SECONDARY UNDULATIONS OF OCEANIC TIDES. 57 



remaining portion of the bay extending to both sides seems to 

 have httle influence on these modes of oscillation. 



By exciting waves of periods ranging from 3.P to 3.5', the 

 water in tlie bay energetically oscillated with tlie fundamental 

 mode of oscillation, having its node at Golden Gate and its loop 

 at the West Berkeley side. The most easily excitable mode of 

 oscillation was a binodal seiches between the narrowest mouth 

 line and West Berkeley side ; the positions of the loops are 

 clearly seen from the photograph No. 12 and Fig. 12 (a chief 

 part of the model). The period of the exciting wave, which gave 

 a marked resonance to the binodal seiches of the bay, ranged 

 from 1.1' to 1.4". By slightly changing the period of tlie wave, 

 the corresponding displacement of nodal line was observed. We 

 could also produce a trinodal seiches of the bay, whose period 

 of oscillation was 0.8\ Multiplying these periods by f, we get 

 107^-122'", 38'"-48'", and 28.'" The period 116"\ which probably 

 corresponds to tlie fundamental oscillation of the bay, was act- 

 ually found in the sea wave from South Anierica, 1808, observed 

 in the bay. Periods corresponding to the bi nodal and trinodal 

 oscillations were often observed in the bay in the case of 

 several sea waves. 



§ 6. FORMULA FOR CALCULATING THE PERIODS 

 OF THE UNDULATION IN BAYS, 



{a) Picctangular bay of constant depth. 



The oscillation of the water in a bay is the same as the 

 seiches in a lake of double length, the mouth correction being 

 taken into account. Hence if / and Ji denote respectively the 

 length and the depth of a rectangular bay of a constant depth, 



