60 



s. Nakamnra and K. Honda : 



shall try to work out his theory as applied to this case. Now he 

 shows that in a rectilinear lake where the depth at a point x is 

 given by h (^i — ^j, the horizontal and the vertical displace- 



Fig. 13, 



ments f and C of a particle at the free surface will be given by 



çw = \AJi,{iu)-\-BYi,{w)\5in n{t—T), 



where 



n=- 



10 =z. 



2r 

 2na 



A, and B being arbitrary constants, and J,niw) and Y^^(iv) being the 

 Bessel and the Neumann functions of the order m. We shall apply 

 this formula to the normal curve of liakoné lake. 



Let h be the least depth at C, and /'i, Ih the greatest depths 

 at B and D. Let AB=i>,', BC=i)„ CJ)=p,, DE^p,' ; and let the 



law of depth be Ih (^~"^) ^oi' -^^^\ '^i (^~~) ^^r BC, where x is 

 measured both ways from B and K (l— -^^ for CD, hJl—-^) for 



