202 Long Waves in Canals and Standing Waves in Closed Basins 



and not yet fully solved; neither is there any certainty yet as to the extent 

 of the influence exercised by the Strait of Kertsch. 



We want to mention the variations of the level of the great North American 

 lakes, which were investigated by Henry (1902). These investigations were 

 followed by the extensive work of Hayford (1922) towards determining 

 the correct mean level of the lakes. Endros (1908) determined the principal 

 period of Lake Erie from the curves added to the paper by Henry. He found 

 a main period of 14-3 h, and the harmonic oscillation of 8-8 h to be a two- 

 nodal, those of 5 7 and 41 h three- and four-nodal seiches respectively. All 

 periods and phases agree with the theory. Another wave of long duration 

 which averages 12 65 h is — as shown by Endros (1930) — the semi-diurnal 

 tide. These results seem to be in contradiction with the findings of Hayford, 

 who found periods of 12 8, 130 and 13-8 h for the principal oscillation in 

 Buffalo, and periods of 12 5, 12 9 and 13-9 h in Cleveland, whereas the 

 harmonic oscillations agree with the values given by Endros. This deviation 

 from the value of 14-3 h indicated previously can be explained from the fact 

 that Hayford has not eliminated the tidal waves from the curves, so that 

 the values found by him represent the superposition of the free oscillations 

 with the ever present tidal wave. This superposition, however, gives oscil- 

 lations with a period varying between 12 5 and 13 9 h. Endros found for 

 Lake Erie a large logarithmic decrement of A = 237 h, which is caused 

 by the islands located in the western part. 



Hayford did not find in Lake Michigan and Lake Huron well-developed 

 oscillations, because of special conditions in the basins. Endros proved in 

 both lakes a distinct oscillation with a period of approximately 45 h, which 

 he explains as a compensating motion between these two great lakes through 

 the connecting Straits of Mackinac. 



A theoretical investigation of the seiches in Lake Michigan was made 

 by Fr. Defant(1953). He computed the free periods of the uni-nodal and two- 

 nodal seiches after different methods. In the mean, 9 05 h were found for 

 uni-nodal seiches and 4-84 h for two-nodal seiches. The simple, swinging 

 motion of the seiches is changed into weak amphidromies contra solem when 

 the Coriolis force is taken into account. Then the amplitude of the transverse 

 oscillations amounts to about one fifth of that of the longitudinal oscillations. 

 It seems that there are as yet no actual observations. 



5. Influence of the Earth's Rotation on Tidal Waves and Seiches 



(a) Horizontal Motions in Progressive and Standing Waves 



It is customary to observe principally the vertical displacements of the 

 water-masses rj, whereas little attention is paid to the horizontal displace- 

 ments f. In the simplest case of progressive and standing waves in a uniform 

 canal of constant depth /;, we have the following relations for these dis- 

 placements : 



