32 ZEILON, ON TIDAL BOUNDARY-WAVES. 



dary-waves of the tidal period travelling rightwards (with a constant relative velocity 

 against the tide, if account is taken of the magnitude of the tidal current- velocity). 



Similarly, for the left channel, there will be, for the point b of the boundary, the 

 forced motion: 



'/= «/',(0, 

 and there will be waves propagated of the form: 



lx — b 



*l> 



ix — b \ 



It is important to remark that there is now no necessity why there should be similar 

 arrangements as to density distribution etc. on both sides of the ridge. Indeed, for the 

 most important and interesting cases in Nature, the ridge will be a barrier between two 

 hydrographically distinct systems. 



Even in those very extreme cases, this general principle will pro ve to hold true: 

 The tide in heter ogeneous water, when impinging upon a suboceanic barrier, will cause 

 boundary-ivaves of the tidal period, to be formed, moving according to the rules of the pre- 

 ceding theory. 



PART II. 

 A. On Conclusioiis from the Experiments. 



With the extremely small frequency value and correspondingly great wave-length 

 of the tides, there will unfortunately be no possibility of reproducing tidal phenomena on 

 a true relative scale. You will always have to work with wave-lengths far smaller in 

 comparison with the vertical linear dimensions than is the case with the tides, and for this 

 reason there will be no immediate use for the very convenient and, apart from frictional 

 effects, also very exact principles of geometrical similarity. To obtain a method of com- 

 parison, we thus are to have recourse to the special approximative theory. 



Imagine then an experiment entering fairly into the conditions of the theory. Ta- 



king the amplitude of the boundary- waves of period - and wave-length as a measure 

 of the effect as a whole, this amplitude will, with sufficient approximation, be equal to: 



A _ 2o*q.M ,(xc\ -fe 



" z8,n,,ZÄ -rMsinh^Ä ' sinh^) + ^^ ^) 



M 1 



Here f denotes the maximum elevation of the ridge, and - represents the ratio of its 



liorizontal extension to the wave-length of the boundary-waves. ' We put: 



1 If this expression .1 for a given o and given values of // and // is drawn as a functipn of g— o, it will 

 give ;i curve that for increasing values of o— ^' asymptotioally approaches the limit A. Thus, as soon 

 as the boundary waves generated may be tteated as long waves, the amplitude will be independeht of the 



