64 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI. 



^.=(n)„ll4/(f + |)eo.ÄV.] (4) 



by taking r„ and A„ sncli that Jv and JA vanish, and putting 



By mechanical integration, we can easily evaluate the values 

 — I àb cos — — dx and — / à S cos — dx , 



and thus arrive at an expression representing tlie change of 

 period due to a slight variation in the area and volume of 

 the oscillating liquid. The expression shows that any con- 

 traction or expansion at the middle part of tlie lake prolongs 

 or shortens its natural period respectively, and that a con- 

 traction or expansion at the end portion shortens or prolongs 

 it respectively. 



To apply the above expression to the case of a bay, we 

 need only to consider a lake whose shape is symmetrical witli 

 respect to the vertical plane through the mouth line, and to 

 find the period of tlie seiches in the lake. This period, if it 

 be corrected for the mouth, is the required period of the 

 oscillation of the bay water. 



(c) Dumb-bell- shaped bay. 



The above assumption does not hold for the case, when a 

 portion of the lake is very much contracted. In such case, 

 however, we may treat the problem in quite a different wav. 

 When two basins communicate with each other by a narrow 

 canal, the gravest mode of oscillation takes place such that 

 the levels of the two basins rise and fall respecti /ely. If the 

 breadth of the canal is very narrow compared witli the two 



