SEœNDARY UNDULATIONS OF OCEANIC TIDES. 77 



as those of the usual secondary undulation. He explained the 

 phenomenon by supposing that a bay or a certain portion of 

 sea oscillates like a fluid pendulum with its own proper period, 

 when it is excited by an earthquake or any other disturbing causes. 

 We have also investigated the periods of the sea waves for 

 different bays and found that the above relation is generally 

 well satisfied, especialh' in the sea waves of distant origin. As 

 we shall see soon below, the period of a sea wave in a bay is, 

 in most cases, given by the formula 



T=-4L 

 l/gh ' 



It is then very probable that in such cases, the sea waves are 

 of a similar nature to the secondary undulations. Now the sea 

 waves are probably of such a complex nature as to be repre- 

 sented by the sum of a series of long waves of different periods 

 and amplitudes. If a group of these waves proceeds towards a 

 bay, the bay takes up and resonates to the undulation, whose 

 period approximately coincides with that given by the above 

 relation. 



This consideration chiefly applies to the sea waves of dis- 

 tant origin. If however its origin is not very far from a bay 

 or an open coast, progressive waves of long wave length, irre- 

 spectively of their period, are sufficient to cause a disastrous 

 effect on the coast ; for by Green's law of amplitudes long waves 

 considerably increase their amplitudes as they approach a 

 shallow shore. Thus in actual destructive sea waves, we almost 

 always have reports of high wave fronts approaching towards 

 the shore, indicating that the waves are of the progressive 

 nature, but not of the stationary character. For the sea waves 

 of 1896, on the coasts of Sanriku, there are instances which 



