334 
Proceedings of Royal Society of Edinburgh. 
Quinquinodal Seiche. 
c 5 ~ 5.6 ; T 5 = id J(30gh) . . . . 
• (31) 
£ = — (a 4 - 14 a 2 x 2 + x 4 ) sin nt , 
s ha 4 ’ 
^ = A(30akc - 140 ah? + 1 26a; 5 ) sin nt , 
• (32) 
Nodes 
x — 0, + -5384 . ... a , + -9058 ... a , 
■ (33) 
T 5 /T 1 = -2582 . . . . , . . . . 
■ (34) 
Lake with Symmetric Longitudinal Section of Parabolic 
Convex Form h(x) = h x (1 + x 2 /a 2 ). 
Fig. 2. 
If q , C 2 , C 3 i v • • • • be the real positive roots 
taken in order of magnitude of the equations ($(c, 1) = 0 and 
( B(c , 1) = 0, so that q is the smallest positive root of q(c, 1) = 0, 
C 2 the smallest positive root of @(c, 1 ) = 0, and so on, then, for 
seiches with an odd number of nodes, 
A (£(C 2s-!, * 
h 1 + w 2 
sin ni , w ) sin nt 
(35) 
for seiches with an. even number of nodes 
IS ©(Ca-i, w) 
h 1 + w 2 
sin nt , 
ll 
A 
w) sin nt , . (36) 
Uninodal Seiche. 
c a = 2.77... , %, = *:/ J(2-77 ...gh), . . (37) 
Hence X 1 < T x ; that is to say, for the same central depth and 
the same length, the uninodal period is less when the lake is 
convex than when it is concave. 
