622 PROFESSOR CHRYSTAL 
In either case, if T, be the period of the v-nodal seiche, we have 
T, =22/n, = 27a/,/(¢,gh) , 
=al/ /{v(v+1)gh}, . : ; : . (35) , 
if 7 denote the whole length of the lake. 
UNINODAL SEICHE. 
§ 28. 
¢,=1.2. T, =al/,/(2gh) 
C(c,,w)=1-w?, C(c,,w)= -2u. 
AS 2An . 
— sinn(t-r), l= a sin n,(t—7). 
One node 
z/a=0. 
In this case the amplitude of the horizontal displacement is constant; and the 
free surface is a plane which oscillates about the line of the uninode. 
If ¢ be the maximum rise of the water at the end of the lake above the undis- 
turbed level, then (=2A/a=4A/l. Hence A=/¢/4. Hence the maximum horizontal 
displacement of a water particle from its mean position is £=/¢/4h; and the maximum 
velocity of the horizontal stream is nlC@/4h=7l@/2hT,. For example, if Loch Ness 
were a symmetric parabolic lake, every inch of maximum vertical seiche at one end 
would give over 40 inches of maximum horizontal displacement; and a maximum 
horizontal stream velocity of over 8 inches per minute. 
BINODAL SEICHE, 
N 29. 
C= 2.3, T, =7l/,/(6gh), 
S(c.,w)=w-w>, S'(c.,w)=1- 3w?, 
Ba. B(3az2 — a?) . 
=e un na(t -T), C= a sin ,(t-7). 
Two nodes at 
t/aatht fS= +5774... . 
The amplitude of £ increases uniformly from the centre to the ends of the lake; and 
the free surface is parabolic, 
TT: Qi /G= bomen eee 
Hence the period of the binodal seiche is greater than half the period of the 
uninodal seiche. 
Also the nodes are more than half way from the middle of the lake towards the 
ends ; 1.e. they are displaced towards the shallows. 
If — and ¢ be the maximum horizontal and vertical displacements at the end of 
the lake, we find £/(=1/4h, as before, also £/C=27&/T,¢. For Loch Ness we get 
