SECONDARY UNDULATIONS OF OCEANIC TIDES. 15 



propagated in the direction of the length of the liay and re- 

 flected at its end. By the interference of the incident and 

 reflected waves, a stationary wave is formed, liaving its loop at 

 the end of the bay. If the wave length be s ach as to form 

 the node at tlie mouth of tlie bay, the period is the same as 

 that of the fundamental oscillation of a tank having double the 

 length of the bay, and therefore the amplitude of oscillation 

 must necessarily be magnified by the successive incidence of the 

 long wave. The case is just analogous to the acoustical re- 

 sonance of the air column to the vibration of a tuning fork 

 placed over its mouth. Tlie period of the oscillation is then, 

 neglecting the mouth correction, expressed by the relation 



l/gh 

 where i^gh~ is velocity of the long wave. 



If the waves of different periods proceed from the ocean 

 toward the shore, the one whose period coincides with that of 

 the oscillation liaving its node at the mouth of the bay, will 

 excite the most energetic oscillation of the bay water. Thus 

 bays on the coast line may be compared with a series of re- 

 sonators, each of which takes up selectively and resonates to 

 the note of its proper period from the chaos of very complicated 

 sounds or noises from the exterior. The plausibility of such 

 an idea seems to be established in a rather unexpected degree 

 by the present investigation. Moreover, the fact that the motion 

 of the level of a liay in the principal undulation is in the same 

 phase for several stations, stands in favour of the above view. 

 G. H. Darwin and Otto Krümmer'' seem to have entertained an 

 analogous idea. 



*) Darwin, The Tides, CL. X, p. 1C9. O. Krümme!, Ueber Gezeitenwellen, Rede bei 

 Antritt d. Rektorates d. Königl. Christ.-Albr.-Uhiv. z. Kiel, 5 Marz, 1897. 



