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



the period T of the free oscillation of the bay, having the node 

 at its mouth and the loop at its end, will be given by the 

 formula 



provided the correction due to the mouth be neglected. This 

 correction may easily be found in the following way. 



Take the origin of the rectangnlar co-ordinates at the 

 middle point on the month of the bay, .I'-axis in the direction 

 of length, positive inwards, and y/-axis upwards. Assume the 

 vertical displacement -q inside the bay to be given by 



. nx Int 



T, = a sm— r^ cos 



21 T • 



If we neglect the vertical acceleration, we have 



where ç is the horizontal displacement of the lipuid element ; 

 thus 



21 nx 27rt 



q=a—r COS -7^7- COS 



Tth 21 T ' 



4Z 7tx . 2nt 



and ç-=-rt^^ cos -—sm— - , 



If h be the breadth of the bay, the kinetic and the potential 

 energy inside the bay are respectively given by 



-^ pliblqrdx = 



WlH)p . .,27tt 

 sm- 



T'h T 



_ aHhgp „ 2nt 



and TT ü^^P \ 'ffd^ - — -A — cos- 



— ghpjr/dx = 



4 2^ • 



Assume the kinetic energy outside the bay to be 



