14 ZEILON, ON TIDAL BOUNDAKY-WAVES. 



resonance phenomena) considerable tidal boimdary-waves could be excited; however a 

 rough quantitative discussion of the case of the single bottom elevation, for the tidal case, 

 will still possess a certain interest. 



Taking a semi-diurnal tide with 



— = 12 . 60 3 , 



a 



it is evident that, but for absurdly small differences of density, also the greater root x 

 of the determinant will be quite a small number, and that the same, for reasonable depths, 

 will be true for: 



y.h and y.h'. 



The equation: 



D = o 4 (q coth kh coth kh' + </') — o*gkQ(coth kh + oothifcÄ') + g 2 k 2 (p — Q') = 

 then is reduced to: 



k 

 or: 



^-^4 + ll) +g2kH «-^= o 



i g^ 8 /l , 1\ , ^Q 



g{f>-e')\h + h'} + g*hh'(<>-<>') 



Since one root certainly is: 



a 2 

 K 2 = 



g(h + h'y 

 the other is determined by: 



°*Q (l , M ?!_ 



and it appears that the second term here, for small values of q— q and great depths, 

 will be small compared to the first. Neglecting it, /. is in fact the approximate solu- 

 tion of: 



o 2 o(coth kh + coth kh') — gk{(j — o') = 0, 



so the approximation previously used will, also here, be fairly (but not always very) good. 

 Taking for example 



h = h"= 50 

 gr =10 



— p' = 0,004, 



the units being seconds and meters, we have very nearly: 



■/. — a. 



