ON THE HYDRODYNAMICAL THEORY OF SEICHES. 643 
Then 
En(a? - #) =u= A(a?- w?)’sin {2 7 (log ~- log =) \ sin n,(t —7), 
ou 
CS eet : ; . mn FOD)2 
and 
=2rl/y /{gd(4v?7r?/k?2+1)}5 ; ; ; (96) ; 
where 
ACI E EA CEIVED 
afitll-a pedal 
i y/ ah/ siete ne) 
When the end barriers P and Q approach more and more nearly to the infinitely 
shallow theoretical ends A and A’, the periods of all the seiches become more and more 
nearly equal to each other and to z//,/(gd), which I have called the period of the 
anomalous seiche. 
(97). 
Convex QuartTIc LAKE. 
§ 53. The symbols being defined as in § 52, we now have 
mili): eral) 
ba Aa & eel J 5-2) ) } =ay, say, _ (98). 
Eh(a? +27)? = u = (a? + x?) sin ae =— tan” *2) i sin n,(t—T), 
a 
eas, : ; - , : : (99) ; 
On 
and Y, = 2l/y J {gd(4v?x?/k? —1)} ; : ‘ : f s (100) ; 
Jl OV 4-9 
z=2tnr, /(,/2- 1)- tant, /(, /4-1). ; : acy. 
§ 54. In constructing a theoretical curve to represent the normal curve of any lake 
deduced from bathymetric data we can, of course, combine pieces of parabolas, straight 
lines or quartics at will; and the variety of formule above given is probably sutfticient 
for most practical purposes, although the labour of the calculation, even in simple cases, 
isnot small. To this part of the subject I shall have occasion to return in subsequent 
communications to the Society. 
where 
