218 Long Waves in Canals and Standing Waves in Closed Basins 



longitudinal current. The amplitude of these transverse oscillations, according 

 to the explanations given on p. 204, is given by 



A' = ^tany 



bf 



2g 



U, 



if U is the amplitude of the periodic variations of the current in the longi- 

 tudinal direction of the lake; its phase is shifted by one quarter period against 

 that of the longitudinal oscillation. 



Thus, at any point of the lake the vertical displacement of the transverse 

 oscillation r\ = A' sin at is added to the vertical displacement of the longi- 

 tudinal oscillation r\ = ,4coso7, so that the superposition takes the form 



Z = ^coso-Z+^'sincr/ 1 = Mcosa(t— t) 



in which M = ) (A 2 +A' 2 ) and tan err = A' /A. From the latter relation we 

 can compute the time of the maximum and minimum height. 



There are not many cases in which the influence of the earth's rotation 

 has thus been determined. Neumann has calculated, according to the above 

 method, from the computed current velocities of the longitudinal oscillations 

 (period 27 "5 h), the amplitudes of the transverse oscillations A' for several 

 localities of the Baltic and found the following values for the Gulf of Finland: 



The time (t = 0) is counted here from the moment of high water in Koivisto 

 (innermost part of the Gulf of Finland). Consequently, there is a delay in 

 Helsinki and in Hango, on the northern side of the gulf, of 11 and 1-8 h 

 respectively, whereas on the southern side, in Tallinn, high water occurs IT h 

 earlier than in Koivisto. Between Helsinki and Tallinn the difference in time 

 of the high water is 2-2 h, and the extremes occur earlier in Tallinn than in 

 Helsinki. 



All cases closely investigated by Neumann on the basis of gauge registra- 

 tions show the phase displacement required by the theory, which averages 

 2-3 h. Figure 93 shows two of these cases, illustrating clearly the earlier 

 occurrence of the maximums in Tallinn against Helsinki. The longitudinal 



