The Aether as an Elastic Solid. 141 



The terms which involve b and those which involve c must 

 be separately zero, since they represent respectively the irrota- 

 tional and the circuital parts of the equation. Thus, c satisfies. 

 the pair of equations 



02- 



p T-J- = ?iV 2 c, div c = ; 



vt 



while b is to be determined from 



dt 

 A particular solution of the equations for c is easily seen to be 



c x = A sin A (2 - t /-), 



/-), c y = B sinXfz - t /-), c z = 0, 

 \PJ V \PJ 



which represents a transverse plane wave propagated with 

 velocity ^/(n/p). It can be shown that the general solution of 

 the differential equations for c is formed of such waves as this, 

 travelling in all directions, superposed on each other 

 A particular solution of the equations for b is 



-t E 



V 



p 

 which represents a longitudinal wave propagated with velocity 



the general solution of the differential equation for b is formed 

 by the superposition of such waves as this, travelling in all 

 directions. 



Poisson thus discovered that the waves in an elastic solid 

 are of two kinds : those in c are transverse, and are propagated 

 with velocity (n/p)b ; while those in b are longitudinal, and are 

 propagated with velocity {(k+ $n)/p}%. The latter are* waves 

 of dilatation and condensation, like sound-waves ; in the c-waves, 

 on the other hand, the medium is not dilated or condensed, but 



* Cf . Stokes, "On the Dynamical Problem of Diffraction," Camb. Phil. 

 Trans., ix (1849). 



