Seiches in Some Lakes of Japan. 47 



are forced to say that ^3 belongs to T^ and consequently to assert 

 that the seiche with a period of 4.63 minutes is the quadrinodal 

 seiche in Hakoné lake. We are also inclined to say that T^ and 

 Ts are minor seiches developing respectively at the Hakoné and 

 Umijiri ends. 



The positions of nodes as determined by studying several 

 motions of the model lake are as follows. For the nninodal seiche, 

 it lies at 0.56 of the total length of the lake from southern Hakoné 

 end ; while those for the binodal are at 0.33 and 0.80 from the same 

 end. The nodal lines for the third mode of oscillation are too 

 curved to admit of defining their positions in this manner. 



3. Comparison with theories. 



Several formulae have been given by different authors such 

 as Mérian, Du Boys et al., for the calculation of the period. For 

 a rectangular lake of a uniform depth h and of a length L, the 

 period T of the uninodal seiches is given by 



V gh 



When we wish to apply this formula to tlie case of a lake with a 

 variable depth and breadth, we must take for h its mean value but 

 this gives only an approximate value or values, for we can estimate 

 this mean depth in several different ways. According to Du 

 Boys,* when the lake is symmetrical with respect to its median 

 line, the period for the uninodal seiches is given by 



rp^ 2 f. dx 



V g J V 



h 



* Essai tht'orctiqno sur los seiches. Archives d. sciences Phys. ct Nat. Genève XXV. 

 1891, p. 62S. 



