KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 47. N:() 4. 33 



av. 2 hg (o— o') l \o 



Now, let A x be the same number found for a case with another a but having: 



1) the same densities g and q; 



M 



2) the same ratio 77^7 between maximum elevation of the ridge and mean depth of 



the lower fluid; 



3) the same ratio — between maximum current-velocity and velocity of propa- 



gation of the boundary-waves; 



4) the same ratio between the horizontal extension of the ridge and the wave-length 

 of the boundary-waves (same value of «); 



it follows that: 



where r and r, denote the respective boundary wave-velocities. Now, in cases of 

 long wave-motion it is easily proved that the numbers Ä and A x will give the corre- 

 sponding amplitudes with a very good approximation, so that 



4, 



n 



1 1 



h + h' 



A 



n 



h l h x 



and if corresponding quantities are related in the way defined, you have this simple law: 

 The amplitude will increase in a proportion equal to the second power of the ratio of 



the corresponding boundary wave-velocities. 



For example, a tank experiment may show a boundary-wave propagating itself 



with a velocity of 5 — , and the amplitude will perhaps be 0,5 cm. Enlarged to tidal 



dimensions, the velocity of propagation will be, say 100 — , and other circumstances 



being determined by the above stipulations, you will find a boundary-wave of an amplitude 



about equal to 



100 2 

 0,5 -^- = 200 cm. 



This method of comparison will be true only as long as both cases fall within the 

 theory. Certainly, however, extreme cases, not covered by the theory, will on account 



difference of density. Of course this expressiv implies that the horizontal extension of the ridge should be conti- 



2iT 



nually enlarged in the same proportion to the wave-length 



It thus seems that, to obtain geometrically the most similar circumstances possible, there should be a certain 

 advantage to arrange the small-scale experiment with a rather great difference of density and compare this to 

 a tidal case with a small such difference. The relation of the amplitudes will (see above!) now be: 



4, 



_r\ g, (q- ?') 



h + k' 



A 



r° QiQi—Qi) 



h { + v 



K. Sv. Vet. Akad. Handl. Band 47. N:o 4. 



