BARS 123 



accurate in all cases, provided R denote the radius of curvature 

 at the point considered. 



In the present application drj/dx is a small quantity, so that 

 we may put R~* = &rj/dx?, and therefore 



(6) 

 Substituting in (3) we obtain 



(7) 



For most purposes this equation may be simplified by the 

 omission of the second term, as we shall see immediately. 

 The kinetic energy of the bar is 



The second term, which represents the energy of rotation of the 

 elements, is usually negligible. 



The potential energy is found, in accordance with 42 (16), 

 by integrating the expression %Ee z , =\Ey' i lJ&, first over the 

 area of the cross-section, and then over the length; thus 



. .............. .(9) 



Consider for a moment the propagation of a system of waves 

 of simple-harmonic profile along an unlimited rod, assuming 



v)=Ccosk(ct-x) ................... (10) 



Since everything here recurs whenever # is increased by 2-Tr/fc, 

 the constant k is connected with the wave-length A. by the 

 relation 



fc=27T/X ......................... (11) 



On substitution the equation (7) is found to be satisfied 

 provided 



This gives the wave-velocity c, which is seen not to be a definite 

 quantity fixed by the constitution of the rod, but to depend also 

 on the wave-length. To trace the progress of a wave of any 

 type other than (10), it would be necessary to resolve the wave- 



