Long Waves in Canals and Standing Waves in Closed Basins 169 



o 



5 

 10 



b 

 ■\ 20 



b 25 



30 



35 



0-2 0-4 0-6 08 10 12 1-4 16 1-8 2-0 

 v In units 



Fig. 72. Normal curve of the Lake of Geneva (each unit represents 17052km). 



(v) The method of Hidaka. Hidaka (1932, 1936) has also devised a method 

 for computing the period of oscillation and the distribution of vertical dis- 

 placement for enclosed water-masses, taking fully into account the variable 

 cross-sections and depths of the basins. It is based on the application of the 



0-6 



04 



2 







/ -0-2 



-04 



-0-6 



-0-8 



-10 



- 0-2 0-4 0-6 0-8 10 12 



v In units 



1-4 1-6 1-8 20 



Fig. 73. Range of the uni- and bi-nodal seiches in the Lake of Geneva. Same scale as 

 Fig. 72. , uni-nodal; , bi-nodal. 



Ritz theorem of the calculus of variations to the integration of the Chrystal 

 differential equation (VI. 57). If we introduce via = : as a new variable and 

 if a(z) is the normal curve of the lake as a function of z, we obtain 



