NODAL LINES. 



309 



(15). 



187] 



where k is determined by 



The roots of this are 



&a/7r=-586, 1-697, 2'7l7, (16)*. 



We have now one nodal diameter (6 = JTT), whose position is, 

 however, indeterminate, since the origin of 6 is arbitrary. In the 

 corresponding modes for an elliptic boundary, the nodal diameter 

 would be fixed, viz. it would coincide with either the major or 

 the minor axis, and the frequencies would be unequal. 



The accompanying diagrams shew the contour-lines of the free 

 surface in the first two modes of the present species. These lines 

 meet the boundary at right angles, in conformity with the general 

 boundary condition (Art. 186 (2)). The simple-harmonic vibrations 



of the individual particles take place in straight lines perpen- 

 dicular to the contour-lines, by Art. 185 (4). The form of the 



* See Lord Bayleigh's treatise, Art. 339. 



