SEICHES AND OTHER OSCILLATIONS 
43 
of the lake than a quarter of its length, and a ventral point in the 
middle. At the ventral point the motion of the water is wholly verti- 
cal, whereas at the two nodes it is wholly horizontal. This kind of 
motion is called a pure binodal seiche. The orbits of the particles at 
various parts of the liquid will be understood from the lowest part of 
%. 15. 
With equal ease a trinodal seiche may be stirred up. 
It should be noticed that the uninodal water surface for a para- 
bolic lake is always a plane, which oscillates about the nodal line 
between the full-drawn and the dotted positions in fig. 15. For the 
same kind of lake the binodal water surface is a parabola, which varies 
in position and curvature between the dotted and full-drawn positions. 
In the case of a lake of uniform depth, the coi'responding surface 
curves are sinusoids, as shown in the upper part of fig. 15. 
Hydrodynamical Theory 
In a memoir (H.T.S.) already referred to I have discussed the 
theory of seiches in an elongated lake on the assumption that a seiche 
may be treated as a " long stationary wave. So far as seiches of the 
lower nodalities are concerned, this amounts to assuming that the 
square of the ratio of the range of the seiche at the ends of the lake 
to the leno-th of the lake is necj;lio;ible. 
From this discussion it results that : — 
1. In any given lake, pure seiches of all degrees of nodalitv, 
i.e. uninodal, binodal, trinodal, etc., are possible ; and any actual 
seiche is either one of these or a superposition of several of them. 
A compound seiche, which is a superposition of two pure seiches, 
we call a dicrote seiche ; and so on, following the nomenclature 
of Forel. 
2. When the lake is of uniform breadth and depth, the periods 
are proportional to — 
Y' • (narmonic series) 
and the quarter wave length, i.e. the distance from each node to the 
next ventral point, is the same all over. 
3. When the depth or breadth, or both, varies, the periods are in 
general no longer commensurable. Thus, for a complete parabolic lake 
the jy-nodal period is given by "T„ = 7rlj J {v{v + '\)gh}, where / is the 
length and h the maximum depth ; that is to say, the periods are 
proportional o 
1 1 1 1 
