Long Waves in Canals and Standing Waves in Closed Basins 185 



In recent times, also, other lakes were investigated according to the methods 

 described above. Fr. Defant computed the seiches of Lake Michigan, 

 applying methods by Defant, Christal and Ertel. The results obtained were 

 in good agreement, so that all these methods seem to be equivalent. 



A comprensive study by Servais (1957) on the seiches of Lake Tanganyika 

 was published recently. Besides an exact computation of the seiches of this 

 lake after methods by Defant and Hidaka as well as newer formulae by Fred- 

 holm and Goldberg, it gives a detailed review of all seiche theories, to which 

 special attention is drawn. For the results see Table 23. Furthermore, Servais 

 gives a special theory for transversal seiches and obtains good results, apply- 

 ing it to the Lakes of Geneva and Tanganyika. 



The seiches in their simplest form only appear, of course, in oblong lakes, 

 and the previous theories pertain to this special case. If the bottom con- 

 figuration of the lake is more complicated, the seiches become more involved. 

 Seiches of different periods are produced, depending on which parts of the 

 lake are oscillating and of the direction of the forces causing the oscillations. 

 A typical example of this are the seiches of the Chiemsee (Bavaria), which 

 have been thoroughly examined by Endros (1903). The complicated oro- 

 graphical configuration of this lake favours several oscillation axes, and parts 

 of the lake oscillate separately, so that there can be simultaneously eight 

 oscillations in the lake. It is obvious that the seiches of such a lake can only 

 be studied by detailed pictures taken simultaneously at different points on 

 shore. Generally, all observed periods could be assigned to specific areas 

 and the periods did agree with the ones computed from the dimensions of 

 the oscillating water-masses. 



Only in few lakes did the theory fail to be successfully applied. These excep- 

 tions occurred always when the configuration of the basins was very excep- 

 tional. Endros has drawn attention to several cases where, besides the regular 

 seiches, there are also oscillations of an exceptionally great period. He has been 

 able to prove that this is due to the rising and falling of the entire level of the 

 lake, and that this process should be considered as a periodic compensation 

 with a second basin through a narrow canal. Such cases have been fully ex- 

 plained by the impedance theory of Neumann. 



If the oscillating system consists of two different basins 1 and 2, connected 

 by a canal (b,h,l) which has a cross-section q, then the impedance of the 

 entire system equals the sum. of the impedances of each individual part. 

 With equations (VI. 93) and (VI. 95) we obtain 



Z x +Zq +Z 2 = — -^r cot— H -^r cot — = 



or 



2n I c, 7\ , Co To 



-S7 - = TT COtTT -£ + -=- COtTT ~ 



T q Ox T So, T 



