in an Annular Trough. 
207 
Section at CC Section at BE. 
Fig. 2. Annular Trough. 
n=2: gravest mode. 
will be of the same type as those in Fig. 2. It is therefore un- 
necessary to trace the contour lines for the higher harmonics : and 
it is obvious how the curves will be arranged when the number of 
nodal diameters is increased, that is when n increases. In the 
simpler case of a circular trough, we can see what the general 
character of the contour lines is by drawing a graph of J n (oc): then 
the boundary of the trough will be at the 1st, 2nd, 3rd... maximum 
or minimum values of J n ( x ) for the 1st, 2nd, 3rd... gravest modes 
of the species considered. By simply examining the graphs we 
therefore see that for each species there is one nodal circle for the 
second gravest mode, two nodal circles for the next gravest and so 
on. A few cases are roughly illustrated below. 
