626 PROFESSOR CHRYSTAL 
general determine these constants. We assume, as in general probable, that any 
concave lake whose form is not unusual will be intermediate in character between a 
complete parabolic and a semiparabolic lake. It follows that the periods, nodes, and 
ventral points will be intermediate; and it is found in practice that in many cases a 
good first approximation is obtained by taking the arithmetic mean between the two 
extreme cases. As an example, we should expect that the distances of the uninode and 
deep binode from the deeper end would lie between ‘5 and ‘58, and between -78 and 
‘87 respectively. 
In this connection we have found the following table of the ratios of the periods 
useful :— . 
T,/T, | T,/T, T,/T, T;/T, | T,/T, T,/T, T,/T, T/T, 
| Parabolic Lake : odd LOS oO 2b Se 218 eel e9 167 149 
| Semiparabolic Lake : | ‘548 | 378 | 289 | -234 | -196 | 169 | -1485 | -134 
SEICHES IN A TRUNCATED PARABOLIC LAKE. 
§ 36. By means of the seiche functions we can readily find the solution for a 
parabolic lake which is bounded by vertical cross walls at distances «=p, x=q from 
Fic.;4. 
f 
its deepest point. The formule are, in our previous notation, 
Eh(1 — w?) {S(c, p/a)C(e, w) -— Cle, p/a)S(c, w)}sin n(t — 7) ; 
be tee 
S(«, p/a) 
& = we am p/a)C(c, w) —C(e, p/a)S'(c, w)}sin n(t— 7) . 
And the values of c are given by the period equation 
C(c, p/a)S(e, g/4) — Sc, p/a)C(c, g/a)=0. 
In the case of a symmetric lake g= —p; and the period equation reduces to 
C(c, p/a)S(c, p/a)=0. 
If, further, p= a, we get 
O(c, 1)S(e, 1)=0; 
and return to the case of a complete parabolic lake already discussed. 
