37-1 BELL SYSTEM TECHNICAL JOURNAL 



be equal to w and all of the wave will be traveling positively. A similar 

 argument applies at the negative side of the wave. Thus the initial disturb- 

 ance breaks up into two parts which travel in opposite directions without 

 reflection. More generally, these considerations hold for any medium in 

 which the stress is a function of the strain only. 



For the ether model, since we have assumed the displacements are normal 

 to the direction of propagation, the velocity of wave propagation relative to 

 the medium is the same as that relative to the axes. 



If now, following Riemann, we let 



i» = 1 rf g) , (10) 



so that now 



then from (7) and (6) 



= /^^©' 



Adding and subtracting gives 



d 



dt 



d 

 d't 



r) f 



which are to be compared with (8) and (9). Hence when — is not zero the 



dt 



values of zt' + (/ and w — q are not propagated without change. 



To show that reflection occurs, consider a disturbance at a point .v at 



time /, characterized by (/ and tv. At .v and / + A/, Ti' + </ will difi"cr from the 



d ^ 2 df 



value It had at .v — <A/, /, or ic + (/ — ~ {w + u)cH, bv — ^ 7" A/. The 



dx ' pc dt 



increment at .v in time \l is 



Ak' + Ar/ = - |- (k' + q)c\t - 1 ^ A/, 

 dx pc dt 



