332 
Proceedings of Royal Society of Edinburgh . [sess. 
Lake with Symmetric Longitudinal Section of Parabolic 
Concave Form li ( x ) = h x (1 - ofijcd ). 
If Cj = v{y+ 1) , and T v be the period of the y-nodal seiche, then 
T v ==27rJn = 27raJ s /(c v gIt) = Trl/J{v(v +l)gh)} . . (13) 
where l( = 2 a) is the whole length of the lake. 
A a o a A 
h 
Fig. 1. 
For seiches with odd and even numbers of nodes we have 
A 
A C(c 2s _, , w) 
h 
1 
A 
sin nt, P = - — CXAs-i , «0 sin nt ; 
(14) 
and 
B S(c 0 o , iv) B c .,, \ ■ . / 1 n \ 
t= T T ’ ■ sin nt, Y = - — & (<‘ 2s , w) sm nt, . (15) 
s h 1 - iv 2 5 S a 
respectively. 
Node 
Uninodal Seiche. 
^■1.2; T 1 = 7 rZ/V(2^) • • 
sin nt 
h ' ^ a 
x = 0 . 
~ 2Ax ■ / 
r = — ^ 2 ~ sm nt , . 
(IB) 
(17) 
If £, £ denote the maximum horizontal and vertical displace- 
ments of a particle on the surface at the end of the lake, and £ the 
maximum horizontal velocity of displacement, then 
1 = 77111211 ^ (is) 
It should be observed that here, and in the cases that follow 
under the present head, the boundary condition at A and A' is not 
that £ — 0 , but that the motion be tangential to the shore. 
