in an Annular Trough. 



207 



Period for long waves 



■ s -405 x 



h = depth in inches 



Form of Free Surface. 



Section at CC 



Section at BB. 



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 {x): 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. 



