204, 205, 206] WAVES IN SOLID. 549 



If there are no bodily forces we have the equations of motion 



da 



226) e=(* + 



d*w ,. . N dff . 

 V ~W = ( + **' Tz + P w ' 



Differentiating respectively by x, y, z and adding we obtain 



227) e = (i 



which is the equation for the propagation of wave -motion, the 

 dilatation being propagated with a velocity b = y- - Taking 

 the curl of equations 226) we have 



228) 



Thus the components of the curl are propagated independently, each 

 with a velocity ay - The velocity of the compressional wave 



which is unaccompanied by rotation depends upon the bulk modulus 

 and the modulus of shear. The velocity of the torsional wave which 

 is unaccompanied by change of density depends only upon the mo- 

 dulus of shear. The general motion of an elastic body is a com- 

 bination of waves of compression and of torsion. The wave of 

 torsion is that upon which the dynamical theory of light is founded. 

 Inasmuch as p vanishes for a perfect fluid no wave of torsion is 

 propagated, so that the luminiferous ether must have the properties 

 of a solid and not those of a fluid. 



2O6. Viscous Fluids. We have now to consider a class of 

 bodies intermediate in their properties between solids and perfect 

 fluids, namely the viscous fluids. By definition a perfect fluid is one 

 in which no tangential stresses exist. We have then 



229) X x = Y, = Z, = -p, X, = Y 2 = Z X = 0. 



In a fluid which is not perfect no tangential stresses can exist in a 

 state of rest, but during motion such stresses can exist. While in a 

 solid the stresses depend on the change of size and shape of the 

 small portions of the solid, in the case of a viscous fluid the stresses 



