BARS 



119 



the former component (17) alone, we see that the strain at 

 any point consists in a shear of amount drj/dx. The consequent 

 stress across any plane perpendicular to Ox is parallel to Oy, 

 and its intensity is fidrj/dx. Hence forming the equation of 

 motion of a portion of matter defined as before we have 



or 



if V=dp (5) 



Some values of the wave-velocity b are tabulated below. 



Wave-velocities (metres per second). 



It may be shewn that any local disturbance in an unlimited 

 elastic medium breaks up into two waves, diverging with the 

 velocities a and 6, which tend ultimately to assume the 

 " longitudinal " and " transverse " characters, respectively. 

 The theory is historically important in relation to Optics, 

 but in our present subject great caution is necessary in 

 drawing inferences as to the propagation of waves in limited 

 solids. We have already seen that in a cylindrical or prismatic 

 rod the velocity of longitudinal waves is quite distinct from a, 

 and the theory becomes altogether different in the case of 

 flexural vibrations, to be referred to presently. In these cases 

 a modification was of course to be expected, since the wave- 

 length is understood to be large compared with the dimensions 



