176 Long Waves in Canals and Standing Waves in Closed Basins 



this. An oblong lake communicates at one end with a second basin through 

 a narrow canal. If the opening to the second basin is sufficiently narrow, 

 there will be in the oblong lake seiches, with, in first approximation, an anti- 

 node at the end partially closed, so that the oscillation of the lake will reach 

 approximately the narrow connecting passage. In this connecting canal there 

 will be variations in the water level and consequently periodical horizontal 

 currents. Oscillations can start also in the second basin. In this way, the water- 

 masses in the connecting canal oscillate back and forth with the period of 

 the free oscillation of the lake, but the physical process in the canal is quite 

 different from the seiches in a lake. However, it reacts back on the oscillations 

 in the oblong lake, and the resulting period of the whole oscillatory system 

 is somewhat different from the period of the free oscillation of the oblong 

 lake when it is completely closed and also completely different from the 

 case where the oscillation in the connecting canal is unhampered. Such con- 

 necting oscillatory systems have been described in the well-known work on 

 the oscillations of Japanese bays by Honda (1908) and his collaborators. 

 An interesting case has been computed by Sterneck(1916) (see also Defant, 

 1917, p. 329) in his solution of the Euripus problem. Endroes (1927, p. 74) 

 has pointed out the remarkable long period of oscillation of lakes composed 

 of separate basins and explained them to be compensating oscillations of 

 connected systems. Zeilon (1913), too, has dealt with similar problems 

 in investigating the oscillations of the Gullmar- Fjord. Neumann (1943, 

 p. 409) has given an extensive analysis according to a new method. We will 

 first explain, with the help of hydrodynamics, the case of free oscillations 

 in two lakes communicating by means of a narrow canal. 



Let us assume that a short and narrow rectangular canal II connects an 

 oblong rectangular basin I with a smaller basin III. Let their length be /, 

 their width b and their depth h and the suffixes 1, 2, 3 refer to each quantity 



4V° 



Fig. 75. Computation of the free periods of linked systems. 



