ON THE HYDRODYNAMICAL THEORY OF SEICHES. 625 
ratio for any seiche of the amplitude at the end of the lake to the amplitude at the 
ventral point at or nearest to the centre :— 
SEICHES IN A CONCAVE SEMIPARABOLIC LAKE. 
§ 34. Since all the pure seiches in a symmetric parabolic lake have ventral points 
at the ends, and the seiches of even nodality have also a ventral point at the centre, 
where there is no horizontal displacement, we could build a wall across the middle of 
the lake without disturbing these seiches. It follows that the pure seiches of a semi- 
0 a A 
Fig. 3. 
parabolic lake have the same periods as the seiches of even nodality in a complete 
parabolic lake of double the length. The nodes and ventral segments will also be the 
same as in one of the halves of the complete parabolic lake. 
If, therefore, T,’ be the period of the v-nodal seiche in a semiparabolic lake of length 
/and maximum depth h, we shall have 
T= 2al/ /{2v(2v + 1)gh} - - : ; (36) . 
If T, have the meaning of § 27, we find 
T,/T.= A(t Viv +3)}- 
Hence every period of a semiparabolic lake is longer than the corresponding period 
of a complete parabolic lake of the same length and the same maximum depth ; but 
the ratio of the periods comes nearer unity the higher the nodality. 
The nodes and ventral points for the uninodal and binodal, ete. seiches will be given 
by Tables I. and III. of § 33, provided we remember that x is now measured from the 
deeper end of the lake, and no longer from the middle, and that @ is now the whole 
length of the lake, and not half the length as before. 
§ 35. The results for parabolic and semiparabolic lakes are of great use in forming 
rough estimates of the constants and periods, either for experimental purposes, or in 
order to get first approximations to the roots of the transcendental equations which in. 
