1903-4.] Prof. Chrystal on Mathematical Theory of Seiches. 335 
Binodal Seiche. 
C 2 = 12 • 34 , X 2 = 7rZ/V(12.34. . . gh), . . . (38 
Hence ^ 2 <T 2 . 
Also 7(2-77 . . . /12-34 . . . } = -474 . . . (39) 
In other words, in a convex lake of symmetric parabolic section 
the period of the binodal seiche is less than half the period of the 
nninodal seiche. 
It follows, of course, from the fact that the seiche functions 
degenerate into the circular functions when the curvature of the 
bottom is infinitely small, that when the lake bottom is flat 
T 2 /Ti = |, etc., as in the case of vibrating rods, or strings. 
Case of Concave Lake with Unsymmetric Biparabolic 
Section. 
The depth from 0 to A is given by h(x) = h(l - x^/a 2 ) ; from 
0 to A' by h(x) = h( 1 - x 2 ja' 2 ). 
If iv = x/a, iv' = x/d; c~-=n 2 a 2 jgh , c =n 2 a' 2 /gh, then for the two 
portions 0 A and 0 A' we have respectively 
A' a ' 0 
h 
Fig. 3. 
and 
