182 Long Waves in Canals and Standing Waves in Closed Basins 

 The natural frequency then results from 



If we introduce the values for Z x from (VI. 93), we obtain as the equation 

 for the period of the system 



Vitan^ 1 + 6 2 c 2 tan— " + V 3 tan — = . (VI. 98) 



C l C 2 C 3 



Similarly, we obtain: 



If canal I is open towards the ocean, II and III being closed 



i oh r Glo J olo ^ 



— b&cot h& 2 c 2 tan \-b 3 c 3 tan — = . 



Cl c 2 c 3 



If canals I and II are open, III being closed 



, oh i oL , ah . 



— OiCiCot— - — 2 c 2 cot \-b 3 cAsLn — = 0. 



Ci c 2 c 3 



If all three canals are open: 



i oh i o7 9 , oh n 



biCxCot ho 2 c 2 cot— +o 3 c 3 cot — = . 



Ci c 2 c. 



These frequencies are identical with those derived by Zeilon (1913) in 

 the usual hydrodynamical way. Neumann has also derived the equations for 

 the periods for other basins with different configurations. 



(4) Observed Standing Waves in Lakes, Bays and Adjacent Seas 



(a) Seiches in Lakes 



It is not our intention to give here an extensive review of oscillations 

 observed in lakes, as this would fit better into a text-book of hydrology. 

 A compilation of older literature can be found in Forel, in Chrystal, as well 

 as in the text-book of limnology by Halbfass (1923). Good reviews have 

 also been given by Endros (1908, p. 39; 1927, p. 74). We will only mention 

 here a few essential points of these phenomena which are particularly cha- 

 racteristic and which are connected with the theoretical explanations given 

 previously. 



At present, there are only a limited number of obling lakes, for which 

 a complete analysis of the seiches and a comparison between observations 

 and theory has been given. Table 23 contains a compilation of observed and 

 computed periods for some lakes, as well as enumerations of the methods 

 used for the computation. We can see that the agreement between observa- 

 tion and theory is always very good, and even better than could be expected 

 when influences of a secondary nature (friction, Coriolis-force, etc.) are 



