SECOND AKY UNDULATIONS OF OCEANIC TIDES. 61 



iilarly shaped bay is also reducible to that of seiches in an 

 irregularly shaped lake. Professor Chrystar=' in his hydrody- 

 namical theory of seiches, worked out this problem in a most 

 elegant manner ; he compared the oscillation of an irregularly 

 shaped lake with vibration of a string with variable linear 

 density, and gave a minute discussion on a number of special 

 cases. 



When the shape of a lake does not much differ from a 

 rectangular tank, the following method of calculating the period 

 may be of some practical importance. In accordance with the 

 above supposition, we may assume that the normal velocity at 

 any section S is constant over it, and that the elevation of the 

 free surface is the same along the entire breadth corresponding 

 to the section S. The vertical acceleration is neglected in com- 

 parison with the horizontal. 



Take the origin of rectangular co-ordinates at one end of 

 the lake, .r-axis being in the direction of the length, c, /;, h 

 have the same meaning as before. Then the kinetic and the 

 potential energy are respectively given by 



K E. — — jpSç'dx iiiid P.E. = — I cjhfr/j'dx 



where S is the sectional area. 



Again, from the equation of continuity, we have, putting 



hence l^.^.^\p^^dx and ^•^' --\ ^JP Wi^)'^"^' 



*) Prof. Chrystal, Trans. Roy. Soc. Edin. Vol. XLT, p. 599, 1905. Prof. Chrystal and E. 

 Maclngen-Wedderburn, do, p. 823, 1905. 



