108 Messrs. K. Honda, T. Terada, and D. Isitani on the 
Lord Rayleigh * found the reaction of air upon a vibrating 
rectangular piston, whose length y is very great compared 
with its breadth b, to be equal to the addition of a mass 
y 
where 7^0*5772 and «=~, X being the wave-length. If 
the reaction be uniform over the piston, we have for y — h 
-( 2 -7-logy> 
Now, in a problem of long waves, we usually neglect vertical 
acceleration and consider horizontal acceleration nearly con- 
stant for different depths. Vertical planes, which are 
parallel to wave ridges and fixed relative to water, make a 
to-and-fro motion similar to the case of aerial vibration. 
The node of an aerial stationary wave corresponds to the 
loop of the water wave and vice versa. If we use the analogy 
for the expression of the kinetic energy, we have 
■D . 1 /3 i 7T/A 
. 1 /3 , *b\ 
This relation seems to be sufficient for the estimation of the 
order of magnitude of the mouth correction. 
r> 
(ii) Irregularly shaped bay. 
Professor Chrystalf, in his hydrodynamical theory of 
seiches, has satisfactorily worked out the problem of seiches 
for irregularly shaped lakes. When the shape of a lake 
does not considerably differ from that of a rectangular tank, 
the following method of calculating the period may be of 
some practical importance, though not very rigorous. 
Consider a nearly rectangular lake of the length I and 
the mean transverse section S . The section S = S + AS 
varies slightly such that square of A8/S may be neglected 
in comparison with unity. If the variation of S be every- 
where gradual, we may assume that the horizontal displace- 
ment of water in every section is in the direction of the 
* Lord Rayleigh, Phil. Mag. vol. viii. 1904. 
f Chrjstal, Trans. Roy. Soc. Edin. vol. xli. 1905. 
