30 ZEILON, ON TIDAL BOUNDARY-WAVES. 



K„C 



which, — being a small number, will decrease very rapidly with increasing values of v. 



Further, returning to the series representing the boundary-wave in the proper meaning 

 of the word, if a is small, there will be no sensible dispersion for the values of v to be 

 taken account of. In that case, the waves generated, though not simple-harmonic, will 

 still advance without changement of fort». 



Returning now, through the above transformation, to the »fixed-ridge » problem, 

 there will however be a considerable influence upon the manner of propagation. The 

 tidal current-velocity 



— c cos Kx . cos ut 



adding itself everywhere, the boundary-waves will now advance with a pulsatory velocity, 

 being checked up when moving against, and accelerated when moving with the current. 

 With a view to obtain some idea of the magnitude of the influence upon the shape 

 of the waves, we might take a case approaching to the experimental circumstances pic- 

 tured in Pl. I of this paper. With a = 2 and x = 0,5, rather a similar arrangement 

 is obtained by putting « = 0,5. Then the exponentials of the series 1 ) will simply de- 

 crease as 



and it follows that in this case already the octave should be quite insensible, even for a 

 relatively very strong current. 



However, under different circumstances, the formation of harmonics may well 

 be apparent. The relative amplitudes of the different components being determined by 

 the construction of the ridge, it is even possible, with an obstacle of suitable extension 

 and configuration, that one or other of the harmonics may gain in importance upon the 

 fundamental wave itself. On the other hand, if the impinging long wave was from the 

 beginning made up from several simple-harmonic constituents, the form and dimensions of 

 the ridge will strongly influence the relative importance of the different boundary-tides 

 produced, and it is obvious that these two effects may combine in forming peculiar and 

 characteristic resonance phenomena. 



For the tides of Nature, assuming in accordance with the dates of pag. 14 as a 

 fair mean value: 



o _ meter 

 k second ' 



a current velocity of the order of magnitude of the boundary wave-velocity is very plau- 

 sible. Since suboceanic barriers generally are relatively flat and of considerable horizontal 

 extension, to the statements of pag. 16 we may add the following: 



A strong tidal current in heterogeneous water, crossing a submarine, barrier, will cause 

 boundary-waves to be formed of a profile determined by the configuration and extension of 

 the ridge. These waves will diverge from above the ridge without sensibly changing their form 

 and will advance against the current with a constant relative velocity. 



