in an Annular Trough. 
205 
Hence in the symmetrical class the longest period is 
2tt 
coth ’396 . J 
32. 12. 396 
or 1*62 seconds. 
The next longest is 
27 r 
coth *787 . J 
32.12.-78T 
or 0 8 2 seconds. 
In the un symmetrical class where n— 1 the longest period is 
2tT 
V ' gh 
seconds or l s ‘-60. 
and the next longest is 
27 r / 1 
V ~gh 
seconds or 0 S ‘81. 
There is thus very little difference between the periods for the 
two cases of n — 0, n = 1 : that is to say, the period is almost 
exactly the same when there is one nodal diameter as when there 
is not one. In either case each successive period is very nearly 
half the next longest. 
Between the floating instrument mentioned in the first para- 
graph and the trough containing the mercury there is everywhere 
half an inch of free surface. Thus in the actual case, there are 
two narrow annular free surfaces each \ inch in width, the one 
having a mean radius of 19f inches, the other 12J : the depth of 
fluid is about \ inch. The two longest periods of a free wave on 
these surfaces are the same for both the inner and the outer 
surface, viz. 0 S T3 and 0 s ’09 : these periods practically do not differ 
for the two cases of n = 0 or n = 1. 
It may be here stated that the observed period of oscillation of 
the floating instrument is 9 S, 40. 
It is interesting to compare the periods in the corresponding 
ones for a circular trough of the same outside diameter and with 
the same depth of liquid. The values of k are given by Lamb, 
Hydrodynamics, Art. 187 ; they are 
*„« = 1-2197^: /c 0 (2, = 2*233 ^. 
0-586 
20 ' 
= 1-697 
20 ‘ 
