fe. 



(59) 



and since by assumption A„ is not a multiple of 2L, all k ^ are not 



equal to zero. 



The same expansion for w(x,y,z,t) is 



w (x, y, z, t) = y 2_^ W ^ Jz) exp 





and with 



follows from equation 53 



„ dW d'^W 



d'^^.n. ^^"'^^ 



f <^'- 



dz^ 2 f2 



W , „ = for 2 = and z = H 



^0 ' 



(60) 



(61) 



(62) 



23 



