308 



TIDAL WAVES. 



[CHAP, viii 



where m = 0, 1, 2,..., 51. The indeterminateness disappears, 

 and the frequencies become unequal, if the boundary deviate, 

 however slightly, from the circular form. 



In the case of the circular boundary, we obtain by super 

 position of two fundamental modes of the same period, in different 

 phases, a solution 



S=C,J s (kr).co8(&amp;lt;rt+86 + e) (13). 



This represents a system of waves travelling unchanged round 

 the origin with an angular velocity a/s in the positive or 

 negative direction of 6. The motion of the individual particles 

 is easily seen from Art. 185 (4) to be elliptic-harmonic, one 

 principal axis of each elliptic orbit being along the radius 

 vector. All this is in accordance with the general theory referred 

 to in Art. 165. 



The most interesting modes of the unsym metrical class are 

 those corresponding to 5 = 1, e.g. 



f = AJ 1 (kr)cos0.cos(&amp;lt;rt+e) (14), 



