SEICHES AND OTHER OSCILLATIONS 
51 
amplitude of the corresponding displacement of the recording pen is 
very small — it may be, quite imperceptible. 
Applying the theory of fluid friction in tubes given in a classical 
memoir by Osborne Reynolds, it is easy to calculate the damping of the 
amplitude, and the lag of any pure seiche, due to a given well and tube. 
If a be the diameter of the well, h the diameter, and / the length, 
of the access tube ; and 
^ = 2813b'^/la^ (reduction constant), 
then an outside periodic disturbance 
y = A sin nt 
is rendered inside the cylinder by 
x = A cos nr sin 7i{i — r) ; 
where r is given by 
tan ?iT --nj^. 
This means that there is a lag of r seconds ; and the seiche amplitude 
is damped in the ratio cos nr-.l. 
The two following tables show the effects of different well and 
access tubes on seiches of widely differing periods : — 
Sarasin Limnograph at the Binode 
Z = 60 feet=1830 cm., a = 35 cm., & = inches = 3 '75 cm. x-"^ '2483. 
T 
r/T 
T 
cos llT 
sec. 
sec. 
870 
•00463 
4*02 
■9996 
486 
•00828 
4^02 
•9986 
342 
•01175 
4-02 
•9973 
60 
•06351 
3-81 
•9-215 
Index Limnograph with 6-inch Well, and 6 feet Tube of |-inch, 
l-iNCH, OR i\-iNCH Bore 
Z = 182 cm., a — lh cm. 
6 = 
^•27 cm. 
h 
= •es cm. 
-47 cm. 
X = 
= •1788 
= •01083 
X= -003355 
T 
t/T 
T 
cos m 
t/T 
T 
cos nr 
t/T 
T 
COS m 
sec . 
sec. 
sec. 
sec. 
870 
•0064 
5^59 
•9992 
0937 
8r5 
•8320 
•1808 
157-3 
•4213 
486 
•0115 
5^58 
•9974 
•1390 
67^6 
•6421 
•2096 
101-8 
•2512 
342 
•0163 
5^57 
•9948 
•1569 
53-7 
•5078 
•2213 
72^5 
•1797 
60 
•0843 
5-06 
•8630 
•2336 
14^0 
•1028 
•2449 
14-7 
•0320 
