1903 - 4 .] Prof. Chrystal on Mathematical Theory of Seiches. 333 
Binodal Seiche. 
By 
ah 
C 2 = 2.3 ; T 2 = 7rl/\J(Qyh) , . . . 
• (19) 
. . Y P(3-c 2 - a 2 ) . , 
sin nt , C, = — sin nt , 
a 6 
• (20) 
x= ±a/jJS— ± *7)7 ... a . . . . 
• (21) 
T 2 / T i = x/2/v/6 = -574 
• (22) 
Nodes 
We have 
Hence the period of the binodal seiche in a concave lake of 
symmetric parabolic section is greater than half the period of 
the uninodal seiche. 
Also the nodes are more than half way towards the ends ; i.e. 
they are displaced towards the shallows. 
If l , and £ have the same meanings as before, we have 
l=m £=7tZ£/2/*T 2 
(23) 
at the ends of the lake. At a node the values of $ and £ are 
reduced in the ratio *57 . . . : 1. At the centre £= 0 at all 
times ; and £ has half its value at the end of the lake. 
Trinodal Seiche. 
c 3 = 3.4 ; T,--=7rl/J(V2yh). 
P =— Ja 2 - 5x 2 ) sin nt , ?= —-(12 a 2 x- :20a; 8 ) sin nt. . (24) 
^ ha 2 a 4 
Nodes a; = 0, x = ±a x /3/ x /5= ±-7746 . ... a, . . . (2b) 
T 8 /T 1 = n /2/V12 = 4082 (26) 
Quadrinodal Seiche. 
ha 
c 4 = 4.5; T i = irl/ J(20gh) (27) 
7 x 2 ) sin nt, F= -5_( - 3a 4 + 30a 2 x 2 - 35'aj 4 ) sin vt (28) 
o a o 
±-3400 . . . a, ±-8621 a, . . (29) 
T 4 /T 1 = *3162 (30) 
N odes 
